11.1: Introduction
Now it's time to talk about the other key atom, C , the ratio of 13 C / 12 C and corresponding δ 13 C values, not only in Ca C O 3 but also in C O 2 and the organic molecules it transforms into through photosynthesis and the heterotrophic organisms that consume them. 13 C partitions not only into inorganic carbon but also into organic molecules throughout life. Hence we need a more detailed understanding of the carbon cycle .
The carbon cycle is likely discussed in introductory chapters in biology textbooks, but probably never in chemistry texts. It is fundamental to an understanding of climate, its control and change, and human processes that alter it. Figure \(\PageIndex{1}\) shows a representation of the carbon cycle. Calculated amounts of carbon found in the lithosphere (the solid part of the earth), the atmosphere (specifically the lower part, the troposphere), and the hydrosphere are shown. (The cryosphere , the frozen ice found in Greenland and Antarctica, is not shown). The biosphere includes part of each of these "spheres" that harbor life. Since life has been shown to exist 10 km down in the crust, we'll refer to the entire region in the diagrams as the biosphere. Figure \(\PageIndex{1}\) presents carbon stores in petagrams (10 15 g) or gigatons of carbon (GtC), as 1 petagram equals 1 billion metric tons (or approximately 1.1 billion US tons).
Figure \(\PageIndex{1}\): The carbon cycle. https://commons.wikimedia.org/wiki/F...te_diagram.svg
In addition to the total amount of carbon stored in each region, (GtC), the net changes in carbon per year as it moves into and out of reserves (GtC/yr) are shown in blue arrows with attached numbers.
The exchanges of carbon in the cycle occur at different time scales. Geologically "fast" exchange, on a time scale up to 1000s of years, occurs among the oceans, atmosphere, and land, while a slow exchange (over hundreds of thousands to millions of years) occurs in deep soils, deep ocean sediments, and rocks. We will mostly consider exchanges among the atmosphere, land, and oceans.
CO 2 in the terrestrial biosphere is removed by photosynthesis and returned by respiration by autotrophs like plants, and heterotrophs like microbes that consume soil carbon and plant remains. CO 2 in the atmosphere is also removed by ocean autotrophs like ocean phytoplankton and through partitioning into dissolved inorganic carbons (DIC) molecules like HCO 3 - and CO 3 2 - into the oceans.
 To do that, we must put numbers on the cycle to quantify it.
Quantitating the carbon cycle
We use parts per million (ppm) as a unit for expressing the amount of CO 2 in the atmosphere. Table \(\PageIndex{1}\) below shows how to translate the percentage (parts per 100) for each component gas in the atmosphere (with which you are familiar) into ppm.
| Gas | % (parts per 100) in atm | part per million |
|---|---|---|
| N 2 | 78.09 | 780,900 |
| O 2 | 20.94 | 209,400 |
| Ar | 0.93 | 9300 |
| CO 2 | 0.0415 | 415 |
Table \(\PageIndex{1}\): Unit conversion - % to ppm
Climate scientists use ppm instead of concentration (in molecules/m 3 ) since they wish to know the relative percent or ppm increase with time, which does not depend on temperature and pressure. In contrast, concentration does depend on T and P, as you will remember from the ideal gas law, PV=nRT or n/V=P/RT that you studied in introductory chemistry.
It is important to use dimensional analyses to interconvert units as well. Table \(\PageIndex{2}\) below shows conversion factors to switch between GtC, Gt CO 2 , and ppm.
| Convert from | to | conversion factor |
|---|---|---|
| GtC (Gigatons of carbon) | ppm CO 2 | divide by 2.124 |
| GtC (Gigatons of carbon) | PgC (Petgrams of carbon) | multiply by 1 |
| Gt CO 2 (Gigatons of carbon) | GtC (Gigatons of C) | divide by 3.664 = 44.01/12.01) |
| GtC (Gigatons of carbon) | MtC | multiply by 10000 |
Table \(\PageIndex{2}\): Unit conversion - GtC and Gt CO 2
To be more technical, atmospheric CO 2 concentrations are expressed in mol fraction of CO 2 in the dry air atmosphere. The ppm for CO 2 is hence μmol CO 2 per mole of dry air.
We have to put numbers on the components of the carbon cycle to quantitatively analyze changes in its components, otherwise, we can't know what is presently happening nor will we be able to predict with some certainty the future. Stoichiometry and reaction kinetics are probably the least liked parts of chemistry for many, but they are critical in understanding climate change We have to apply them on a global scale. Two key terms are important:
Stocks or reserves: How much carbon (mass in Gigatons or petagrams) is stored in given locations in the biosphere. This allows us to understand what % of all carbon stocks are in the ocean, for example. Stocks are usually reported as gigatons of carbon (GtC), not gigatons of carbon dioxide , since many stocks (like fossil fuels) consist of mostly C and H without oxygen. As in stoichiometry calculations in introductory chemistry courses, GtC in the atmosphere can be converted to gigatons of CO 2 by using dimensional analysis.
Fluxes (rates): How much carbon is transferred from one reserve to another per year (Gigatons/yr). Climate scientists are simply applying the Law of Mass Conservation that you learned in introductory chemistry, to the entire biosphere.
Figure \(\PageIndex{2}\) shows the reserves/stock (GtC) for reserves and decadal (2012-2021) average fluxes (large and small arrows, GtC/yr) for individual or aggregated stocks.
Figure \(\PageIndex{2}\): Schematic representation of the overall perturbation of the global carbon cycle caused by anthropogenic activities averaged globally for the decade 2012–2021 . E represents emission and S "sink". Earth Syst. Sci. Data, 14, 4811–4900, 2022. https://doi.org/10.5194/essd-14-4811-2022 . © Author(s) 2022. This work is distributed under the Creative Commons Attribution 4.0 License.
The abbreviations used are: E FOS (emissions, fossil fuels), E LUC (emissions land use changes - mostly deforestation), S LAND (terrestrial CO 2 sink), S OCEAN (ocean CO 2 sink), G ATM (Growth Rate CO 2 atm), B IM (carbon budget imbalance). Uncertainties are also shown except for the atmospheric CO 2 growth rate which is known precisely and accurately through modern measurements. (It's also the easiest to measure). Human (anthropogenic changes) occurs on top of the carbon cycle.
The upward arrows indicate release into the atmosphere and the downward arrows the absorption in the oceans and land. The thickness of the arrows gives a relative measure of the size of emission or absorption. The thickest arrow and highest value (9.6 GtC/yr) is for the anthropogenic emission of carbon from our use of fossil fuels. Think about that! Humans are presently the biggest contributor to the carbon cycle . Before the industrial revolution, human contributions were minimal.
Figure x above shows that on average, 9.6 GtC/yr was released from fossil fuel use between 2012-2021. The actual flux of anthropogenic carbon release in 2021 was 9.9 GtC , equivalent to 36.4 Gt CO 2 .
If you add the up arrows and subtract from that sum the down ones, you get +4.8 GtC/yr. This represents the net average increase in GtC in atmosphere CO 2 per year for 2012-2021. That is close to the accurately, and precisely known value of +5.2 GtC/yr increase from the CO 2 we pour into the atmosphere through our use of fossil fuels. Hence the figure above is a bit out of balance (about 0.3 GtC too low - the B IM carbon budget imbalance), but given the difficulty in calculating these values, it is remarkably close to "mass balance" as you learned in introductory chemistry classes. In general, before the industrial revolution, the sum of the fluxes leading to the addition of CO 2 into the atmosphere was equal to the sum of the fluxes that removed it. That is, the system was in a steady state. That is no longer the case.
Figure \(\PageIndex{3}\) shows a breakdown of the factors contributing to annual (left) and cumulative (right) fluxes of carbon (GtC/yr), a metric for CO 2 flux, over time since 1850.
Figure \(\PageIndex{3}\): Combined components of the global carbon budget as a function of time for fossil CO 2 emissions ( E FOS , including a small sink from cement carbonation; grey) and emissions from land-use change ( E LUC ; brown), as well as their partitioning among the atmosphere ( G ATM ; cyan), ocean ( S OCEAN ; blue), and land ( S LAND ; green). Panel (a) shows annual estimates of each flux ( GtC yr −1 , and panel (b) shows the cumulative flux (the sum of all prior annual fluxes) since the year 1850. Again, the graph shows GtC not Gt CO 2 . . © Author(s), ibid
You might ask why the atmospheric growth in CO 2 (shown in green) is negative. We'll answer that question below.
Lastly, let's think about the total cumulative changes in GtC released and absorbed since 1850 (pre-US civil war and before the big release of CO 2 in modern times). Those data are shown in a bar graph in panel A of Figure \(\PageIndex{4}\). The bar graph in the right panel shows the mean decadal averages that are shown in Figure 2 above.
Figure \(\PageIndex{4}\): Total cumulative changes in GtC released and absorbed since 1850 (panel A) and mean decadal fluxes (panel B). E FOS (emissions, fossil fuels), E LUC (emissions land use changes - mostly deforestation), S LAND (terrestrial CO 2 sink), S OCEAN (ocean CO 2 sink), G ATM (Growth Rate CO 2 atm), B IM (carbon budget imbalance). © Author(s), ibid
The positive emission and negative absorption contributions are easy to see in the bar graph. The blue bar represents the net emission of carbon from fossil fuels and fills the gap to complete mass balance as we discussed above. It also explains the negative blue region in Figure 3. Just keep in mind that the blue net flux from fossil fuels is positive.
The cumulative contributions from fossil fuel emissions required to close the gap and fulfill mass balance is is +275 GtC, which when multiplied by the conversion factor (1ppm/2.124 GtC) translates into a 129.5 ppm increase in atmospheric CO 2 over that time. This is very close to independent measurements of a rise of 129.3 ppm (14.7-284.7) over that time.
The data from Figure \(\PageIndex{4}\) has been entered in the first four columns of Table \(\PageIndex{3}\) below.
| Source | Subtype | Stock reserves (GtC) |
J (Fluxes) GtC/yr
+ emission
|
J=k app [stock] |
|---|---|---|---|---|
| Atmosphere | - | 875 | ||
| Buried Fossil Fuels | Coal | 560 | +9.6 |
J=+9.6=k[905] k=0.0106 |
| Oil | 230 | |||
| Gas | 115 | |||
| Terrestrial | Permafrost | 1,400 |
+1.2 (Land use Δ)
|
J
use
=+1.2=k
use
[3550]; k
use
=0.000338
|
| Soil | 1,700 | |||
| Vegetation | 450 | |||
| Oceans | Coasts | 10-45 | -2.9 |
J=-2.9=k[
875
]
|
| Ocean Surface Sediments | 1,750 | |||
| Organic carbon | 700 | |||
| Marine Biota | 3 | |||
| Dissolve Inorganic Carbon (DIC) | 37,000 |
We can use this data to develop our own crude computational model predicting future CO 2 emissions using Vcell, the program we used to produce time course (concentration vs time) graphs for both simple and coupled signal transduction reaction pathways.
Vcell can be used to calculate fluxes (J) in reaction pathways, where J is the change in concentrations of a species with time, given the initial concentration or amount of a reactant, and the rate constants affecting its production or removal. If we use the amount of carbon (GtC) in each reservoir in the biosphere and crust as a relative measure of "concentration" and the known fluxes (GtC/yr) for the transfer of carbon to and from the atmosphere as given in Table 3, we could calculate an "apparent rate constant for each flux using this equation:
J stock = k app [stock] (where stock is given in GtC).
\begin{equation}
\mathrm{J}_{\text {stock }}=\mathrm{k}_{\mathrm{app}}[\text { stock in } \mathrm{GtC}]
\end{equation}
These "apparent" rate constants are needed to run the Vcell simulation that can reproduce the actual fluxes shown in Figures 2 and 4). The simulation can be run over time
A simple four-term model based on Figures 2 and 4 is shown below. Run the simulation and see how atmospheric CO 2 changes with time. This model is offered only to show how climate models are made and used, and also for fun. The graphs are valid and sound based on the input parameters, but the outputs are based on many assumptions that vastly simplify the model.
Model :
Initial Values: k f = 2, k r = 4, A t=0 = A 0 = 10
ActivityNote: Y-axis values on the generated plots are scaled incorrectly in the Vcell plots . This will be fixed in a future update. However, the shapes of the curves are accurate. To get the correct Y-axis values, download the .csv file and scale all concentration values by normalizing them to the actual intended initial concentrations of the reactants. An update will occur when the newest version of Vcell is released.
The simulation shows CO 2 atm levels peaking at about 982 GtC in 51 years (2073) from its average decadal (2011-2021) value of 875. That is an increase of 107 GtC over now (50 ppm CO 2 rise from the present 414 to 463 ppm). Over a 50-year period, this gives an average annual rise of 2.14 GtC/yr or about 1 ppm CO 2 /yr. A comparison of the predicted atmospheric CO 2 (ppm) levels through 2100 for the IPCC SSP1-2.6 scenario ( blue ) and simple Vcell model ( red ) is shown in Figure \(\PageIndex{5}\).
Figure \(\PageIndex{5}\): Predicted atmospheric CO 2 (ppm) for SSP1-2.6 scenario ( blue ) and simple Vcell model ( red )
SSP1-2.6 data - History: Meinshausen et al. GMD 2017 ( https://doi.org/10.5194/gmd-10-2057-2017 ); Future: Meinshausen et al., GMD, 2020 ( https://doi.org/10.5194/gmd-2019-222 ). https://climateanalytics.org/media/g...-3571-2020.pdf . https://gmd.copernicus.org/articles/13/3571/2020/
However imperfect the Vcell model is (incorrect assumptions, lack of complexity and feedback mechanisms, etc), the results shown above are remarkably close to the projected increases in carbon dioxide in ppm described in IPCC reports for the SSP1-2.6 socioeconomic pathways, shown in the right panel (dark blue line) of Figure \(\PageIndex{6}\). This pathway predicts a rise of approximately 1.8 0 C in average global temperatures.
Figure \(\PageIndex{6}\): IPCC, 2021: Summary for Policymakers. In: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I
to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L.
Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K.
Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)].
Again, remember that the model is based on a ten-year average of CO 2 emissions. Think of all the other assumptions in this model (other than the stock reserves and fluxes) that would give higher or lower values of future CO 2 levels. One major one is that flux values are all held constant to allow calculations of the apparent rate constants for Vcell use. The model depletes much of the fossil fuel reserve. In addition, CO 2 emissions in 2021 were actually 9.9 GtC/yr and going up!
In addition, a change in one parameter can affect the others. For example, the net uptake of atmospheric CO 2 into the land and oceans has increased from 1960-2010, which makes sense given increased CO 2 in the air forcing additional uptake (think LaChatelier's Principle). The oceans have taken up nearly 40% of the CO 2 from fossil fuel use since the industrial revolution. If the rate of uptake decreases (i.e. if we start to saturate the uptake into oceans), CO 2 accumulation in the atmosphere would accelerate. Data also suggest that if we successfully decrease CO 2 in the atmosphere, the oceans would respond by decreasing uptake as well, which would slow the progress in reducing temperatures.
An interesting example relating atmospheric and ocean CO 2 occurred from 1990-2000 when it has been shown that the ocean acted as a weaker sink. This occurred because of a decreasing gradient (the Δ or"effective concentration differences") between atmospheric CO 2 and ocean "CO 2 ", which decreased the ability of the ocean to act as a sink for CO 2 . You can decrease the Δ in two ways:
- decreasing the rate of entry of CO 2 into the atmosphere from fossil fuel use. There indeed was a temporary slowdown in this decade.
- paradoxically, by briefly making the ocean in a shorter term a better sink. This happened in 1991 after the eruption of Mt. Pinatubo, which led to decreased air and ocean temperatures. CO 2 is a nonpolar gas, which has higher solubility in water at lower temperatures (think about soda). This was a short-term and more minor effect than the decreased rate of fossil fuel emissions.
More complex models with more terms for emissions and absorptions of CO 2 can be made. One is shown in Figure \(\PageIndex{7}\). This model adds CO 2 release from the soil through respiration by microorganisms, as well as from plant respiration (CHO to CO2atm). Another term has been added for release by oceans.
Figure \(\PageIndex{7}\): More complicated Vcell climate model.
Fortunately, we don't have to rely on these simple models to predict future trends in temperature and CO 2 . A complex dynamic model simulator that is in accord with many different climate models is available at your fingertips. Developed at MIT and Climate Interactive, and available for free from any web browser, the EN-ROADS program allows users to change sliders for key inputs and see future predicted temperature and CO 2 levels. In accordance with RCP and SSP IPCC pathways that tie future emissions to socio-economic policies (discussed in Chapter 31.1), the program allows users to change variables such as carbon pricing and incentives to move to clean energy in transportation, building and energy supplies sectors. Access the program directly from this page by clicking the Close icon in the program window in Figure \(\PageIndex{8}\) below.
Figure \(\PageIndex{8}\): EN-ROADS global climate simulator
Here is also an external link to the En-Roads global climate simulator ( Developed by Climate Interactive, the MIT Sloan Sustainability Initiative , and Ventana Systems )
Move the interactive sliders and see the effect on greenhouse gas emissions and global temperatures. Here is a link to a one-page tutorial on its use.
We should all be skeptical of models, especially ones that predict changes 80 or more years into the future. We gain confidence in a model if it accurately fits data going back in time and into the future data as well. We mentioned in Chapter 31.1 that oil company scientists knew of the likely climatic effects arising from fossil fuel emissions, but the company executives did not act on their models. Their models were startlingly accurate as shown in Figure \(\PageIndex{9}\) below, which shows their predictions for both CO 2 levels and the associated increases in temperature caused by them.
Figure \(\PageIndex{9}\): Historically observed temperature change (red) and atmospheric carbon dioxide concentration (blue) over time, compared against global warming projections reported by ExxonMobil scientists. Supran, G., Rahmstorf, S., and Oreskes, N. Assessing ExxonMobil's global warming projections. Science (2023). https://www.science.org/doi/abs/10.1...cience.abk0063 . Reprinted with permission from AAAS. Not for reuse.
Panel (A) shows “Proprietary” 1982 Exxon-modeled projections.
Panel (B) shows a summary of projections in seven internal company memos and five peer-reviewed publications between 1977 and 2003 (gray lines).
Panel (C) shows a 1977 internally reported graph of the global warming “effect of CO2 on an interglacial scale.” (A) and (B) display averaged historical temperature observations, whereas the historical temperature record in (C) is a smoothed Earth system model simulation of the last 150,000 years.
As these graphs clearly show, oil companies knew since the late 1970s, over 40 years ago, of the climatic effects of CO 2 emissions. They could even predict the temperatures since the last ice age. In the 70s, solar and wind energy were much more expensive to produce and use than now, but if we had subsidized their development back then as we have done for decades for the fossil fuel industries, our climatic situation now would be much less precarious. Figure \(\PageIndex{10}\) below shows worldwide fossil fuel subsidies in US $billion and in % global GDP from 2015 to 2020 and projections after that.
Figure \(\PageIndex{10}\): Worldwide subsidizes in US $billion and in % global GDP. Bar graphs are for US$biillons and the circles and triangles for % global GDP. IMF. ttps://www.imf.org/en/Publications/W...bsidies-466004
The subsidies are broken down into explicit subsidies (tax breaks or direct payments to help fossil fuel companies to fund their uncompensated costs) and implicit ones (undercharging for environmental costs of fossil fuel use that the oil companies don't pay). These latter "hidden" costs are passed down to countries, states, and individuals. In 2020, global subsidies were $5.9 trillion or 6.8% of the world's GDP. The explicit subsidies given to fossil fuel companies, about 8% of the total, amounted to $472 billion just in 2020!
"Company executives chose to publicly denigrate climate models, insist there was no scientific consensus on anthropogenic climate change, and claim the science was highly uncertain when their own scientists were telling them the opposite" ( ref ). They also propagated the myth that the global climate was actually cooling. This is a powerful and unsettling example of disinformation with enormous consequences.
Now that we have seen the big picture, let's look at how carbon moves through various pools of carbon-containing molecules. We have already discussed photosynthesis in great detail in Chapter 5, so we fill focus our attention more on dissolved inorganic carbons (DIC) including species such as HCO 3 - and CO 3 2 - . Another view of the carbon cycle that includes weathering of rocks to produce silicates and bicarbonates, and the formation of shells in the ocean from HCO 3 - , CO 3 2 - and silicates, is shown in Figure \(\PageIndex{10}\).
Figure \(\PageIndex{10}\):
Let's focus on the oceans first. The reversible movement of CO 2 from the atmosphere to the oceans, CO 2 atm ↔ CO 2 ocean , depends on the difference in the partial pressures of CO 2 (ΔpCO 2 ) in the atmosphere and surface waters. The reaction is also driven to the right by the removal of CO 2 (aq) as it forms carbonic acid (H 2 CO 3 ), which then forms bicarbonate (HCO 3 – ) and carbonate (CO 3 2 – ). These coupled reactions chemically buffer ocean water, thus regulating ocean pCO 2 and pH.
pCO 2 is not homogenous in ocean surface waters and varies with different conditions of current and temperature. CO 2 can be more readily released from upwellings of nutrient-rich and warm waters, especially in the tropics. In cold Northern waters and also in the Southern Ocean, where water sinks, it is taken up from the atmosphere (again CO 2 is more soluble in cold water).
As we discussed in Chapter 31.1, the ocean chemistry of CO 2 determines in large part the levels of atmospheric CO 2 . The coupled reactions of CO 2 in the oceans are shown below.
\begin{equation}
\mathrm{CO}_2(\mathrm{~g}, \mathrm{~atm}) \leftrightarrow \mathrm{CO}_2(\mathrm{aq}, \text { ocean) }
\end{equation}
\begin{equation}
\mathrm{CO}_2(\mathrm{aq} \text {, ocean })+\mathrm{H}_2 \mathrm{O}(\mathrm{I} \text {, ocean }) \leftrightarrow \mathrm{H}_3 \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HCO}_3^{-}(\mathrm{aq})
\end{equation}
\begin{equation}
\mathrm{H}_2 \mathrm{O}(\mathrm{I})+\mathrm{HCO}_3^{-}(\mathrm{aq}) \leftrightarrow \mathrm{H}_3 \mathrm{O}^{+}(\mathrm{aq})+\mathrm{CO}_3{ }^{2-}(\mathrm{aq} \text {, sparingly soluble })
\end{equation}
These reactions should be familiar to all chemistry students and were presented previously in Chapter 31.1 and in Chapter 2. A significant contributor to ocean bicarbonate is weathering of rocks like limestone. and marble, which are both forms of CaCO 3 . The relevant reactions are shown below.
\begin{equation}
\begin{aligned}
&\mathrm{CaCO}_3(\mathrm{~s})+\mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{CO}_3{ }^{2-}(\mathrm{aq}) \\
&\mathrm{CO}_3{ }^{2-}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{HCO}_3{ }^{-}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})
\end{aligned}
\end{equation}
CO 2 is nonpolar and not very soluble in water. Either is CO 3 2 - in the presence of divalent cations like Ca 2 + . However HCO 3 - is and can be considered a "soluble" form of carbon. This soluble form from terrestrial weatherings ends up in rivers and eventually enters the ocean. It is also the form of carbonate that is transferred into cells by anion transporters for eventual shell formation. HCO 3 - is also a chief regulator of both blood and ocean pH. Weathering is slow compared to anthropogenic emissions of CO 2 from fossil fuel use, but it is nevertheless a key player in the carbon cycle and the regulation of ocean pH.
The same weathering reactions on silicate rocks lead to the transfer of silicate ions into rivers and then into the ocean, where they can be taken up by diatoms in the formation of CaSiO 4 shells. As the oceans take up more CO 2 , they become more acidic, which leads to the equivalent of "weathering" of shells of living organisms, leading to their potential death. Silicon is directly underneath carbon in the periodic table so the following simplified reaction is analogous to those we seen with CO 2 and its inorganic ions.
\begin{equation}
\mathrm{H}_4 \mathrm{SiO}_4=\mathrm{SiO}_2+2 \mathrm{H}_2 \mathrm{O}
\end{equation}
H 4 SiO 4 is silicic acid.
13 C/ 12 C ratios in ice core and ocean sediments
We are now in the position to explore how isotopes of carbon can be used for more than radio- 14 C dating, which is quite limited in climate studies. 13 C, a stable isotope of carbon, however, is extremely useful because C- 13 C bond dynamics are influenced by it. Reaction rates are affected by the presence of 13 C when C-C bonds are made or cleaved. This isotope effect leads to different 13 C/ 12 C ratios in reactants and products, and hence different δ 13 C values.
Isotopes have a long history in the study of biochemical reactions. The k cat and k cat /K M values for enzyme-catalyzed reactions can be affected if the rate-limiting step involves cleavage or the creation of a C- 13 C, C-D (deuterium) or C-T (tritium) bond. Substrates labeled with the isotopes have similar transition state energies for the formation/cleavage of a bond involving an isotope, but the ground state vibrational energy for the isotope-substituted atom are proportionately lower, as illustrated in Figure \(\PageIndex{11}\).
Figure \(\PageIndex{11}\): Kinetic Isotope Effects .
This primary kinetic isotope effect leads to higher activation energy for the formation/cleavage of a bond with the isotope. For C-D and C-T bond cleavages that are rate-limiting, the rates are 7X and 16X slower than the cleavage of a C-H bond, respectively. Cleavage or formation of bonds to heavy isotopes of carbon, oxygen, nitrogen, sulfur, and bromine have much smaller isotope effects (between 1.02 and 1.10). The difference in the magnitude of the kinetic isotope effect is directly related to the percentage change in mass. Large effects are seen when hydrogen is replaced with deuterium because the percentage mass change is very large (mass is being doubled). .
Hence the kinetic isotope effect is at play in carbon fixation in photosynthesis, for example. This is evidenced by the observation that the 13 C/ 12 C ratios are lower in plants than in the atmosphere, showing that 12 CO 2 is preferentially "fixed" in the ribulose bisphosphate carboxylase/oxygenase reaction in plants and other photosynthetic organisms. Also, 12 CO 2 , a lighter molecule, has a faster rate of diffusion through the stromata, regulated pores in leaves that facilitate the passage of CO 2 , O 2 and H 2 O.
In Chapter 31.2, we discussed the use of δ 18 O values in ice core and ocean core sediments for measuring past CO 2 and temperatures.
\[\delta^{18} O=\left[ \dfrac{\left(\dfrac{^{18} O}{^{16} O}\right)_{\text {sample }}}{\left(\dfrac{^{18} O}{^{16} O}\right)_{\text {reference }}}-1\right] * 1000 \nonumber \]
δ 18 O values for ice core water samples werer easier to interpret than δ 18 O values for CaCO 3 sampls, since the deposition of ice is a simple physical process compared to the complexity of the deposition of CaCO 3 in ocean sediments, which depends on chemical reactions and nonequilbrium processes (as described in Chapter 31).
Climate scientists can determine and use δ 13 C values. An analogous equation for it is shown below.
\(
\delta^{13} C=\left[\dfrac{\left(\frac{13}{12} C\right)_{\text {sample }}}{\left(\frac{13}{12} \mathrm{C}\right)_{\text {reference }}}-1\right] * 1000
\)
As for using δ 18 O in carbonate samples, using δ 13 C is more difficult as well. The shells of ocean sediment foraminifera were made from dissolved inorganic carbon (DIC) in the ocean at the time so their δ 13 C values reflect that. However, shell formation is not a simple equilibrium process since biological shells are formed rapidly so kinetic effects in carbonate and hence isotope fractionation are important. In addition, the biochemistry of shell formation is complicated.
In the open ocean, planktic foraminifera are perhaps the most important marine organism that forms shells given that they produce and export into the ocean about 2.9 Gt CaCO 3 /yr. Their shells form in a process involving many metastable calcite phases. It starts with a soft template that contains Mg 2 + and Na + ions which play a key role in crystallization. Growth occurs by successive additions of "chambers" to the shell. An F-actin mesh, which forms microtubular structures, leads to the formation of protective envelopes for chamber formation. The layered templates sequester and help control the mineralization of shells and separate bulk sea water for a more intracellular vs extracellular process for biomineralization. Seawater containing minerals becomes vacuolized in a process which for some foraminfera excludes a competing cation, Mg 2 + . In addition, both Ca 2 + and HCO 3 - transporters are required. This all combines to form an environment low in Mg 2 + and supersaturated in Ca 2 + and CO 3 2 - for calcite formation. The kinetic fractionation of 13 C isotopes into shells is also different than for 18 O isotopes since the "pool" of oxygen in the oceans is much greater than carbon. Likewise, the δ 13 C is more location-dependent that the δ 18 O.
Buried organic matter can also be studied. The δ 13 C value for buried organic matter depends on primary productivity on land and in the oceans. As mentioned above, autotrophs preferentially take up 12 CO 2 . Heterotrophs that eat them also become enriched in 12 C. Hence organisms have negative δ 13 C values, typically around −25‰, with the number depending on pathways of incorporation and metabolism. Methane in hydrates in the ocean can be either biogenic, made by methanogens, for example, at low temperatures, or thermogenic, made during high-temperature reactions. Biogenic methane has a δ 13 C of around - 60‰, while thermogenic methane has a value of around −40‰. Terrestrial plants have different δ 13 values. δ 13 C in C 4 plants range from -16 to −10‰ while for C 3 plants they range from −33 to −24‰.
Changes in δ 13 C in ice cores and ocean sediments are used in climate studies. Sometimes it's confusing to understand the cause and effect of the changes. This following explanation for changes in the already negative values of δ 13 C might offer help to those with a chemistry-centric view of biochemistry who struggle with mass balance outside of simple chemical equations.
Under climatic conditions, when there is an abundance of terrestrial plants that lock in and sequester atmospheric 12 CO 2 , the atmosphere becomes depleted in 12 CO 2 and correspondingly enriched in 13 CO 2 . Hence primary production (fixing of carbon and anabolic metabolism) by photoplankton in the oceans, under robust growing conditions, would sequester more 13 C, causing an increase in δ 13 C (i.e. more positive) values for buried organic and calcite sediments.
During times of mass extinction, when terrestrial plant primary production drops precipitously, the δ 13 C becomes more negative with the decrease in primary production and release of plant carbon, leaving more 12 CO 2 in the atmosphere. This drop is called a negative δ 13 C excursion . When life is robustly favored and carbon is fixed by autotrophs, and the organic carbon resulting from them is eventually buried in sedimentary rocks, the rise in δ 13 C is called a positive δ 13 C excursion .
Examples of climatic events accompanied by changes in δ 13 C.
Late Devonian period
Fossil evidence from the late Devonian, when large terrestrial plants evolved and expanded, is characterized by increases in δ 13 C.
Paleocene/Eocene Thermal Maximum
We saw in Chapter 31.1 that around 55 MYA, sediment records indicate a spike in temperatures of about 5 0 F occurring over about a 100K year timeframe. This was accompanied by a dramatic spike in CO 2 and a dramatic drop in ocean pH as measured by the loss of deep sea CaCO 3 (chalk). This very short time frame is called the Paleocene/Eocene thermal maximum (PETM), which shows very quick spikes (on the geological time scale) can and do occur. Sediment records for this time indicate a large negative δ 13 C excursion, consistent with a loss of plants with their preferential uptake of 12 CO 2 , leading to an accompanying increase in 12 CO 2 in the atmosphere.
1500-1650 CE
We examined δ 18 O values during the Little Ice Ages in Chapter 31.2. What about δ 13 C values? CO 2 and δ 13 C values from 1000 to 1900 are shown in Figure \(\PageIndex{12}\).
Figure \(\PageIndex{12}\): CO 2 and δ 13 C values from 1000 to 1900. Koch et al. Quaternary Science Reviews, 207, 2019, 13-36. https://doi.org/10.1016/j.quascirev.2018.12.004 . CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
Panel (A) shows the CO2 concentrations recorded in two Antarctic ice cores: Law Dome (grey, MacFarling Meure et al., 2006) and West Antarctic Ice Sheet (WAIS) Divide (blue, Ahn et al., 2012).
Panel (B) shows the carbon isotopic ratios recorded in CO2 from the WAIS Divide ice core (black, Bauska et al., 2015) showing an increased terrestrial carbon uptake over the 16th century (B). The yellow box is the span of the major indigenous depopulation event (1520e1700 CE). Loess smoothed lines for visual aid.
Koch et al have strong evidence to suggest that the cooling after 1510 (area in the yellow box in the above figure) was associated with a dip in CO 2 caused by the reforestation of indigenous peoples' land in Meso and South American after epidemics of European disease killed upwards of 90% (around 55 million) of the indigenous peoples. The open and agricultural land reverted back to forests. The diseases included smallpox, measles, influenza, the bubonic plague, and eventually malaria, diphtheria, typhus and cholera. Domesticated farm animals brought from Europe to the Americans led to most of the disease. Along with the death of so many people was a concomitant return of cleared and agricultural lands (about 56 million hectares or 212,000 mi 2 ) to forest and plant growth. This may have led to a 7-10 ppm drop in CO 2 in the late 1500s and early 1600s, peaking in 1601 (middle of the yellow box). This decrease in temperature was associated with a small rise (small positive excursion) in the δ 13 C values, as 12 CO 2 was preferentially removed from the atmosphere. Global surface air temperatures decreased by around 0.15 o C. This "Great Dying" of Indigenous peoples shows the power of humankind to globally alter climate in calamitous ways, even before the use of fossil fuels. The decrease in δ 13 C values before 1500 was unexplained.
1800-the present
δ 13 C values can also be used to unequivocally prove that the increase in CO 2 since the industrial revolution is from the burning of fossil fuels, which is of biogenic origin and hence have more negative δ 13 C values. Figure \(\PageIndex{13}\) shows atmospheric CO 2 levels in ppm plotted along with δ 13 C values. There is a perfect correlation between the rise in atmospheric CO 2 starting with the industrial revolution with the decrease in the δ 13 C values over the same time.
Figure \(\PageIndex{13}\): CO 2 concentration (black circles) and the δ 13 C (brown circles) from 1000 to 2010. Rubino et al. Journal of Geophysical Research: Atmospheres. https://doi.org/10.1002/jgrd.50668 . With permission (Copyright Clearance Center)
Summary
In the first three sections of Chapter 31 (31.1, 31.2, and this one), we have introduced the basics of climate change, and how climate scientists obtain, analyze and interpret climate data. We emphasized the scientific rigor by which they do that and offered a detailed analysis of the use of isotopes to document past and present changes in climate, Finally, we offered models to predict and mitigate future climate changes. After reading this material, you should be enabled to discuss climate change with others from a sound and valid position. More importantly for this book, you will have a better knowledge base and understanding for the rest of the chapter sections, which will address specific topics in "biochemistry and climate change".
- The carbon cycle is the process by which carbon moves through the Earth's systems, including the atmosphere, oceans, and biosphere.
- The carbon cycle is driven by the exchange of carbon between different reservoirs, such as the atmosphere, oceans, and living organisms.
- The main processes involved in the carbon cycle include photosynthesis, respiration, and the formation and weathering of rocks.
- Human activities, such as burning fossil fuels and deforestation, have significantly increased the amount of carbon dioxide (CO2) in the atmosphere, disrupting the natural balance of the carbon cycle.
- The increase in atmospheric CO2 is the primary driver of climate change, as it causes the greenhouse effect, trapping heat in the atmosphere and warming the Earth's surface.
- The ocean also plays a critical role in the carbon cycle, as it acts as a sink for CO2, absorbing about 25% of the CO2 emitted by human activities.
- The acidification of the ocean caused by the uptake of CO2 is having a significant impact on marine ecosystems, altering the chemistry of seawater and making it more difficult for some organisms to build and maintain their shells and skeletons.
- Understanding the carbon cycle and carbon chemistry is crucial for understanding the causes and impacts of climate change and for developing strategies to mitigate and adapt to its effects.


7.2: Know What to Avoid
“When in doubt, throw it out.”
In order to become a mindful communicator, especially with respect to public speaking, consider the audience when deciding what words, terminology, and phrases to use. Being cautious and mindful about the language used goes beyond what some may call “P.C.” or politically correct, which has become a loaded term in contemporary politics. If the language of a speech triggers a negative response from individuals in the audience, then it is highly likely that those audience members will no longer listen with the intent to understand. They have likely either turned off their attention spans or started to listen with the intent to defend themselves later.
In keeping this goal in mind, stay mindful of the language used and incorporate words that resonate with the audience. Some categories of language to consider avoiding include political, religious, racial, ethnic, or sexual references that some may consider offensive or, at the very least, off-putting. For example, words that may have once been acceptable may need slight edits before using them in front of a potentially diverse audience. These words include “stewardess” (flight attendant), “fireman” (firefighter), and “cleaning lady” (housekeeper).
Note to Self


6.2.1: Learning Objectives
After this lab you should be able to:
- Define pH.
- Explain the quantitative difference between two different pH values, for example, pH 4 and pH 6.
- Describe the major effects pH changes can have on a cell.
“Growth of the bacterium Clostridium botulinum in canned food may cause botulism—a deadly form of food poisoning. These bacteria exist either as spores or as vegetative cells. The spores, which are comparable to plant seeds, can survive harmlessly in soil and water for many years. When ideal conditions exist for growth, the spores produce vegetative cells, which multiply rapidly and may produce a deadly toxin within 3 to 4 days of growth.
Acidity may be natural, as in most fruits, or added, as in pickled food. Low-acid canned foods are not acidic enough to prevent the growth of these bacteria. Acid foods contain enough acid to block their growth, or destroy them more rapidly when heated. The term "pH" is a measure of acidity; the lower its value, the more acid the food. The acidity level in foods can be increased by adding lemon juice, citric acid, or vinegar.”
National Center for Home Food Preservation: http://nchfp.uga.edu/how/general/ensuring_safe_canned_foods.htm l


9.9E: Exercises
Practice Makes Perfect
In the following exercises,
- Solve graphically
-
Write the solution in interval notation
- \(x^{2}+6 x+5>0\)
- \(x^{2}+4 x-12<0\)
- \(x^{2}+4 x+3 \leq 0\)
- \(x^{2}-6 x+8 \geq 0\)
- \(-x^{2}-3 x+18 \leq 0\)
- \(-x^{2}+2 x+24<0\)
- \(-x^{2}+x+12 \geq 0\)
- \(-x^{2}+2 x+15>0\)
- Answer
-
1.
-
Figure 9.8.16 - \((-\infty,-5) \cup(-1, \infty)\)
3.
-
Figure 9.8.17 - \([-3,-1]\)
5.
-
Figure 9.8.18 - \((-\infty,-6] \cup[3, \infty)\)
7.
-
Figure 9.8.19 - \([-3,4]\)
-
In the following exercises, solve each inequality algebraically and write any solution in interval notation.
- \(x^{2}+3 x-4 \geq 0\)
- \(x^{2}+x-6 \leq 0\)
- \(x^{2}-7 x+10<0\)
- \(x^{2}-4 x+3>0\)
- \(x^{2}+8 x>-15\)
- \(x^{2}+8 x<-12\)
- \(x^{2}-4 x+2 \leq 0\)
- \(-x^{2}+8 x-11<0\)
- \(x^{2}-10 x>-19\)
- \(x^{2}+6 x<-3\)
- \(-6 x^{2}+19 x-10 \geq 0\)
- \(-3 x^{2}-4 x+4 \leq 0\)
- \(-2 x^{2}+7 x+4 \geq 0\)
- \(2 x^{2}+5 x-12>0\)
- \(x^{2}+3 x+5>0\)
- \(x^{2}-3 x+6 \leq 0\)
- \(-x^{2}+x-7>0\)
- \(-x^{2}-4 x-5<0\)
- \(-2 x^{2}+8 x-10<0\)
- \(-x^{2}+2 x-7 \geq 0\)
- Answer
-
1. \((-\infty,-4] \cup[1, \infty)\)
3. \((2,5)\)
5. \((-\infty,-5) \cup(-3, \infty)\)
7. \([2-\sqrt{2}, 2+\sqrt{2}]\)
9. \((-\infty, 5-\sqrt{6}) \cup(5+\sqrt{6}, \infty)\)
11. \(\left(-\infty,-\frac{5}{2}\right] \cup\left[-\frac{2}{3}, \infty\right)\)
13. \(\left[-\frac{1}{2}, 4\right]\)
15. \((-\infty, \infty)\)
17. no solution
19. \((-\infty, \infty)\)
- Explain critical points and how they are used to solve quadratic inequalities algebraically.
- Solve \(x^{2}+2x≥8\) both graphically and algebraically. Which method do you prefer, and why?
- Describe the steps needed to solve a quadratic inequality graphically.
- Describe the steps needed to solve a quadratic inequality algebraically.
- Answer
-
1. Answers may vary.
3. Answers may vary.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?


7.10.3: Figuring for Yourself
Figuring for Yourself
Calculate the density of Jupiter. Show your work. Is it more or less dense than Earth? Why?
32.
Calculate the density of Saturn. Show your work. How does it compare with the density of water? Explain how this can be.
33.
What is the density of Jupiter’s moon Europa (see Appendix G for data on moons)? Show your work.
34.
Look at Appendix F and Appendix G and indicate the moon with a diameter that is the largest fraction of the diameter of the planet or dwarf planet it orbits.
35.
Barnard’s Star, the second closest star to us, is about 56 trillion (5.6 × 10 12 ) km away. Calculate how far it would be using the scale model of the solar system given in Overview of Our Planetary System.
36.
A radioactive nucleus has a half-life of years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?


7.E: Photosynthesis (Exercises)
7.1: Overview of Photosynthesis
Multiple Choice
What two products result from photosynthesis?
A. water and carbon dioxide
B. water and oxygen
C. glucose and oxygen
D. glucose and carbon dioxide
- Answer
-
C
Which statement about thylakoids in eukaryotes is not correct?
A. Thylakoids are assembled into stacks.
B. Thylakoids exist as a maze of folded membranes.
C. The space surrounding thylakoids is called stroma.
D. Thylakoids contain chlorophyll.
- Answer
-
B
From where does a heterotroph directly obtain its energy?
A. the sun
B. the sun and eating other organisms
C. eating other organisms
D. simple chemicals in the environment
- Answer
-
C
Free Response
What is the overall purpose of the light reactions in photosynthesis?
- Answer
-
To convert solar energy into chemical energy that cells can use to do work.
Why are carnivores, such as lions, dependent on photosynthesis to survive?
- Answer
-
Because lions eat animals that eat plants.
7.2: Light-Dependent Reactions of Photosynthesis
Multiple Choice
What is the energy of a photon first used to do in photosynthesis?
A. split a water molecule
B. energize an electron
C. produce ATP
D. synthesize glucose
- Answer
-
B
Which molecule absorbs the energy of a photon in photosynthesis?
A. ATP
B. glucose
C. chlorophyll
D. water
- Answer
-
C
Plants produce oxygen when they photosynthesize. Where does the oxygen come from?
A. splitting water molecules
B. ATP synthesis
C. the electron transport chain
D. chlorophyll
- Answer
-
A
Which color(s) of light does chlorophyll a reflect?
A. red and blue
B. green
C. red
D. blue
- Answer
-
B
Three of the same species of plant are each grown under a different colored light for the same amount of time. Plant A is grown under blue light, Plant B is grown under green light, and Plant C is grown under orange light. Assuming the plants use only chlorophyll a and chlorophyll b for photosynthesis, what would be the predicted order of the plants from most growth to least growth?
A. A, C, B
B. A, B, C
C. C, A, B
D. B, A, C
- Answer
-
A
Free Response
Describe the pathway of energy in light-dependent reactions.
- Answer
-
The energy is present initially as light. A photon of light hits chlorophyll, causing an electron to be energized. The free electron travels through the electron transport chain, and the energy of the electron is used to pump hydrogen ions into the thylakoid space, transferring the energy into the electrochemical gradient. The energy of the electrochemical gradient is used to power ATP synthase, and the energy is transferred into a bond in the ATP molecule. In addition, energy from another photon can be used to create a high-energy bond in the molecule NADPH.
7.3: Using Light Energy to Make Organic Molecules
Multiple Choice
Where in plant cells does the Calvin cycle take place?
A. thylakoid membrane
B. thylakoid space
C. stroma
D. granum
- Answer
-
C
Which statement correctly describes carbon fixation?
A. the conversion of CO
2
to an organic compound
B. the use of RuBisCO to form 3-PGA
C. the production of carbohydrate molecules from G3P
D. the formation of RuBP from G3P molecules
E. the use of ATP and NADPH to reduce CO
2
- Answer
-
A
Which order of molecular conversions is correct for the Calvin cycle?
A. RuBP + G3P→3-PGA→sugar
B. RuBisCO→CO2→RuBP→G3P
C. RuBP + CO2→[RuBisCO]3-PGA→G3P
D. CO2→3-PGA→RuBP→G3P
- Answer
-
C
What is the molecule that leaves the Calvin cycle to be converted into glucose?
A. ADP
B. G3P
C. RuBP
D. 3-PGA
- Answer
-
B
Free Response
Which part of the Calvin cycle would be affected if a cell could not produce the enzyme RuBisCO?
- Answer
-
None of the cycle could take place, because RuBisCO is essential in fixing carbon dioxide. Specifically, RuBisCO catalyzes the reaction between carbon dioxide and RuBP at the start of the cycle.
Explain the reciprocal nature of the net chemical reactions for photosynthesis and respiration.
- Answer
-
Photosynthesis takes the energy of sunlight and combines water and carbon dioxide to produce sugar and oxygen as a waste product. The reactions of respiration take sugar and consume oxygen to break it down into carbon dioxide and water, releasing energy. Thus, the reactants of photosynthesis are the products of respiration, and vice versa.
Contributors and Attributions
Remixed and/or curated from the following works:
Clark, M. A., Douglas, M., & Choi, J. (2018). 2.5.8 Review Questions and 2.5.9 Critical Thinking Questions . In Biology 2e . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/biology-2e/pages/1-introduction ).


4.5: Nutrition
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Learning Objectives
- Explain the merits of breastfeeding
- Discuss the importance of nutrition to early physical growth, including nutritional concerns for infants and toddlers such as marasmus and kwashiorkor
Good nutrition in a supportive environment is vital for an infant’s healthy growth and development. Remember, from birth to 1 year, infants triple their weight and increase their height by half, and this growth requires good nutrition. For the first 6 months, babies are fed breast milk or formula. Starting good nutrition practices early can help children develop healthy dietary patterns. Infants need to receive nutrients to fuel their rapid physical growth. Malnutrition during infancy can result in not only physical but also cognitive and social consequences. Without proper nutrition, infants cannot reach their physical potential.
Benefits of Breastfeeding
Breast milk is considered the ideal diet for newborns due to the nutritional makeup of colostrum and subsequent breastmilk production. Colostrum, the milk produced during pregnancy and just after birth, has been described as “liquid gold.” Colostrum is packed with nutrients and other important substances that help the infant build up his or her immune system. Most babies will get all the nutrition they need through colostrum during the first few days of life (CDC, 2018). [1] Breast milk changes by the third to fifth day after birth, becoming much thinner, but containing just the right amount of fat, sugar, water, and proteins to support overall physical and neurological development. It provides a source of iron more easily absorbed in the body than the iron found in dietary supplements, it provides resistance against many diseases, it is more easily digested by infants than formula, and it helps babies make a transition to solid foods more easily than if bottle-fed.
The reason infants need such a high fat content is the process of myelination which requires fat to insulate the neurons. There has been some research, including meta-analyses, to show that breastfeeding is connected to advantages with cognitive development (Anderson, Johnstone, & Remley, 1999) [2] . Low birth weight infants had the greatest benefits from breastfeeding than did normal-weight infants in a meta-analysis that of twenty controlled studies examining the overall impact of breastfeeding (Anderson et al., 1999). This meta-analysis showed that breastfeeding may provide nutrients required for rapid development of the immature brain and be connected to more rapid or better development of neurologic function. The studies also showed that a longer duration of breastfeeding was accompanied by greater differences in cognitive development between breastfed and formula-fed children. Whereas normal-weight infants showed a 2.66-point difference, low-birth-weight infants showed a 5.18-point difference in IQ compared with weight-matched, formula-fed infants (Anderson et al, 1999). These studies suggest that nutrients present in breast milk may have a significant effect on neurologic development in both premature and full-term infants.
For most babies, breast milk is also easier to digest than formula. Formula-fed infants experience more diarrhea and upset stomachs. The absence of antibodies in formula often results in a higher rate of ear infections and respiratory infections. Children who are breastfed have lower rates of childhood leukemia, asthma, obesity, type 1 and 2 diabetes, and a lower risk of SIDS. For all of these reasons, it is recommended that mothers breastfeed their infants until at least 6 months of age and that breast milk be used in the diet throughout the first year (U.S. Department of Health and Human Services, 2004a in Berk, 2007).
Several recent studies have reported that it is not just babies that benefit from breastfeeding. Breastfeeding stimulates contractions in the uterus to help it regain its normal size, and women who breastfeed are more likely to space their pregnancies farther apart. Mothers who breastfeed are at lower risk of developing breast cancer, especially among higher-risk racial and ethnic groups (Islami et al., 2015). [3] Other studies suggest that women who breastfeed have lower rates of ovarian cancer (Titus-Ernstoff, Rees, Terry, & Cramer, 2010) [4] , and reduced risk for developing Type 2 diabetes (Gunderson, et al., 2015) [5] , and rheumatoid arthritis (Karlson, Mandl, Hankinson, & Grodstein, 2004). [6]
A historic look at breastfeeding
The use of wet nurses, or lactating women, hired to nurse others’ infants, during the middle ages eventually declined, and mothers increasingly breastfed their own infants in the late 1800s. In the early part of the 20th century, breastfeeding began to go through another decline, and by the 1950s it was practiced less frequently by middle class, more affluent mothers as formula began to be viewed as superior to breast milk. In the late 1960s and 1970s, there was again a greater emphasis placed on natural childbirth and breastfeeding and the benefits of breastfeeding were more widely publicized. Gradually, rates of breastfeeding began to climb, particularly among middle-class educated mothers who received the strongest messages to breastfeed.
Today, new mothers receive consultation from lactation specialists before being discharged from the hospital to ensure that they are informed of the benefits of breastfeeding and given support and encouragement to get their infants accustomed to taking the breast. This does not always happen immediately, and first-time mothers, especially, can become upset or discouraged. In this case, lactation specialists and nursing staff can encourage the mother to keep trying until the baby and mother are comfortable with the feeding.
Most mothers who breastfeed in the United States stop breastfeeding at about 6-8 weeks, often in order to return to work outside the home (United States Department of Health and Human Services (USDHHS), 2011 [7] ). Mothers can certainly continue to provide breast milk to their babies by expressing and freezing the milk to be bottle fed at a later time or by being available to their infants at feeding time, but some mothers find that after the initial encour agement they receive in the hospital to breastfeed, the outside world is less supportive of such efforts. Some workplaces support breastfeeding mothers by providing flexible schedules and welcoming infants, but many do not. And the public support of breastfeeding is sometimes lacking. Women in Canada are more likely to breastfeed than are those in the United States, and the Canadian health recommendation is for breastfeeding to continue until 2 years of age. Facilities in public places in Canada such as malls, ferries, and workplaces provide more support and comfort for the breastfeeding mother and child than found in the United States.
In addition to the nutritional and health benefits of breastfeeding, breast milk is free! Anyone who has priced formula recently can appreciate this added incentive to breastfeeding. Prices for a month’s worth of formula can easily range from $130-$200. Prices for a year’s worth of formula and feeding supplies can cost well over $1,500 (USDHHS, 2011).
Links to Learning
- Watch this video from the Psych SciShow “Bad Science: Breastmilk and Formula” to learn about research related to both breastfeeding and formula-feeding.
- To learn more about breastfeeding, visit this resource from the U.S. Department of Health and Human Resources: Your Guide to Breastfeeding.
- Visit Kids Health on Breastfeeding vs. Formula Feeding to learn more about the benefits and challenges of each. Click on the speaker icon to listen to the narration of the article if you would like.
When Breastfeeding Doesn’t Work
There are occasions where mothers may be unable to breastfeed babies, often for a variety of health, social, and emotional reasons. For example, breastfeeding generally does not work:
- when the baby is adopted
- when the biological mother has a transmissible disease such as tuberculosis or HIV
- when the mother is addicted to drugs or taking any medication that may be harmful to the baby (including some types of birth control)
- when the infant was born to (or adopted by) a family with two fathers and the surrogate mother is not available to breastfeed
- when there are attachment issues between mother and baby
- when the mother or the baby is in the Intensive Care Unit (ICU) after the delivery process
- when the baby and mother are attached but the mother does not produce enough breast-milk
One early argument given to promote the practice of breastfeeding (when health issues are not the case) is that it promotes bonding and healthy emotional development for infants. However, this does not seem to be a unique case. Breastfed and bottle-fed infants adjust equally well emotionally (Ferguson & Woodward, 1999). This is good news for mothers who may be unable to breastfeed for a variety of reasons and for fathers who might feel left out as a result.
Introducing Solid Foods
Breast milk or formula is the only food a newborn needs, and the American Academy of Pediatrics recommends exclusive breastfeeding for the first six months after birth. Solid foods can be introduced from around six months onward when babies develop stable sitting and oral feeding skills but should be used only as a supplement to breast milk or formula. By six months, the gastrointestinal tract has matured, solids can be digested more easily, and allergic responses are less likely. The infant is also likely to develop teeth around this time, which aids in chewing solid food. Iron-fortified infant cereal, made of rice, barley, or oatmeal, is typically the first solid introduced due to its high iron content. Cereals can be made of rice, barley, or oatmeal. Generally, salt, sugar, processed meat, juices, and canned foods should be avoided.
Though infants usually start eating solid foods between 4 and 6 months of age, more and more solid foods are consumed by a growing toddler. Pediatricians recommended introducing foods one at a time, and for a few days, in order to identify any potential food allergies. Toddlers may be picky at times, but it remains important to introduce a variety of foods and offer food with essential vitamins and nutrients, including iron, calcium, and vitamin D.
Milk Anemia in the United States
About 9 million children in the United States are malnourished (Children’s Welfare, 1998). More still suffer from milk anemia , a condition in which milk consumption leads to a lack of iron in the diet. The prevalence of iron deficiency anemia in 1- to 3-year-old children seems to be increasing (Kazal, 2002) [8] . The body gets iron through certain foods. Toddlers who drink too much cow’s milk may also become anemic if they are not eating other healthy foods that have iron. This can be due to the practice of giving toddlers milk as a pacifier when resting, riding, walking, and so on. Appetite declines somewhat during toddlerhood and a small amount of milk (especially with added chocolate syrup) can easily satisfy a child’s appetite for many hours. The calcium in milk interferes with the absorption of iron in the diet as well. There is also a link between iron deficiency anemia and diminished mental, motor, and behavioral development. In the second year of life, iron deficiency can be prevented by the use of a diversified diet that is rich in sources of iron and vitamin C, limiting cow’s milk consumption to less than 24 ounces per day, and providing a daily iron-fortified vitamin.
Global Considerations and Malnutrition
In the 1960s, formula companies led campaigns in developing countries to encourage mothers to feed their babies on infant formula. Many mothers felt that formula would be superior to breast milk and began using formula. The use of formula can certainly be healthy under conditions in which there is adequate, clean water with which to mix the formula and adequate means to sanitize bottles and nipples. However, in many of these countries, such conditions were not available and babies often were given diluted, contaminated formula which made them become sick with diarrhea and become dehydrated. These conditions continue today and now many hospitals prohibit the distribution of formula samples to new mothers in efforts to get them to rely on breastfeeding. Many of these mothers do not understand the benefits of breastfeeding and have to be encouraged and supported in order to promote this practice.
The World Health Organization (2018) recommends:
- initiation of breastfeeding within one hour of birth
- exclusive breastfeeding for the first six months of life
- introduction of solid foods at six months together with continued breastfeeding up to two years of age or beyond
Link to Learning
Breastfeeding could save the lives of millions of infants each year, according to the World Health Organization (WHO), yet fewer than 40 percent of infants are breastfed exclusively for the first 6 months of life. Most women can breastfeed unless they are receiving chemotherapy or radiation therapy, have HIV, are dependent on illicit drugs, or have active untreated tuberculosis. Because of the great benefits of breastfeeding, WHO, UNICEF and other national organizations are working together with the government to step up support for breastfeeding globally.
Find out more statistics and recommendations for breastfeeding at the WHO’s 10 facts on breastfeeding . You can also learn more about efforts to promote breastfeeding in Peru: “Protecting Breastfeeding in Peru” .
Children in developing countries and countries experiencing the harsh conditions of war are at risk for two major types of malnutrition. Infantile marasmus refers to starvation due to a lack of calories and protein. Children who do not receive adequate nutrition lose fat and muscle until their bodies can no longer function. Babies who are breastfed are much less at risk of malnutrition than those who are bottle-fed. After weaning, children who have diets deficient in protein may experience kwashiorkor, or the “disease of the displaced child,” often occurring after another child has been born and taken over breastfeeding. This results in a loss of appetite and swelling of the abdomen as the body begins to break down the vital organs as a source of protein.
Watch It
Watch this video to learn more about the signs and symptoms of kwashiorkor and marasmus.
Glossary
- colostrum
- the first secretion from the mammary glands after giving birth, rich in antibodies
- infantile marasmus
- starvation due to a lack of calories and protein
- kwashiorkor
- also known as the “disease of the displaced child,” results in a loss of appetite and swelling of the abdomen as the body begins to break down the vital organs as a source of protein
- malnutrition
- a condition that results from eating a diet in which one or more nutrients are deficient
- milk anemia
- an iron deficiency in infants who have been maintained on a milk diet for too long
- What to Expect While Breastfeeding . CDC. Retrieved from https://www.cdc.gov/nutrition/InfantandToddlerNutrition/breastfeeding/what-to-expect.html<EMAIL_ADDRESS>- Anderson, J.W., Johnstone, B.M., & Remley, D.T. (1999). Breast-feeding and cognitive development: a meta-analysis. The American Journal of Clinical Nutrition, 70, 4, 525–535, https://doi.org/10.1093/ajcn/70.4.525<EMAIL_ADDRESS>- Islami, F., Liu, Y., Jemal, A., Zhou, J., Weiderpass, E., Colditz, G., Boffetta, P., & Weiss, M. (2015). Breastfeeding and breast cancer risks by receptor status- a systematic review and meta-analysis. Annals of Oncology, 26,12. 2398–2407<EMAIL_ADDRESS>- Titus-Ernstoff, Rees, L. Terry, R.R., & Cramer, D. W. (2010). Breast-feeding the last born child and risk of ovarian cancer. Cancer Causes Control. 21(2), 201–207<EMAIL_ADDRESS>- Gunderson, E.P., Hurston, S.R., Dewey, K.G., Faith, M.S., Charvat-Aguilar, N., Khoury, V. C., Nguyen, V.T., & Quesenberry, C.P. (2015). The study of women, infant feeding and type 2 diabetes after GDM pregnancy and growth of their offspring (SWIFT Offspring study): prospective design, methodology and baseline characteristics. BMC Pregnancy and Childbirth, 15,150 https://doi.org/10.1186/s12884-015-0587-z<EMAIL_ADDRESS>- Karlson, E.W., Mandl, L.A., Hankinson, S. E., & Grodstein, F. (2004). Do breast-feeding and other reproductive factors influence future risk of rheumatoid arthritis? Results from the Nurses' Health Study. Arthritis Rheum. 50,11, 3458-67<EMAIL_ADDRESS>- United States Department of Health and Human Services, Office of Women’s Health (2011). Your guide to breast feeding . Washington D.C<EMAIL_ADDRESS>- KAZAL, L.A. (2002). Navajo Health Foundation/Sage Memorial Hospital, Ganado, Arizona Am Fam Physician. 66(7): 1217-1225<EMAIL_ADDRESS>Contributors and Attributions
- Modification, adaptation, and original content. Authored by : Tera Jones for Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution
- Psyc 200 Lifespan Psychology. Authored by : Laura Overstreet. Located at : http://opencourselibrary.org/econ-201/ . License : CC BY: Attribution
- From Colostrum to Breastmilk. # Days after birth. Authored by : Amada44. Located at : https://commons.wikimedia.org/wiki/File:From_Colostrum_to_Breastmilk_-_4241.jpg . License : CC BY-SA: Attribution-ShareAlike
- Infant Nutrition. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Infant_nutrition . License : CC BY-SA: Attribution-ShareAlike
- Toddler Nutrition. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Toddler_nutrition . License : CC BY-SA: Attribution-ShareAlike
- Child Malnutrition - What? How? And when to Refer. Provided by : iheed. Located at : https://www.youtube.com/watch?v=bqEIcMMmj5M . License : Other . License Terms : Standard YouTube License
- Girl eating rice. Authored by : tigerpuppala_2. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Infant_nutrition#/media/File:First_rice.jpg . License : CC BY: Attribution


10.15: Favorable versus Unfavorable Variances
Learning Outcomes
- Differentiate between favorable and unfavorable variances
Favorable and unfavorable variances can be confusing. As a manager at a local movie theatre, you notice the expense for popcorn was way higher than budgeted, causing an unfavorable variance in that expense line. But, you also see a much higher revenue line for popcorn! So, the revenue variance is favorable. How can you calculate whether the increase in expense and the increase in revenue make sense?
Let’s go back now to our Simply Yoga example. Remember we have some variances we identified as favorable, and some unfavorable. Here is the flexible budget as a reminder:
| Simply Yoga Flexible and Planning Budget | ||||
|---|---|---|---|---|
| Planning Budget | Flexible Budget | Activity Variance | Favorable or Unfavorable | |
| Classes taken | 500 | 600 | ||
| Revenue ($14/class) | $7,000 | $8400 | $1400 | Favorable |
| Expenses | ||||
| Wages and Salaries | $3500 | $4200 | $700 | Unfavorable |
| Yoga supplies | $250 | $300 | $50 | Unfavorable |
| Utilities | $500 | $600 | $100 | Unfavorable |
| Rent | $500 | $500 | ||
| Insurance | $100 | $100 | ||
| Other Expenses | $250 | $300 | $50 | Unfavorable |
| Total Expense | $5,100 | $6,000 | $900 | Unfavorable |
| Net Operating Income | $1900 | $2400 | $500 | Favorable |
Favorable variances are defined as either generating more revenue than expected or incurring fewer costs than expected. Unfavorable variances are the opposite. Less revenue is generated or more costs incurred. Either may be good or bad, as these variances are based on a budgeted amount.
As an example, when Simply Yoga had more students attend classes, their wages and salaries line went up, creating an unfavorable variance. As you can see, their revenue was substantially higher, so that favorable variance more than offsets the unfavorable variance of the additional wages!
So you can see here, that Simply Yoga showed some unfavorable variances in their expenses, but had an overall favorable change in their net operating income! So favorable or unfavorable variances don’t mean much if you look at them individually. We need to look at the whole picture!
If the number of classes had remained at 500, and we still saw the increase in wages, there would be more cause for concern., right? But, what if the wages had gone up, more than the increase in revenue? Each favorable and unfavorable variance needs to be examined individually, as noted in the popcorn example in the video! Analysis is the key to making sure that increases (favorable variances) in revenue or increases (unfavorable variances) in expenses are appropriate.
We need to review what would be the expected increase in expense, based on the increase in classes, or popcorn sales or item sales. In the Simply Yoga example, for each $14 increase in revenue (one additional class taken), we would expect a $7 increase in payroll expense, since we pay our instructors $7 per student for each class taken. If we would have seen a different increase in expense, it would have been cause for concern, and further review. Thinking back to our example, where each instructor is paid a minimum of $84 per class (12 students), if we had increased our number of classes, thus more classes were attended, but each of those classes was only getting 8 students, we may have seen the following:
| 10 additional classes x 8 students each | $1,120 additional revenue |
| 10 classes x $84/instructor | $840 additional payroll expense |
We would have expected and additional $560 in payroll expense, so we have an unfavorable variance of $280 of additional expense, even adjusting for the additional revenue.
In this case, we would need to examine which classes we would like to keep on the schedule, and which to eliminate. More decisions will need to be made with this new information!
Practice Questions


11.11: Sentence Variety
Have you ever ordered a dish in a restaurant and been not happy with its taste even though it contained most of your favorite ingredients? Just as a meal might lack the finishing touches needed to spice it up, so too might a paragraph contain all the basic components but still lack the stylistic finesse required to engage a reader. Sometimes writers have a tendency to reuse the same sentence pattern throughout their writing. Like any repetitive task, reading text that contains too many sentences with the same length and structure can become monotonous and boring. Experienced writers mix it up by using an assortment of sentence patterns, rhythms, and lengths.
In this chapter, you will follow a student named Noemi who has written a draft of an essay but needs to refine her writing. This section discusses how to introduce sentence variety into writing, how to open sentences using a variety of techniques, and how to use different types of sentence structure when connecting ideas. You can use these techniques when revising a paper to bring life and rhythm to your work. They will also make reading your work more enjoyable.
Sentence Variety Lesson . Provided by: VirtualTeacherGirl. License: All Rights Reserved. License Terms: Standard YouTube License.
Incorporating Sentence Variety
Experienced writers incorporate sentence variety into their writing by varying sentence style and structure. Using a mixture of different sentence structures reduces repetition and adds emphasis to important points in the text. Read the following example:
During my time in office, I have achieved several goals. I have helped increase funding for local schools. I have reduced crime rates in the neighborhood. I have encouraged young people to get involved in their community. My competitor argues that she is the better choice in the upcoming election. I argue that it is ridiculous to fix something that isn’t broken. If you reelect me this year, I promise to continue to serve this community.
In this extract from an election campaign, the writer uses short, simple sentences of a similar length and style. Writers often mistakenly believe that this technique makes the text clearer for the reader, but the result is a choppy, unsophisticated paragraph that does not grab the audience’s attention. Now read the revised paragraph with sentence variety:
During my time in office, I have helped increase funding for local schools, reduced crime rates in the neighborhood, and encouraged young people to get involved in their community. Why fix what isn’t broken? If you reelect me this year, I will continue to achieve great things for this community. Don’t take a chance on an unknown contender; vote for the proven success.
Notice how introducing a short rhetorical question among the longer sentences in the paragraph is an effective means of keeping the reader’s attention. In the revised version, the writer combines the choppy sentences at the beginning into one longer sentence, which adds rhythm and interest to the paragraph.
Tip
Effective writers often implement the "rule of three," which is basically the idea that things that contain three elements are more memorable and more satisfying to readers than any other number. Try to use a series of three when providing examples, grouping adjectives, or generating a list.
Exercise 1
Combine each set of simple sentences into a compound or a complex sentence. Write the combined sentence on your own sheet of paper.
1. Shakespeare's writing is still relevant today. He wrote about timeless themes. These themes include love, hate, jealousy, death, and destiny.
2. Prewriting is a vital stage of the writing process. Prewriting helps you organize your ideas. Types of of prewriting include outlining, brainstorming, and idea mapping.
3. Walking out in nature can be a very relaxing activity. By nature, I mean the ocean, the woods, mountains, or even a neighborhood with a lot of trees.
4. Reading is like travelling in the mind. A reader can feel like they've gone to Turkey, Nepal, and Belize all in one evening.
5. Vaping can be a dangerous habit, especially if vaping THC. Vitamin E oil is sometimes added to vaping cartriges. Hundres of young people have had permanent lung damage from vaping THC.
Collaboration
Please share with a classmate and compare your answers. Remember, there are many ways to combine sentences, but if you have questions, ask them in class.
Writing at Work
At some point in your career, you will probably find you need to write a cover letter or statement of interest for a job. Writers of cover letters usually find that their initial draft has too much "I" in it, and it sounds a little self-centered, perhaps. While you must use "I" in a cover letter/statement of interest because it is about you , varying your sentence structure will allow you to say a lot about yourself without sounding like you are overusing "I."
Using Sentence Variety at the Beginning of Sentences
Read the following sentences and consider what they all have in common:
- John and Amanda will be analyzing this week’s financial report.
- The car screeched to a halt just a few inches away from the young boy.
- Students rarely come to the exam adequately prepared.
If you are having trouble figuring out why these sentences are similar, try underlining the subject in each. You will notice that the subject is positioned at the beginning of each sentence— John and Amanda , the car , students . Since the subject-verb-object pattern is the simplest sentence structure, many writers tend to overuse this technique, which can result in repetitive paragraphs with little sentence variety.
Noemi wrote an essay about the 2008 government bailout. Read this excerpt from Noemi’s essay:
Starting a Sentence with an Adverb
One technique you can use so as to avoid beginning a sentence with the subject is to use an adverb. An adverb is a word that describes a verb, adjective, or other adverb and often ends in – ly . Examples of adverbs include quickly , softly , quietly , angrily , and timidly . Notice the difference between the following sentences:
- She slowly turned the corner and peered into the murky basement.
- Slowly, she turned the corner and peered into the murky basement.
In the second sentence, the adverb slowly is placed at the beginning of the sentence. If you read the two sentences aloud, you will notice that moving the adverb changes the rhythm of the sentence and slightly alters its meaning. The second sentence emphasizes how the subject moves—slowly—creating a buildup of tension. This technique is effective for fiction writing.
Note that an adverb used at the beginning of a sentence is usually followed by a comma. A comma indicates that the reader should pause briefly, which creates a useful dramatic effect. Read the following sentences aloud and consider the effect of pausing after the adverb:
- Cautiously, he unlocked the kennel and waited for the dog’s reaction.
- Solemnly, the policeman approached the mayor and placed him under arrest.
- Suddenly, he slammed the door shut and sprinted across the street.
In an academic essay, moving an adverb to the beginning of a sentence serves to vary the rhythm of a paragraph and increase sentence variety.
Exercise 2
On your own sheet of paper, rewrite the following sentences by moving the adverbs to the beginning .
1. The red truck sped furiously past the camper van, blaring its horn.
2. Jeff snatched at the bread hungrily, polishing off three slices in under a minute.
3. The firefighters bravely tackled the blaze, but they were beaten back by flames.
4. Mayor Danielson privately acknowledged that the budget was excessive and that further discussion was needed.
5. The dancer lithely glided across the stage before she began the pas-de-deux.
Starting a Sentence with a Prepositional Phrase
A prepositional phrase is a group of words that behaves as an adjective or an adverb, modifying a noun or a verb. Prepositional phrases contain a preposition (a word that specifies place, direction, or time) and an object of the preposition (a noun phrase or pronoun that follows the preposition).
| above | beneath | into | till |
| across | beside | like | toward |
| against | between | near | under |
| after | beyond | off | underneath |
| among | by | on | until |
| around | despite | over | up |
| at | except | past | with |
| before | for | since | without |
| behind | from | through | |
| below | inside | throughout |
Read the following sentence:
- The child opened his birthday present with excitement .
In this sentence, the prepositional phrase is underneath the table. The preposition underneath relates to the object that follows the preposition— the table . Adjectives may be placed between the preposition and the object in a prepositional phrase.
- The child opened his birthday present with extreme excitement .
Some prepositional phrases can be moved to the beginning of a sentence in order to create variety in a piece of writing. Look at the following revised sentence:
- With excitement, the child opened his birthday present.
Notice that when the prepositional phrase is moved to the beginning of the sentence, the emphasis shifts from the subject—the child—to the manner in which the child is opening the present. Words that are placed at the beginning or end of a sentence generally receive the greatest emphasis. Take a look at the following examples. The prepositional phrase is bold in each:
- The bandaged man waited in the doctor’s office .
- In the doctor’s office , the bandaged man waited.
- My train leaves the station at 6:45 a.m .
- At 6:45 a.m. , my train leaves the station.
- The teenagers exchanged drugs and money under the railway bridge .
- Under the railway bridge , the teenagers exchanged drugs and money.
Prepositional phrases are useful in any type of writing. Take another look at Noemi’s essay on the government bailout.
The underlined words are all prepositional phrases. Notice how they add additional information to the text and provide a sense of flow to the essay, making it less choppy and more pleasurable to read.
Unmovable Prepositional Phrases
Not all prepositional phrases can be placed at the beginning of a sentence. Read the following sentence:
- I would like a chocolate sundae without whipped cream .
In this sentence, without whipped cream is the prepositional phrase. Because it describes the chocolate sundae, it cannot be moved to the beginning of the sentence. “Without whipped cream I would like a chocolate sundae” does not make as much (if any) sense. It dangles because it is not right next to what it describes. Just like a verbal phrase or any modifying phrase, a prepositional phrase needs to be placed right next to what it describes. To determine whether a prepositional phrase can be moved, we must determine the meaning of the sentence.
Overuse of Prepositional Phrases
Experienced writers often include more than one prepositional phrase in a sentence; however, it is important not to overload your writing. Using too many modifiers in a paragraph may create an unintentionally comical effect as the following example shows:
The treasure lay buried under the old oak tree, behind the crumbling fifteenth-century wall, near the schoolyard, where children played merrily during their lunch hour, unaware of the riches that remained hidden beneath their feet.
A sentence is not necessarily effective just because it is long and complex. If your sentence appears cluttered with prepositional phrases, divide it into two shorter sentences. The previous sentence is far more effective when written as two simpler sentences:
The treasure lay buried under the old oak tree, behind the crumbling fifteenth-century wall. In the nearby schoolyard, children played merrily during their lunch hour, unaware of the riches that remained hidden beneath their feet.
In addition, writers can sometimes transform prepositional phrases into adjectives when the prepositional phrase originally described a noun.
Sentence with too many prepositional phrases (in bold): Oftentimes, the governor revises the California budget in May when the revenue numbers from taxes are in, but that only leaves two months until the end of the fiscal year to change spending.
Sentence with some prepositional phrases (in bold) turned into adjectives (in blue): Oftentimes, the governor revises the California budget in May when the tax revenue numbers are in, but that only leaves the the final two months of the fiscal year to change spending.
Exercise 3
On a separate piece of paper, move prepositional phrases around in the following paragraph to add variety or add some to appropriate places in the text.
Suburban economic development largely depends on three factors: proximity to a major economic center, transportation access, and the education level of the local workforce. The most successful suburban economic centers are located at the crossroads of two major interstates and have public and private transportation options available. It may be in the best interest of suburban areas within 30 miles of an urban area and looking to expand economically to invest in public transportation (light rail and/or bus) despite their need for subsidies. Economic analysis may show that a combination of local, state, and federal subsidies will make such investment feasible given the amount of projected growth. Even if the full amount of growth does not materialize, the greater ease with which local residents can commute to urban centers may allow for population growth and more moderate economic expansion of the suburban area and allow it to develop into a smaller hub with its own sphere of influence.
- Collaboration
-
Compare what you did with a classmate.
Writing at Work
The overuse of prepositional phrases often occurs when our thoughts are jumbled and we are unsure how concepts or ideas relate to one another. If you are preparing a report or a proposal, take the time to organize your thoughts in an outline before writing a rough draft. Read the draft aloud, either to yourself or to a colleague, and identify areas that are rambling or unclear. If you notice that a particular part of your report contains several sentences over twenty words (or the equivalent of two lines), you should double check that particular section to make certain that it is coherent and does not contain unnecessary prepositional phrases. Reading aloud sometimes helps detect unclear and wordy sentences. You can also ask a colleague to paraphrase your main points to ensure that the meaning is clear.
Starting a Sentence by Inverting Subject and Verb
As we noted earlier, most writers follow the subject-verb-object sentence structure. In an inverted sentence, the order is reversed so that the subject follows the verb. Read the following sentence pairs:
- A truck was parked in the driveway.
- Parked in the driveway was a truck.
- A copy of the file is attached.
- Attached is a copy of the file.
Notice how the second sentence in each pair places more emphasis on the subject— a truck in the first example and the file in the second. This technique is useful for drawing the reader’s attention to your primary area of focus. We can apply this method to an academic essay. Take another look at Naoei’s paragraph.
Exercise 4
On your own sheet of paper, rewrite the following sentences as inverted sentences.
1. Teresa will never attempt to run another marathon.
2. A detailed job description is enclosed with this letter.
3. Bathroom facilities are across the hall to the left of the water cooler.
4. The well-dressed stranger stumbled through the doorway.
5. My colleagues remain unconvinced about the proposed merger.
Connecting Ideas to Increase Sentence Variety
Reviewing and rewriting the beginning of sentences is a good way of introducing sentence variety into your writing. Another useful technique is to connect two sentences using a modifier, a relative clause, or an appositive. This section examines how to connect ideas across several sentences in order to increase sentence variety and improve writing.
Joining Ideas Using an – ing Modifier
Sometimes it is possible to combine two sentences by converting one of them into a modifier using the – ing verb form— singing , dancing , swimming . A modifier is a word or phrase that qualifies the meaning of another element in the sentence (see "Modifiers" section of this chapter). Read the following example:
Original sentences: Steve checked the computer system. He discovered a virus.
Revised sentence: Checking the computer system, Steve discovered a virus.
To connect two sentences using an – ing modifier, add – ing to one of the verbs in the sentences ( checking ) and delete the one of the subjects ( He ). Use a comma to separate the modifier from the subject of the sentence. It is important to make sure that the main idea in your revised sentence is contained in the main clause, not in the modifier. In this example, the main idea is that Steve discovered a virus, not that he checked the computer system.
In the following example, an – ing modifier indicates that two actions are occurring at the same time:
-
Noticing the police car, she shifted gears and slowed down.
This means that she slowed down at the same time she noticed the police car.
-
Barking loudly, the dog ran across the driveway.
This means that the dog barked as it ran across the driveway.
You can add an – ing modifier to the beginning or the end of a sentence, depending on which fits best.
Beginning: Conducting a survey among her friends , Amanda found that few were happy in their jobs.
End: Maria filed the final report, meeting her deadline .
Tip:
A common mistake when combining sentences using the – ing verb form is to misplace the modifier so that it is not logically connected to the rest of the sentence. This creates a dangling modifier. For more about how to avoid this, see the "Modifiers" page earlier in this chapter.
Joining Ideas Using an – ed Modifier
Some sentences can be combined using an – ed verb form— stopped , finished , played . To use this method, one of the sentences must contain a form of be as a helping verb in addition to the – ed verb form. Take a look at the following example:
- Original sentences: The Jones family was delayed by a traffic jam. They arrived several hours after the party started.
- Revised sentence: Delayed by a traffic jam, the Jones family arrived several hours after the party started.
In the original version, was acts as a helping verb—it has no meaning by itself, but it serves a grammatical function by placing the main verb ( delayed ) in the perfect tense.
To connect two sentences using an – ed modifier, drop the helping verb ( was ) and the subject ( the Jones family ) from the sentence with an – ed verb form. This forms a modifying phrase ( delayed by a traffic jam ) that can be added to the beginning or end of the other sentence according to which fits best. As with the – ing modifier, be careful to place the word that the phrase modifies immediately next to what it modifies in order to avoid a dangling modifier.
Using – ing or – ed modifiers can help streamline your writing by drawing obvious connections between two sentences. Take a look at how Noemi might use modifiers in her paragraph.
Exercise 5
Combine the following sentences so that you have a core clause and a modifying phrase beginning with -ed.
1. Xiana was floored by winning the grand prize. She didn't know what to say.
2. Danielle was sad that her cat passed away.
3. They were shocked at the comedian's punch line. They didn't think it was funny at all.
4. He had mellowed out after the argument. He realized that going to the beach relaxed him.
5. The football was fumbled at the goal line. The football squirted around between players on the opposing teams.
Joining Ideas Using a Relative Clause
Another technique that writers use to combine sentences is to join them using a relative clause. A relative clause is a group of words that contains a subject and a verb and describes a noun. Relative clauses function as adjectives by answering questions such as which one? or what kind? Relative clauses begin with a relative pronoun, such as who , which , where , why , or when . Read the following examples:
- Original sentences: The managing director is visiting the company next week. He lives in Seattle.
- Revised sentence: The managing director, who lives in Seattle, is visiting the company next week.
To connect two sentences using a relative clause, substitute the subject of one of the sentences ( he ) for a relative pronoun ( who ). This gives you a relative clause ( who lives in Seattle ) that can be placed next to the noun it describes ( the managing director ). Make sure to keep the sentence you want to emphasize as the main clause. For example, reversing the main clause and subordinate clause in the preceding sentence emphasizes where the managing director lives, not the fact that he is visiting the company.
- Revised sentence: The managing director, who is visiting the company next week, lives in Seattle.
Relative clauses are a useful way of providing additional, nonessential information in a sentence. Take a look at how Noemi might incorporate relative clauses into her essay.
Tip
To check the punctuation of relative clauses, assess whether or not the clause can be taken out of the sentence without changing its meaning. If the relative clause is not essential to the meaning of the sentence, it should be placed in commas. If the relative clause is essential to the meaning of the sentence, it does not require commas around it.
Exercise 6
Join the following sentences by creating relative clauses .
1. Uncle Bob is a sailor. He has been everywhere.
2. Aunt Edna paints portraits. You met her last year.
3. My new car broke down on the bridge. The car cost a bundle.
4. Save the seat for me. The seat is closest to the front.
5. We had a lovely hotel in Ixtapa. We honeymooned there.
6. Joe's cat was mistaken for a rat. Its tail is hairless.
Joining Ideas Using an Appositive
A noun phrase appositive is a word or group of words that describes or renames a noun or pronoun.  Take a look at the following example:
- Original sentences: Greta Thunberg is a 16-year-old environmental activist. She is from Sweden.
- Revised sentence: Greta Thunberg, a 16-year-old environmental activist, is from Sweden.
In the revised sentence, “a 16-year-old environmental activist" is an appositive because it renames Greta Thunberg. To combine two sentences using an appositive, drop the subject and verb from the sentence that renames the noun and turn it into a phrase. Note that in the previous example, the appositive is positioned immediately after the noun it describes. An appositive may be placed anywhere in a sentence, but it must come directly before or after the noun to which it refers:
- Appositive after noun: No one expected that Scott, a poorly trained athlete, would win the race.
- Appositive before noun: A poorly trained athlete, Scott was not expected to win the race.
Unlike relative clauses, appositives are always punctuated by a comma or a set of commas. Take a look at the way Noemi uses appositives to include additional facts in her essay.
Exercise 7
On your own sheet of paper, rewrite the following sentence pairs as one sentence using the techniques you have learned in this section.
- Baby sharks are called pups. Pups can be born in one of three ways.
- The Pacific Ocean is the world’s largest ocean. It extends from the Arctic in the north to the Southern Ocean in the south.
- Michael Phelps won eight gold medals in the 2008 Olympics. He is a champion swimmer.
- Ashley introduced her colleague Dan to her husband, Jim. She speculated that the two of them would have a lot in common.
- Cacao is harvested by hand. It is then sold to chocolate-processing companies at the Coffee, Sugar, and Cocoa Exchange.
Collaboration
Please share with a classmate and compare your answers.
Exercise 8
Children’s stories are deliberately written in short, simple sentences to avoid confusion. Most sentences are constructed using the standard subject-verb-object format. Choose a children’s story that is suitable for eight- to ten-year-olds. Rewrite a chapter of the story so that it appeals to a slightly older age group, by editing for sentence variety. Experiment with the techniques you learned on this page , including the three different ways to vary sentence structure at the beginning of a sentence and the three different ways to connect ideas between sentences. Compare the revised chapter with the original version and consider how sentence variety can be used to target a particular audience.
Writing at Work
In addition to varying sentence structure, consider varying the types of sentences you are using in a report or other workplace document. Most sentences are declarative, but a carefully placed question, exclamation, or command can pique colleagues’ interest, even if the subject material is fairly dry. Imagine that you are writing a budget analysis. Beginning your report with a rhetorical question, such as “Where is our money going?” or “How can we increase sales?” encourages people to continue reading to find out the answers. Although they should be used sparingly in academic and professional writing, questions or commands are effective rhetorical devices.
Contributors and Attributions
- Adapted from Writing for Success . Provided by: The Saylor Foundation. License: CC-NC-SA 3.0 .
This page most recently updated on June 8, 2020.