7.1: Acid-Base Buffers
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Skills to Develop
- Describe the composition and function of acid–base buffers
- Calculate the pH of a buffer before and after the addition of added acid or base using the Henderson-Hasselbalch approximation
A mixture of a weak acid and its conjugate base (or a mixture of a weak base and its conjugate acid) is called a buffer solution, or a buffer . Buffer solutions resist a change in pH when small amounts of a strong acid or a strong base are added (Figure \(\PageIndex{1}\)). A solution of acetic acid (\(\ce{CH3COOH}\) and sodium acetate \(\ce{CH3COONa}\)) is an example of a buffer that consists of a weak acid and its salt. An example of a buffer that consists of a weak base and its salt is a solution of ammonia (\(\ce{NH3(aq)}\)) and ammonium chloride (\(\ce{NH4Cl(aq)}\)).
Figure \(\PageIndex{1}\): (a) The unbuffered solution on the left and the buffered solution on the right have the same pH (pH 8); they are basic, showing the yellow color of the indicator methyl orange at this pH. (b) After the addition of 1 mL of a 0.01-M HCl solution, the buffered solution has not detectably changed its pH but the unbuffered solution has become acidic, as indicated by the change in color of the methyl orange, which turns red at a pH of about 4. (credit: modification of work by Mark Ott)
How Buffers Work
In order for a buffer to "resist" the effect of adding strong acid or strong base, it must have both an acidic and a basic component. However, you cannot mix any two acid/base combination together and get a buffer. If you mix HCl and NaOH, for example, you will simply neutralize the acid with the base and obtain a neutral salt, not a buffer. For a buffer to work, both the acid and the base component must be part of the same equilibrium system - that way, neutralizing one or the other component (by adding strong acid or base) will transform it into the other component, and maintain the buffer mixture.
Therefore, a buffer must consist of a mixture of a weak conjugate acid-base pair.
The pH a buffer maintains is determined by the nature of the conjugate pair and the concentrations of both components. A mixture of acetic acid and sodium acetate is acidic because the K a of acetic acid is greater than the K b of its conjugate base acetate. It is a buffer because it contains both the weak acid and its salt. Hence, it acts to keep the hydronium ion concentration (and the pH) almost constant by the addition of either a small amount of a strong acid or a strong base. If we add a base such as sodium hydroxide, the hydroxide ions react with the few hydronium ions present. Then more of the acetic acid reacts with water, restoring the hydronium ion concentration almost to its original value:
The pH changes very little. If we add an acid such as hydrochloric acid, most of the hydronium ions from the hydrochloric acid combine with acetate ions, forming acetic acid molecules:
Thus, there is very little increase in the concentration of the hydronium ion, and the pH remains practically unchanged (Figure \(\PageIndex{2}\)).
A mixture of ammonia and ammonium chloride is basic because the K b for ammonia is greater than the K a for the ammonium ion. It is a buffer because it also contains the salt of the weak base. If we add a base (hydroxide ions), ammonium ions in the buffer react with the hydroxide ions to form ammonia and water and reduce the hydroxide ion concentration almost to its original value:
If we add an acid (hydronium ions), ammonia molecules in the buffer mixture react with the hydronium ions to form ammonium ions and reduce the hydronium ion concentration almost to its original value:
The three parts of the following example illustrate the change in pH that accompanies the addition of base to a buffered solution of a weak acid and to an unbuffered solution of a strong acid.
Example \(\PageIndex{1}\): pH Changes in Buffered and Unbuffered Solutions
Acetate buffers are used in biochemical studies of enzymes and other chemical components of cells to prevent pH changes that might change the biochemical activity of these compounds.
- Calculate the pH of an acetate buffer that is a mixture with 0.10 M acetic acid and 0.10 M sodium acetate.
- Calculate the pH after 1.0 mL of 0.10 M NaOH is added to 100 mL of this buffer, giving a solution with a volume of 101 mL.
-
For comparison, calculate the pH after 1.0 mL of 0.10 M NaOH is added to 100 mL of a solution of an unbuffered solution with a pH of 4.74 (e.g. a 1.8 × 10 −5 - M solution of HCl). The volume of the final solution is 101 mL.
Solution
-
Calculate the pH of an acetate buffer that is a mixture with 0.10
M
acetic acid and 0.10
M
sodium acetate.
To determine the pH of the buffer solution we use a typical equilibrium calculation (as illustrated in earlier Examples):
-
Determine the direction of change.
The equilibrium in a mixture of H
3
O
+
, \(\ce{CH3CO2-}\), and CH
3
CO
2
H is:
\[\ce{CH3CO2H}(aq)+\ce{H2O}(l)⇌\ce{H3O+}(aq)+\ce{CH3CO2-}(aq) \]
The equilibrium constant for CH 3 CO 2 H is not given, so we look it up in Table E1: K a = 1.8 × 10 −5 . With [CH 3 CO 2 H] = \(\ce{[CH3CO2- ]}\) = 0.10 M and [H 3 O + ] = ~0 M , the reaction shifts to the right to form H 3 O + .
-
Determine
x
and equilibrium concentrations
. A table of changes and concentrations follows:
-
Solve for x and the equilibrium concentrations.
We find:
\[x=1.8×10^{−5}\:M\]
-
Determine the direction of change.
The equilibrium in a mixture of H
3
O
+
, \(\ce{CH3CO2-}\), and CH
3
CO
2
H is:
\[\ce{[H3O+]}=0+x=1.8×10^{−5}\:M\]
Thus:\[=4.74\]
4. Check the work . If we calculate all calculated equilibrium concentrations, we find that the equilibrium value of the reaction coefficient, Q = K a .
(b) Calculate the pH after 1.0 mL of 0.10 M NaOH is added to 100 mL of this buffer, giving a solution with a volume of 101 mL.
First, we calculate the concentrations of an intermediate mixture resulting from the complete reaction between the acid in the buffer and the added base. Then we determine the concentrations of the mixture at the new equilibrium:
-
Determine the moles of NaOH.
One milliliter (0.0010 L) of 0.10
M
NaOH contains:
\[\mathrm{0.0010\cancel{L}×\left(\dfrac{0.10\:mol\: NaOH}{1\cancel{L}}\right)=1.0×10^{−4}\:mol\: NaOH} \]
-
Determine the moles of CH
3
CO
2
H.
Before reaction, 0.100 L of the buffer solution contains:
\[\mathrm{0.100\cancel{L}×\left(\dfrac{0.100\:mol\:CH_3CO_2H}{1\cancel{L}}\right)=1.00×10^{−2}\:mol\:CH_3CO_2H} \]
-
Solve for the amount of NaCH
3
CO
2
produced.
The 1.0 × 10
−4
mol of NaOH neutralizes 1.0 × 10
−4
mol of CH
3
CO
2
H, leaving:
and producing 1.0 × 10 −4 mol of NaCH 3 CO 2 . This makes a total of:
\[\mathrm{(1.0×10^{−2})−(0.01×10^{−2})=0.99×10^{−2}\:mol\:CH_3CO_2H} \]
[\mathrm{(1.0×10^{−2})+(0.01×10^{−2})=1.01×10^{−2}\:mol\:NaCH_3CO_2} \]
4. Find the molarity of the products. After reaction, CH 3 CO 2 H and NaCH 3 CO 2 are contained in 101 mL of the intermediate solution, so:
\[\ce{[NaCH3CO2]}=\mathrm{\dfrac{1.01×10^{−2}\:mol}{0.101\:L}}=0.100\:M \]
Now we calculate the pH after the intermediate solution, which is 0.098 M in CH 3 CO 2 H and 0.100 M in NaCH 3 CO 2 , comes to equilibrium. The calculation is very similar to that in part (a) of this example:
This series of calculations gives a pH = 4.75. Thus the addition of the base barely changes the pH of the solution.
(c) This 1.8 × 10 −5 - M solution of HCl has the same hydronium ion concentration as the 0.10- M solution of acetic acid-sodium acetate buffer described in part (a) of this example. The solution contains:
As shown in part (b), 1 mL of 0.10 M NaOH contains 1.0 × 10 −4 mol of NaOH. When the NaOH and HCl solutions are mixed, the HCl is the limiting reagent in the reaction. All of the HCl reacts, and the amount of NaOH that remains is:
The concentration of NaOH is:
The pOH of this solution is:
The pH is:
The pH changes from 4.74 to 10.99 in this unbuffered solution. This compares to the change of 4.74 to 4.75 that occurred when the same amount of NaOH was added to the buffered solution described in part (b).
Exercise \(\PageIndex{1}\)
Show that adding 1.0 mL of 0.10 M HCl changes the pH of 100 mL of a 1.8 × 10 −5 M HCl solution from 4.74 to 3.00.
- Answer
-
Initial pH of 1.8 × 10 −5 M HCl; pH = −log[H 3 O + ] = −log[1.8 × 10 −5 ] = 4.74
Moles of H 3 O + added by addition of 1.0 mL of 0.10 M HCl: 0.10 moles/L × 0.0010 L = 1.0 × 10 −4 moles; final pH after addition of 1.0 mL of 0.10 M HCl:
\[\mathrm{pH=−log[H_3O^+]=−log\left(\dfrac{total\: moles\:H_3O^+}{total\: volume}\right)=−log\left(\dfrac{1.0×10^{−4}\:mol+1.8×10^{−6}\:mol}{101\:mL\left(\dfrac{1\:L}{1000\:mL}\right)}\right)=3.00} \]
The Henderson-Hasselbalch Approximation
We have seen in Example \(\PageIndex{1}\) how the pH of a buffer may be calculated using the ICE table method. The method requires knowing the concentrations of the conjugate acid-base pair and the \(K_a\) or \(K_b\) of the weak acid or weak base. However, there is a simpler method using the same information in a convenient formula, based on a rearrangement of the equilibrium equation for the dissociation of a weak acid.
The simplified ionization reaction of any weak acid is \(HA \leftrightharpoons H^+ + A^−\), for which the equilibrium constant expression is as follows:
This equation can be rearranged as follows:
\[[H^+]=K_a\dfrac{[HA]}{[A^−]} \label{Eq6}\]
Taking the logarithm of both sides and multiplying both sides by −1,
\[ \begin{align} −\log[H^+] &=−\log K_a−\log\left(\dfrac{[HA]}{[A^−]}\right) \\[4pt] &=−\log{K_a}+\log\left(\dfrac{[A^−]}{[HA]}\right) \label{Eq7} \end{align}\]
Replacing the negative logarithms in Equation \(\ref{Eq7}\) to obtain pH, we get,
\[pH=pK_a+\log \left( \dfrac{[A^−]}{[HA]} \right) \label{Eq8}\]
or, more generally,
\[pH=pK_a+\log\left(\dfrac{[base]}{[acid]}\right) \label{Eq9}\]
Equation \(\ref{Eq8}\) and Equation \(\ref{Eq9}\) are both forms of the Henderson-Hasselbalch approximation , named after the two early 20th-century chemists who first noticed that this rearranged version of the equilibrium constant expression provides an easy way to calculate the pH of a buffer solution. In general, the validity of the Henderson-Hasselbalch approximation may be limited to solutions whose concentrations are at least 100 times greater than their \(K_a\) values (the "x is small" assumption).
There are three special cases where the Henderson-Hasselbalch approximation is easily interpreted without the need for calculations:
- \([base] = [acid]\): Under these conditions, \[\dfrac{[base]}{[acid]} = 1\] in Equation \(\ref{Eq9}\). Because \(\log 1 = 0\), \[pH = pK_a\] regardless of the actual concentrations of the acid and base.
- \([base]/[acid] = 10\): In Equation \(\ref{Eq9}\), because \(\log 10 = 1\), \[pH = pK_a + 1.\]
- \([base]/[acid] = 100\): In Equation \(\ref{Eq9}\), because \(\log 100 = 2\), \[pH = pK_a + 2.\]
Each time we increase the [base]/[acid] ratio by 10, the pH of the solution increases by 1 pH unit. Conversely, if the [base]/[acid] ratio is 0.1, then pH = \(pK_a\) − 1. Each additional factor-of-10 decrease in the [base]/[acid] ratio causes the pH to decrease by 1 pH unit.
If [base] = [acid] for a buffer, then pH = \(pK_a\). Changing the ratio by a factor of 10 changes the pH by ±1 unit.
Example \(\PageIndex{2}\)
What is the pH of a solution that contains
- 0.135 M \(HCO_2H\) and 0.215 M \(HCO_2Na\)? (The \(pK_a\) of formic acid is 3.75.)
- 0.0135 M \(HCO_2H\) and 0.0215 M \(HCO_2Na\)?
- 0.119 M pyridine and 0.234 M pyridine hydrochloride? (The \(pK_b\) of pyridine is 8.77.)
Given : concentration of acid, conjugate base, and \(pK_a\); concentration of base, conjugate acid, and \(pK_b\)
Asked for : pH
Strategy :
Substitute values into either form of the Henderson-Hasselbalch approximation (Equation \(\ref{Eq8}\) or Equation \(\ref{Eq9}\)) to calculate the pH.
Solution :
According to the Henderson-Hasselbalch approximation (Equation \(\ref{Eq8}\)), the pH of a solution that contains both a weak acid and its conjugate base is
\[pH = pK_a + \log([A−]/[HA]).\]
A
Inserting the given values into the equation,
\[\begin{align*} pH &=3.75+\log\left(\dfrac{0.215}{0.135}\right) \\[4pt] &=3.75+\log 1.593 \\[4pt] &=3.95 \end{align*}\]
This result makes sense because the \([A^−]/[HA]\) ratio is between 1 and 10, so the pH of the buffer must be between the \(pK_a\) (3.75) and \(pK_a + 1\), or 4.75.
B
This is identical to part (a), except for the concentrations of the acid and the conjugate base, which are 10 times lower. Inserting the concentrations into the Henderson-Hasselbalch approximation,
\[\begin{align*} pH &=3.75+\log\left(\dfrac{0.0215}{0.0135}\right) \\[4pt] &=3.75+\log 1.593 \\[4pt] &=3.95 \end{align*}\]
This result is identical to the result in part (a), which emphasizes the point that the pH of a buffer depends only on the ratio of the concentrations of the conjugate base and the acid, not on the magnitude of the concentrations. Because the [A − ]/[HA] ratio is the same as in part (a), the pH of the buffer must also be the same (3.95).
C
In this case, we have a weak base, pyridine (Py), and its conjugate acid, the pyridinium ion (\(HPy^+\)). We will therefore use Equation \(\ref{Eq9}\), the more general form of the Henderson-Hasselbalch approximation, in which “base” and “acid” refer to the appropriate species of the conjugate acid–base pair. We are given [base] = [Py] = 0.119 M and \([acid] = [HPy^{+}] = 0.234\, M\). We also are given \(pK_b = 8.77\) for pyridine, but we need \(pK_a\) for the pyridinium ion. Recall that the \(pK_b\) of a weak base and the \(pK_a\) of its conjugate acid are related:
\[pK_a + pK_b = pK_w.\]
Thus \(pK_a\) for the pyridinium ion is \(pK_w − pK_b = 14.00 − 8.77 = 5.23\). Substituting this \(pK_a\) value into the Henderson-Hasselbalch approximation,
\[\begin{align*} pH=pK_a+\log \left(\dfrac{[base]}{[acid]}\right) \\[4pt] &=5.23+\log\left(\dfrac{0.119}{0.234}\right) \\[4pt] & =5.23 −0.294 \\[4pt] &=4.94 \end{align*}\]
Once again, this result makes sense: the \([B]/[BH^+]\) ratio is about 1/2, which is between 1 and 0.1, so the final pH must be between the \(pK_a\) (5.23) and \(pK_a − 1\), or 4.23.
Exercise \(\PageIndex{2}\)
What is the pH of a solution that contains
- 0.333 M benzoic acid and 0.252 M sodium benzoate?
- 0.050 M trimethylamine and 0.066 M trimethylamine hydrochloride?
The \(pK_a\) of benzoic acid is 4.20, and the \(pK_b\) of trimethylamine is also 4.20.
- Answer a
-
4.08
- Answer b
-
9.68
The Henderson-Hasselbalch approximation ((Equation \(\ref{Eq8}\)) can also be used to calculate the pH of a buffer solution after adding a given amount of strong acid or strong base, as demonstrated in Example \(\PageIndex{3}\).
Example \(\PageIndex{3}\)
The buffer solution in Example \(\PageIndex{2}\) contained 0.135 M \(HCO_2H\) and 0.215 M \(HCO_2Na\) and had a pH of 3.95.
- What is the final pH if 5.00 mL of 1.00 M \(HCl\) are added to 100 mL of this solution?
- What is the final pH if 5.00 mL of 1.00 M \(NaOH\) are added?
Given : composition and pH of buffer; concentration and volume of added acid or base
Asked for : final pH
Strategy:
- Calculate the amounts of formic acid and formate present in the buffer solution. Then calculate the amount of acid or base added.
- Construct a table showing the amounts of all species after the neutralization reaction. Use the final volume of the solution to calculate the concentrations of all species. Finally, substitute the appropriate values into the Henderson-Hasselbalch approximation (Equation \(\ref{Eq9}\)) to obtain the pH.
Solution :
The added \(HCl\) (a strong acid) or \(NaOH\) (a strong base) will react completely with formate (a weak base) or formic acid (a weak acid), respectively, to give formic acid or formate and water. We must therefore calculate the amounts of formic acid and formate present after the neutralization reaction.
A We begin by calculating the millimoles of formic acid and formate present in 100 mL of the initial pH 3.95 buffer:
The millimoles of \(H^+\) in 5.00 mL of 1.00 M HCl is as follows:
B Next, we construct an ICE table:
\[HCO^{2−} (aq) + H^+ (aq) \rightarrow HCO_2H (aq) \]
| \(HCO^{2−} (aq) \) | \(H^+ (aq) \) | \(HCO_2H (aq) \) | |
|---|---|---|---|
| Initial | 21.5 mmol | 5.00 mmol | 13.5 mmol |
| Change | −5.00 mmol | −5.00 mmol | +5.00 mmol |
| Equilibrium | 16.5 mmol | ∼0 mmol | 18.5 mmol |
The final amount of \(H^+\) in solution is given as “∼0 mmol.” For the purposes of the stoichiometry calculation, this is essentially true, but remember that the point of the problem is to calculate the final \([H^+]\) and thus the pH. We now have all the information we need to calculate the pH. We can use either the lengthy procedure of Example \(\PageIndex{1}\) or the Henderson–Hasselbach approximation. The latter approach is much simpler. The Henderson-Hasselbalch approximation requires the concentrations of \(HCO_2^−\) and \(HCO_2H\), which can be calculated using the number of millimoles (\(n\)) of each and the total volume (\(VT\)). Substituting these values into the Henderson-Hasselbalch approximation,
\[pH=pK_a+\log \left( \dfrac{[HCO_2^−]}{[HCO_2H]} \right)=pK_a+\log\left(\dfrac{n_{HCO_2^−}/V_f}{n_{HCO_2H}/V_f}\right)=pK_a+\log \left(\dfrac{n_{HCO_2^−}}{n_{HCO_2H}}\right)\]
Because the total volume appears in both the numerator and denominator, it cancels. We therefore need to use only the ratio of the number of millimoles of the conjugate base to the number of millimoles of the weak acid. So
\[pH=pK_a+\log\left(\dfrac{n_{HCO_2^−}}{n_{HCO_2H}}\right)=3.75+\log\left(\dfrac{16.5\; mmol}{18.5\; mmol}\right)=3.75 −0.050=3.70\]
Once again, this result makes sense on two levels. First, the addition of \(HCl \)has decreased the pH from 3.95, as expected. Second, the ratio of \(HCO_2^−\) to \(HCO_2H\) is slightly less than 1, so the pH should be between the \(pK_a\) and \(pK_a\) − 1.
A The procedure for solving this part of the problem is exactly the same as that used in part (a). We have already calculated the numbers of millimoles of formic acid and formate in 100 mL of the initial pH 3.95 buffer: 13.5 mmol of \(HCO_2H\) and 21.5 mmol of \(HCO_2^−\). The number of millimoles of \(OH^-\) in 5.00 mL of 1.00 M \(NaOH\) is as follows:
B With this information, we can construct an ICE table.
\[HCO_2H (aq) + OH^− (aq) \rightarrow HCO^−_2 (aq) + H_2O (l) \]
| \(HCO_2H (aq) \) | \(OH^−\) | \(HCO^−_2 (aq) \) | |
|---|---|---|---|
| Initial | 13.5 mmol | 5.00 mmol | 21.5 mmol |
| Change | −5.00 mmol | −5.00 mmol | +5.00 mmol |
| Equilibrium | 8.5 mmol | ∼0 mmol | 26.5 mmol |
The final amount of \(OH^-\) in solution is not actually zero; this is only approximately true based on the stoichiometric calculation. We can calculate the final pH by inserting the numbers of millimoles of both \(HCO_2^−\) and \(HCO_2H\) into the simplified Henderson-Hasselbalch expression used in part (a) because the volume cancels:
\[pH=pK_a+\log \left(\dfrac{n_{HCO_2^−}}{n_{HCO_2H}}\right)=3.75+\log \left(\dfrac{26.5\; mmol}{8.5\; mmol} \right)=3.75+0.494=4.24\]
Once again, this result makes chemical sense: the pH has increased, as would be expected after adding a strong base, and the final pH is between the \(pK_a\) and \(pK_a\) + 1, as expected for a solution with a \(HCO_2^−/HCO_2H\) ratio between 1 and 10.
Exercise \(\PageIndex{3}\)
The buffer solution from Example \(\PageIndex{2}\) contained 0.119 M pyridine and 0.234 M pyridine hydrochloride and had a pH of 4.94.
- What is the final pH if 12.0 mL of 1.5 M \(NaOH\) are added to 250 mL of this solution?
- What is the final pH if 12.0 mL of 1.5 M \(HCl\) are added?
- Answer a
-
5.30
- Answer b
-
4.42
Note
Either concentrations OR amounts (in moles or millimoles) of the acidic and basic components of a buffer may be used in the Henderson-Hasselbalch approximation, because the volume cancels out in the ratio of [base]/[acid].
The results obtained in Example \(\PageIndex{3}\) and its corresponding exercise demonstrate how little the pH of a well-chosen buffer solution changes despite the addition of a significant quantity of strong acid or strong base. Suppose we had added the same amount of \(HCl\) or \(NaOH\) solution to 100 mL of an unbuffered solution at pH 3.95 (corresponding to \(1.1 \times 10^{−4}\) M HCl). In this case, adding 5.00 mL of 1.00 M \(HCl\) would lower the final pH to 1.32 instead of 3.70, whereas adding 5.00 mL of 1.00 M \(NaOH\) would raise the final pH to 12.68 rather than 4.24. (Try verifying these values by doing the calculations yourself.) Thus the presence of a buffer significantly increases the ability of a solution to maintain an almost constant pH.
Medicine: The Buffer System in Blood
The normal pH of human blood is about 7.4. The carbonate buffer system in the blood uses the following equilibrium reaction:
\[\ce{CO2}(g)+\ce{2H2O}(l)⇌\ce{H2CO3}(aq)⇌\ce{HCO3-}(aq)+\ce{H3O+}(aq)\]
The concentration of carbonic acid, H 2 CO 3 is approximately 0.0012 M , and the concentration of the hydrogen carbonate ion, \(\ce{HCO3-}\), is around 0.024 M . Using the Henderson-Hasselbalch equation and the p K a of carbonic acid at body temperature, we can calculate the pH of blood:
\[\mathrm{pH=p\mathit{K}_a+\log\dfrac{[base]}{[acid]}=6.1+\log\dfrac{0.024}{0.0012}=7.4}\]
The fact that the H 2 CO 3 concentration is significantly lower than that of the \(\ce{HCO3-}\) ion may seem unusual, but this imbalance is due to the fact that most of the by-products of our metabolism that enter our bloodstream are acidic. Therefore, there must be a larger proportion of base than acid, so that the capacity of the buffer will not be exceeded.
Lactic acid is produced in our muscles when we exercise. As the lactic acid enters the bloodstream, it is neutralized by the \(\ce{HCO3-}\) ion, producing H 2 CO 3 . An enzyme then accelerates the breakdown of the excess carbonic acid to carbon dioxide and water, which can be eliminated by breathing. In fact, in addition to the regulating effects of the carbonate buffering system on the pH of blood, the body uses breathing to regulate blood pH. If the pH of the blood decreases too far, an increase in breathing removes CO 2 from the blood through the lungs driving the equilibrium reaction such that [H 3 O + ] is lowered. If the blood is too alkaline, a lower breath rate increases CO 2 concentration in the blood, driving the equilibrium reaction the other way, increasing [H + ] and restoring an appropriate pH.
Summary
A solution containing a mixture of an acid and its conjugate base, or of a base and its conjugate acid, is called a buffer solution. Unlike in the case of an acid, base, or salt solution, the hydronium ion concentration of a buffer solution does not change greatly when a small amount of acid or base is added to the buffer solution. The base (or acid) in the buffer reacts with the added acid (or base).
Key Equations
- p K a = −log K a
- p K b = −log K b
- \(\mathrm{pH=p\mathit{K}_a+\log\dfrac{[A^- ]}{[HA]}}\)
Glossary
- buffer
- mixture of a weak acid or a weak base and the salt of its conjugate; the pH of a buffer resists change when small amounts of acid or base are added
- Henderson-Hasselbalch equation
- equation used to calculate the pH of buffer solutions
Contributors
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


3.7: Patient Transfers
Transfers are defined as moving a patient from one flat surface to another, such as from a bed to a stretcher (Perry et al., 2014). Types of hospital transfers include bed to stretcher, bed to wheelchair, wheelchair to chair, and wheelchair to toilet, and vice versa.
Patient Transfer from Bed to Stretcher
A bed to stretcher transfer requires a minimum of three to four people, depending on the size of the patient and the size and strength of the health care providers. Patients who require this type of transfer are generally immobile or acutely ill and may be unable to assist with the transfer. Checklist 29 shows the steps for moving patients laterally from one surface to another.
Checklist 29: Moving a Patient from Bed to StretcherDisclaimer: Always review and follow your hospital policy regarding this specific skill. |
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Safety considerations:
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Steps |
Additional Information |
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1. Always predetermine the number of staff required to safely transfer a patient horizontally. |
Three to four health care providers are required for the transfer. | ||
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2. Explain what will happen and how the patient can help (tuck chin in, keep hands on chest). Collect supplies. |
This step provides the patient with an opportunity to ask questions and help with the transfer. |
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3. Raise bed to safe working height. Lower head of bed and side rails. Position the patient closest to the side of the bed where the stretcher will be placed. |
Safe working height is at waist level for the shortest health care provider.
The patient must be positioned correctly prior to the transfer to avoid straining and reaching. May need additional health care providers to move patient to the side of the bed. |
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4. Roll patient over and place slider board halfway under the patient, forming a bridge between the bed and the stretcher. Place sheet on top of the slider board. The sheet is used to slide patient over to the stretcher. The patient is returned to the supine position. Patient’s feet are positioned on the slider board. |
The slider board must be positioned as a bridge between both surfaces.
The sheet must be between the patient and the slider board to decrease friction between patient and board. Ensure all tubes and attachments are out of the way. |
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5. Position stretcher beside the bed on the side closest to the patient, with stretcher slightly lower. Apply brakes. Two health care providers climb onto the stretcher and grasp the sheet. The lead person is at the head of the bed and will grasp the pillow and sheet. The other health care provider is positioned on the far side of the bed, between the chest and hips of the patient, and will grasp the sheet with palms facing up. The two caregivers on the stretcher grasp the draw sheet using a palms up technique, sitting up tall, and keeping their elbows close to their body and backs straight. |
The position of the health care providers keeps the heaviest part of the patient near the health care providers’ centre of gravity for stability. | ||
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6. The caregiver on the other side of the bed places his or her hands under the patient’s hip and shoulder area with forearms resting on bed. |
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7. The designated leader will count 1, 2, 3, and start the move. The person on the far side of the bed will push patient just to arm’s length using a back-to-front weight shift. At the same time, the two caregivers on the stretcher will move from a sitting-up-tall position to sitting on their heels, shifting their weight from the front leg to the back, bringing the patient with them using the sheet. |
Coordinating the move between health care providers prevents injury while transferring patients.
Using a weight shift from front to back uses the legs to minimize effort when moving a patient. |
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8. The two caregivers will climb off the stretcher and stand at the side and grasp the sheet, keeping elbows tucked in. One of the two caregivers should be in line with the patient’s shoulders and the other should be at the hip area. On the count of three, with back straight and knees bent, the two caregivers use a front-to-back weight shift and slide the patient into the middle of the bed. |
The step allows the patient to be properly positioned in the bed and prevents back injury to health care providers. |
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9. At the same time, the caregiver on the other side slides the slider board out from under the patient. |
This step allows the patient to lie flat on the bed. | ||
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10. Replace pillow under head, ensure patient is comfortable, and cover the patient with sheets. |
This promotes comfort and prevents harm to patient. | ||
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11. Lower bed and lock brakes, raise side rails as required, and ensure call bell is within reach. Perform hand hygiene. |
Placing bed and side rails in a safe position reduces the likelihood of injury to patient. Proper placement of call bell facilitates patient’s ability to ask for assistance.
Hand hygiene reduces the spread of microorganisms. |
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| Data source: ATI, 2015c; Perry et al., 2014; PHSA, 2010 |
Transfer from Bed to Wheelchair
Patients often need assistance when moving from a bed to a wheelchair. A patient must be cooperative and predictable, able to bear weight on both legs and take small steps. If any of these criteria are not met, a two-person transfer or mechanical lift is recommended. Always complete a patient risk assessment prior to all patient-handling activities. See Checklist 30 for the steps to transfer a patient from the bed to the wheelchair (PHSA, 2010).
Checklist 30: Bed to Wheelchair TransferDisclaimer: Always review and follow your hospital policy regarding this specific skill. |
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Safety considerations:
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Steps |
Additional Information |
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1. One health care provider is required. |
The patient should be assessed as a 1-person assist. | ||
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2. Perform hand hygiene. Explain what will happen during the transfer and how the patient can help. Apply proper footwear prior to ambulation |
This step provides the patient with an opportunity to ask questions and help with the positioning. |
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3. Lower the bed and ensure that brakes are applied. Place the wheelchair next to the bed at a 45-degree angle and apply brakes. If a patient has weakness on one side, place the wheelchair on the strong side. |
Ensure brakes are applied on the wheelchair. | ||
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4. Sit patient on the side of the bed with his or her feet on the floor. Apply the gait belt snugly around the waist (if required). Place hands on waist to assist into a standing position |
The patient’s feet should be in between the health care provider’s feet. |
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5. As the patient leans forward, grasp the gait belt (if required) on the side the patient, with your arms outside the patient’s arms. Position your legs on the outside of the patient’s legs. The patient’s feet should be flat on the floor. |
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6. Count to three and, using a rocking motion, help the patient stand by shifting weight from the front foot to the back foot, keeping elbows in and back straight. |
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7. Once standing, have the patient take a few steps back until they can feel the wheelchair on the back of their legs. Have patient grasp the arm of the wheelchair and lean forward slightly. |
Ensure the patient can feel the wheelchair on the back of the legs prior to sitting down. | ||
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8. As the patient sits down, shift your weight from back to front with bent knees, with trunk straight and elbows slightly bent. Allow patient to sit in wheelchair slowly, using armrests for support. |
This allows the patient to be properly positioned in the chair and prevents back injury to health care providers. |
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| Data source: ATI, 2015b; Perry et al., 2014; PHSA, 2010 |
Special considerations:
- Do not allow patients to place their arms around your neck. Have them place their arms around your hips.
- Avoid lifting patients. Let them stand using their own strength.
- Stay close to your patient during the transfer to keep the patient’s weight close to your centre of gravity
- If the patient has weakness on one side of the body (e.g., due to a cerebral vascular accident — CVA — or stroke), place the wheelchair on the strong side.
Critical Thinking Exercises
- Prior to moving the patient, where should the patient’s feet be placed?
- As you start to stand your patient, the patient gently places his arms around your neck. How do you proceed?


8.1.1: Education and the Global Perspective
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Education and the Global Perspective
In today’s world, some degree of education is necessary for people in most countries.
Learning Objectives
Discuss recent worldwide trends in education, including mass schooling, the emergence of secondary education in the U.S., indigenous education, higher education, and online learning
Key Points
- Education is the means through which the aims and habits of a group of people are passed from one generation to the next.
- Location contributes to a child’s lack of access to primary education. In certain areas of the world, children have difficulty getting to school.
- Gender often factors into a child’s access to education.
- Costs contribute to a child’s lack of access to primary education. High opportunity costs are often influential in the decision to attend school.
- Mass schooling has perpetuated the idea that everyone has a right to be educated regardless of his/her cultural background and gender.
- A lack of access to education is one of the primary barriers to human development.
Key Terms
- Mass Schooling : The phenomenon that describes the rise in school attendance worldwide.
- Internationalization of Education : The increased emphasis on international cultural exchange in the course of education.
Education Today
In today’s world, some degree of education is necessary for people in most countries. Due to population growth and the proliferation of compulsory education, UNESCO has calculated that in the next 30 years, more people will receive formal education than in any prior period of human history. In fact, illiteracy and the percentage of populations without any schooling have already decreased, from 36% in 1960 to 25% in 2000.
Education in its broadest, most general sense is a means through which the aims and habits of a group of people is passed from one generation to the next. Generally, education results from any experience that affects the way in which one thinks, feels, or acts. In its narrowest, most technical sense, education is the formal process (e.g., instruction in schools) by which society deliberately passes accumulated knowledge, skills, customs, and values from one generation to the next.
Education in the Developing World
India is developing technologies that bypass land-based telephone and internet lines. The country recently launched EDUSAT, an education satellite that can reach a great number of people at a significantly reduced cost. Another initiative, started by the OLPC foundation, involving a group from the MIT Media Lab, and supported by several major corporations, has developed a $100 laptop for the delivery of educational programs. As of 2008, the laptops were already widely available.
In Africa, the New Partnership for Africa’s Development (NEPAD) has launched an e-school program. The goal is to provide 600,000 primary and high schools with computer equipment, learning materials, and internet access within 10 years. Private groups, like Church of Jesus Christ of Latter-day Saints, are also working to improve access to education through such programs as the Perpetual Education Fund.
Internationalization ( Globalization and Education)
Education is becoming increasingly international, and mass schooling has promoted the fundamental idea that everyone has a right to be educated regardless of his/her cultural background. In Europe, for example, the Socrates-Erasmus Program fosters exchanges between European universities, while the Soros Foundation provides educational opportunities to students from central Asia and eastern Europe. Programs such as the International Baccalaureate have also contributed to the internationalization of education. Some scholars argue that, regardless of the perceived quality of different educational systems, experiencing a different system of education can be an important and enriching aspect of an international learning experience. Meanwhile, the global online campus, led by American universities, has promoted free access to class materials and lectures recorded during actual classes. This project further facilitates the globalization of education.
Recent Worldwide Trends
The emergence of secondary education in the United States did not occur until 1910, when a rise in big business and technological advances in factories (for instance, the emergence of electrification) required skilled workers. In order to meet new job requirements, high schools were created with curriculums focused on practical job skills that would prepare students for white- or blue-collar work. This emerging system proved to be beneficial for both the employer and the employee; improved job skills increased efficiency and lowered costs for employers, while skilled employees received higher wages.
Indigenous education refers to the inclusion of indigenous knowledge, models, methods, and content within formal and non-formal educational systems. Often in a post-colonial context, the growing recognition and use of indigenous education methods has been a response to the erosion and loss of indigenous knowledge and language through earlier processes of colonialism. It has also enabled indigenous communities to strengthen links to their traditional languages and cultures, a process that has also been linked to increased academic success.
Higher education generally involves work towards a degree-level or foundation degree qualification. In most developed countries, a high proportion of the population (up to 50%) now obtain higher education at some point in their lives. Higher education is therefore important to national economies as both a significant industry in its own right and a source of trained and educated personnel.
As a result of the Internet, higher education is increasingly open and accessible. Online learning gives students flexibility and choice in terms of what, when, and at what pace they learn. Many universities and organizations are creating open educational resources that self-motivated students can access anywhere and at any time. Unlike traditional forms of higher education, open, online education generally does not take the form of recognized degree programs.
Education and Industrialization
It has been argued that high rates of education are essential for countries to be able to achieve high levels of economic growth.
Learning Objectives
Define education economics, human capital, human capital flight, and educational technology
Key Points
- In the developing world, there is economic pressure from those parents who prioritize sending their children to work to make money in the short term over any long-term benefits of education.
- Education economics is the study of economic issues relating to education, including the demand for education and the financing and provision of education.
- The central idea of human capital is that undertaking education is investment in the acquisition of skills and knowledge which will increase earnings.
- Human capital flight, more commonly referred to as the ” brain drain,” is the large-scale emigration of a large group of individuals with technical skills or knowledge.
- Educational technology is the study and ethical practice of facilitating learning and improving performance by creating, using, and managing appropriate technological processes and resources.
Key Terms
- human capital : The stock of competencies, knowledge, social, and personality attributes, including creativity, embodied in the ability to perform labor so as to produce economic value.
- brain drain : The migration of educated or talented people from less- economically advanced areas to more economically advanced areas, especially to large cities or richer countries.
- Education Economics : The study of economic issues relating to education, including the demand for education and the financing and provision of education.
In developing countries, the number and seriousness of the problems faced is naturally greater. People are sometimes unaware of the importance of education, and there is economic pressure from those parents who prioritize their children’s making money in the short term over any long-term benefits of education. Recent studies on child labor and poverty have suggested, however, that when poor families reach a certain economic threshold where families are able to provide for their basic needs, parents return their children to school. This has been found to be true, once the threshold has been breached, even if the potential economic value of the children’s work has increased since their return to school.
Education and Economic Growth
It has been argued that high rates of education are essential for countries to be able to achieve high levels of economic growth. Empirical analyses tend to support the theoretical prediction that poor countries should grow faster than rich countries because they can adopt cutting edge technologies already tried and tested by rich countries. Education economics is the study of economic issues relating to education, including the demand for education and the financing and provision of education. The dominant model of the demand for education is based on human capital theory. The central idea is that undertaking education is investment in the acquisition of skills and knowledge, which will increase earnings or provide long-term benefits, such as an appreciation of literature. An increase in human capital can follow technological progress as knowledgeable employees are in demand due to the need for their skills, whether it be in understanding the production process or in operating machines. Human capital flight, more commonly referred to as the “brain drain,” is the large-scale emigration of a large group of individuals with technical skills or knowledge. The reasons usually include two aspects which respectively come from countries and individuals. The brain drain is often associated with de-skilling of emigrants in their country of destination, while their country of emigration experiences the draining of skilled individuals.
Educational Technology
Educational technology is the study and ethical practice of facilitating learning and improving performance by creating, using, and managing appropriate technological processes and resources. Technology of education is most simply and comfortably defined as an array of tools that might prove helpful in advancing student learning and may be measured in how and why individuals behave. There are various types of technologies currently used in traditional classrooms. Among these are computers in the classroom; a website for every class; class blogs and wikis; wireless classroom microphones; and online media and interactive whiteboards.
Educational technology is intended to improve education over what it would be without technology. Its benefits include easy-to-access course materials; increased student motivation; improved student writing; subjects made easier to learn; and differentiated instruction.
Education and Liberty in the Developing World
A lack of access to education is one of the primary limits on human development.
Learning Objectives
Discuss the factors that impact education in societies worldwide
Key Points
- International development is a concept that refers to the development of greater quality of life for humanity.
- In 2000, the United Nations signed the United Nations Millennium Declaration, which includes eight Millennium Development Goals to be achieved by 2015 or 2020, one of which is Universal Primary Education.
- Location contributes to a child’s lack of access and attendance to primary education. In certain areas of the world, it is more difficult for children to get to school.
- Gender contributes to a child’s lack of access and attendance to education.
- Costs contribute to a child’s lack of access and attendance to primary education. High opportunity costs are often influential in the decision to attend school.
Key Terms
- Mass Schooling : The phenomenon that describes the rise in school attendance worldwide.
- Internationalization of Education : The increased emphasis on international cultural exchange in the course of education.
- Universal Primary Education : One of the eight Millennium Development Goals developed by the United Nations; An attempt to give all primary school aged children access to education.
International development is a concept that lacks a universally accepted definition, but it is most used in a holistic and multi-disciplinary context of human development–the development of greater quality of life for humans. In 2000, the United Nations signed the United Nations Millennium Declaration, which includes eight Millennium Development Goals to be achieved by 2015 or 2020. This represented the first time that a holistic strategy to meet the development needs of the world had been established, with measurable targets and defined indicators. Universal Primary Education is one of the eight Millennium Development Goals, and great improvements have been achieved in the past decade, yet a great deal remains to be done. The provision of education often focuses on providing free primary level education but also covers secondary and higher education. A lack of access to education is one of the primary limits on human development and is closely related to every one of the other sectors. Almost every development project includes an aspect of education, as development by its very nature requires a change in the way people live.
Universal Primary Education
There has been great progress achieved since 1999 in the achievement of the millennium development goal. UNESCO has found that the number of children enrolled in primary schools worldwide rose by more than 40 million between 1999 and 2007; the net primary enrollment in sub-Saharan Africa rose from 58% to 74% over the same period; and international aid commitments to basic education almost doubled from $2.1 billion in 2002 to $4.1 billion in 2007. However, despite all these important achievements, the world is currently not on course to achieve its target of universal primary education by 2015. Currently, there are more than 75 million children around the world of primary school age who are not in school. The majority of these children are in regions of sub-Saharan Africa and South Asia and within these countries, girls are at the greatest disadvantage in receiving access to education at the primary school age. Moreover, it is estimated that there is a $16.2 billion annual external financing gap between available domestic resources and what is needed to achieve the basic education goals in low income countries. This is due to current aid levels which address only 15% of that gap, resources often not provided to those countries who need it the most, and the amounts pledged not fully honored.
Factors Contributing to Lack of Access and Poor Attendance
Location contributes to a child’s lack of access and attendance to primary education. In certain areas of the world, it is more difficult for children to get to school. For example, in high-altitude areas of India, severe weather conditions for more than seven months of the year make school attendance erratic and force children to remain at home. Gender contributes to a child’s lack of access and attendance to education. Although it may not be as an obvious a problem today, gender equality in education has been an issue for a long time. Currently, there is a gender discrepancy in education. Enrollment is low for both boys and girls in sub-Saharan Africa, with rates of just 27% and 22%. Today, some 78% of girls drop out of school, compared with 48% of boys. Therefore, a child’s gender continues to contribute to access and attendance today.
Costs contribute to a child’s lack of access and attendance to primary education. High opportunity costs are often influential in the decision to attend school. For example, according to UNICEF, an estimated 121 million primary-school-age children are being kept out of school to work in the fields or at home. For many families in developing countries the economic benefits of no primary schooling are enough to offset the opportunity cost of attending.
Internationalization of Education
Education is becoming increasingly international. The most represented case is the spread of mass schooling. Mass schooling has implanted the fundamental concepts that everyone has a right to be educated regardless of his/her cultural background and gender differences. The system has also promoted the global rules and norms of how the school should operate and what is education. In Europe, for example, the Socrates-Erasmus Program stimulates exchanges across European universities. Also, the Soros Foundation provides many opportunities for students from Central Asia and Eastern Europe. Programs, such as the International Baccalaureate, have contributed to the internationalization of education. Some scholars argue that, regardless of whether one system is considered better or worse than another, experiencing a different way of education can often be considered to be the most important, enriching element of an international learning experience.
Contributors and Attributions
CC licensed content, Specific attribution


12.5: STI Prevention
Stigma will not stop the spread of STIs. Testing, treatment and education will.
- Condoms and other barriers, used consistently and correctly, for genital, anal and oral contact can help prevent the spread of STIs.
- Talk to partners about testing, Know the status of your partners.
- Sufficient lubrication for vaginal and anal penetration can help prevent cuts and tears that can allow infections to get in. Be generous when using lube and be sure the lubricant is compatible with condoms if you are using them.
- For HIV prevention, PrEP, PEP and U=U are other powerful tools.
For more on this watch: Planned Parenthood on Getting Tested
Public Hair: Consider Keeping it
Pubic hair provides some protection from STIs, especially those that are passed via skin-to-skin contact. With hair removal (shaving, waxing or tweezing) tiny wounds can be created that create a place for bacteria, parasites and viruses to enter. Also, the hair itself provides a protective layer against skin abrasions and injury that can come with friction during sexual activity. With hair removal, people sometimes end up with bumps and skin irritation they then mistake for an STI, so often it causes more stress than it’s worth. The only upside of pubic hair removal as far as STIs is that pubic lice are rarely seen these days as they have lost their bushy habitat.
Partner Notification
Notifying partners of a possible STI exposure is key in stopping transmission. Some public health departments will do anonymous partner notification as needed. This would usually be for HIV or syphilis. There are apps available to do anonymous notification. Partners should be treated as recommended by the CDC.
Expedited Partner Treament (EPT)
When someone tests positive for chlamydia and receives treatment, it is recommended that all partners be treated with antibiotics in order to prevent re-infection. Often, a medical provider can prescribe partner packs of antibiotics to a patient to give to their partner(s) as needed. This is known as expedited partner treatment . Unfortunately, this is not as easily done for gonorrhea and syphilis, since the preferred treatment for those infections includes an injection. In that case partners are advised to seek medical treatment at a clinic.
A Shameful Legacy of Racism in Medicine: The Tuskegee Study of Untreated Syphilis in the Negro Male
The Tuskegee experiment, first discussed in Chapter 2 serves as an important lesson on multiple fronts. In 1932, the Public Health Service (which later became the CDC) of the United States, along with the Tuskegee Institute, began a syphilis study in Macon County, Alabama. The participants included 600 Black men– 399 with syphilis and 201 without. The men were not told they had syphilis nor that the study had anything to do with syphilis. They were told they were being treated for “bad blood.”  Even when penicillin was discovered to be highly effective treatment for syphilis in the mid-1940s, the researchers did not offer it to subjects, nor were subjects given the choice to quit the study. They were kept off draft lists for World War II, since syphilis testing was done when one entered the armed forces, and the researchers did not want the men to find out they had syphilis and receive treatment. The researchers had decided they wanted to study the progression of the disease without treatment. They made it clear the idea was to follow the men until death so they could study the cadavers for disease progression.
Originally, the study was projected to last 6 months, yet it went on for 40 years, finally ending in 1972, when it was leaked to the press what was happening. There were several whistleblowers inside the CDC who attempted to stop the study for many years before that date, but the CDC chose to continue. By 1972, 28 of the patients had died directly from syphilis, 100 had died from complications related to syphilis. Forty of the patient’s wives had syphilis and 19 of their children had been born with congenital syphilis. This study was an incredible violation of ethical standards. The harm done to the men and their families was egregious. It has also left a legacy of mistrust between the Black community and U.S. public health. It wasn’t until 1997 that the United States gave a formal apology to the few men who had been in the study who were still alive at that time and to their families. There is a Memorial Legacy Museum at Tuskegee University.
The Voices for Our Fathers Legacy Foundation , President Lillie Tyson Head, pictured above (daughter of Freddie Lee Tyson) was started by the families of the men to preserve the legacies and history of the 623 men victimized in the United States Public Health Service Syphilis Study, foster social justice, education and public health.
Talk to partners about testing . If you’ve tested, that can be a conversation starter. You can say “I just did my routine STI testing. When was the last time you tested?” I talk to people sometimes who say “well, he says he doesn’t need to test” or “she looks clean” or “I don’t think I have anything.”
The only way to know for sure is to test . If you test negative, it doesn’t mean your partner is necessarily negative for everything. It’s possible to have an STI and not give it to someone right away. Asking someone to test is not about accusing them of something. It’s about being mature and responsible for your health and the health of your partner(s).
Consider throat and rectal swabs for chlamydia and gonorrhea when testing. They are often only offered to gay men or men having sex with men, but we all have throats and anuses. So, if you’ve given oral sex, ask for a throat swab and if you’ve received anal, ask for a rectal swab. Often you can do them yourself in the restroom at the testing lab.
Avoid language such as someone being “clean” when referring to someone who doesn’t have an STI. This implies that someone with an STI is dirty. This adds to stigma which ultimately makes people less likely to talk about STIs and to test. Instead, one could use the phrase “STI-free” as it is accurate and nonjudgmental.
If you’re having symptoms or a partner has told you they have an STI, and you are going for testing, let the medical provider know your reason for testing. If you have symptoms or have been exposed, they will likely prescribe you medicine right away, even before testing. It is still important to test, but this way you are not waiting for results to come back to get treatment, if needed.
One of the most challenging situations in dealing with STI testing is when there has been infidelity (often referred to as cheating) in a relationship. I talk to people on both sides of this issue. There can be lots of emotions involved from guilt, to shame to anger, resentment and sadness. I affirm that no matter the circumstances, testing is a good idea, for all parties involved. Even if the person who went outside the relationship says they are sure they didn’t get anything, I suggest that testing can be a way to start to rebuild trust in the relationship, if that is the goal.
Routine testing often includes HIV (if the person is HIV negative), syphilis, chlamydia and gonorrhea. If you have questions about herpes, HPV or other STIs, talk to a medical provider.
Just about every STI can be passed easily with oral sex, except HIV . It is highly unlikely that HIV could be passed that way, but chlamydia, gonorrhea, syphilis, HPV and herpes can all be passed with oral sex. Most people don’t use barriers for oral sex, but barriers are an option.


5.20: Introduction to Media and Your Message
What you’ll learn to do: Find the best media to present your message
I hear and I forget. I see and I understand. I do and I remember.
—Confucius
Confucius had the essence of business communication defined back in 500 BC.
Visual media improves a business communicator’s chances of being understood by presenting information with a unique combination of logic and creativity. In this section, we will learn what visual media resources are available to business communicators and how to choose those that will strengthen your messages. We will learn about basic visual design principles and the messages that these principles send to your audience.
Contributors and Attributions
- Introduction to Media and Your Message. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- Confucius Chinese philosopher. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:Konfuzius-1770.jpg . License : Public Domain: No Known Copyright


2.10: Vedic India to the Fall of the Maurya Empire
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Learning Objectives
By the end of this section, you will be able to:
- Explain the caste system and the way it functioned in Indian society
- Identify the main elements of Buddhism
- Describe India’s faith traditions: Brahmanism , Buddhism, and Hinduism
Few areas of the world are as important to our understanding of the emergence of human civilizations as India . Occupying an enormous subcontinent in South Asia, India has three distinct geographic zones: a northern area defined by the Himalayas that forms a natural barrier to the rest of the Asian mainland, the densely populated river valleys of the Indus and Ganges Rivers that lie to the south and northwest of that area, and lastly the tropical south, cut off from those valleys by many mountains and thick forests (Figure 5.20).
Early humans traveled into Asia in waves around sixty thousand to eighty thousand years ago, moving from Africa to the Arabian Peninsula into India and beyond, on routes that hugged the coast. Some of the earliest evidence of this migration was found at Jwalapuram, India. Here, hundreds of stone tools dating to 74,000 BCE were discovered that resemble those of roughly the same age found in Africa, Laos, and Australia. But the roots of India’s ancient civilizations lie in the north, amid the archaeological remains of two ancient cities, Harappa and Mohenjo-Daro .
Harappa and Mohenjo-Daro
Unlike ancient cultures in Mesopotamia (3500–3000 BCE), Egypt (3500–3000 BCE), and China (2200–2000 BCE), the Indus valley civilization shows little evidence of political power concentrated in the hands of hereditary monarchs. Yet its culture and technology spread, in an area running from parts of present-day Afghanistan into Pakistan and western India. There, early human communities capable of agriculture flourished near the fertile plains around the Indus River and other waters fed annually by the region’s monsoons.
Farmers harvested domesticated crops of peas, dates, and cotton, harnessing the power of draft animals such as the water buffalo. The archaeological record shows few traces of any kind of elaborate monumental architecture, burial mounds, or domination by warriors and kings. Instead, a common culture grew that was defined by urban planning, complete with advanced drainage systems, orderly streets, and distinctive bricks made in ovens. Equipped with those tools, the Indus River valley produced two of the ancient world’s most technologically advanced cities, Harappa and Mohenjo-Daro.  Dedicated artisans made jewelry and fabrics. All these aspects of the Indus valley culture left an imprint on later Indian civilizations.
How did a civilization with a high degree of labor specialization and the coordination necessary for irrigated agriculture and large urban centers manage such complexity without a powerful centralized state? There is no consensus answer, though the Indus valley civilization may have developed as a series of small republic-like states, dominated by religious specialists such as priests presiding over an intensely hierarchical class system. It does seem likely, however, that the environmental toll the civilization inflicted upon the surrounding areas led to its decline. Over time, irrigation replaced fertile soil with soil having greater quantities of salt, lowering crop yields. The use of wood as a fuel source, such as for making the oven-fired bricks, led to rapid deforestation and even greater soil erosion. It appears that most communities in and around Harappa and Mohenjo-Daro abandoned the sites around 1700 BCE, when they became unable to feed and supply themselves. Before their decline, however, the two cities housed perhaps as many as forty thousand residents each, most of whom lived in comparatively luxurious homes of more than one story that featured indoor plumbing and were laid out in an orderly pattern along grid-like streets. Public buildings such as bathhouses were quite large, as were the protective city walls and citadels.
The development of a written script , found on clay seals and pottery at the sites, likely made such feats possible. The written language of the Indus valley civilization featured more than four hundred symbols that functioned as pictures of ideas, words, and numbers. While many of the symbols have yet to be deciphered, one of the primary functions of writing appears to have been commerce because many finished goods were stamped with written seals. Writing used as a means of communication and recordkeeping probably also helped the Indus valley civilization profit from long-distance trade with Mesopotamia and Egypt.
Merchants from Sumer traveled to the Indus River valley to establish trade in luxury items such as lapis lazuli. In return, it appears that traders and merchants from cities such as Harappa took up residence in cities in Mesopotamia to facilitate exchange. In this way, Mesopotamia exerted a recognizable influence on India ’s art and culture. Scholars have identified aspects of Greek naturalist art in sculptures found in Harappa, combined with local preferences for representing human bodies in motion rather than adopting the Greek emphasis on anatomical correctness. Art from these early cities helped usher in artistic styles and motifs that created a continuous tradition ingrained within Indian culture. Stone seals with fantastic beasts and anthropomorphic deities were later associated with Indian traditions such as yoga and Hindu deities.
Significant archaeological evidence suggests that urban women in the Indus valley were influential figures who functioned as specialists in rituals. More figurines were found depicting female than male deities, and women were typically buried with female relatives—their mothers and grandmothers—and not with their husbands. This is not to suggest that all women were equals. The prevalence of contrasting hairstyles and clothing on many surviving figurines indicates that women were differentiated by a great number of class and ethnic markers.
Among the more intriguing clues to the way women fared in the Indus valley is a tiny artifact from Mohenjo-Daro called Dancing Girl , a bronze and copper figurine about 4.5 inches tall and dating from around 2500 BCE (Figure 5.21). Created by a method of casting bronze known as the “lost wax” method, the nude figure appears in a confident and relaxed pose, with her hair gathered in a bun. She may have represented a royal woman, a sacred priestess of a temple, or perhaps a lower-born tribal girl. That scholars can draw such a wide array of plausible conclusions speaks to the fact that the Indus valley likely had a very fluid class structure and a highly complex society.
The Aryans and Brahmanism
The Aryans entered the Indian subcontinent as conquerors beginning in 1800 BCE. With them came a new religion, Vedic , named for their hymns called Vedas. Vedas were sung in rituals to celebrate a pantheon of gods representing various aspects of nature and human life and were a useful way of teaching, given that the Aryans were illiterate. Gods such as Varuna ruled the sky, while Indra was the god of war. The Aryans offered ritualistic sacrifices to their gods and built enormous altars of fire, imposing a hierarchy on the people they conquered that emphasized strict observance of the law. The Vedas, along with poems and prayers, were first transmitted orally from one generation to the next; later they were recorded in the written language of Sanskrit . Over time, the Indian peoples added new dimensions to the Vedic religion, changing the nature of Aryan society as well. New gods such as Soma, associated with magical elixirs, storehouses for grain, and the moon, grew in importance as the practice of ritual became ever more meaningful.
A later series of treatises known as the Upanishads , written by a priestly class called Brahmans, developed new expressions of the Vedic religion, gradually transforming it into what many scholars refer to as Brahmanism . These new expressions include samsara and karma . Samsara was a view of humanity and the universe in which the soul left the body after death to be reborn. Karma represented the idea that all human actions, moral and immoral, were counted and weighed, ultimately governing whether a person was reborn higher on the spiritual ladder in the next life, perhaps as a king or priest, or—if ruined by immoral acts—as a lower life form, perhaps a detested reptile, to try again. The ultimate goal of a person’s earthly life was to achieve union with Brahman , the ultimate and universal reality. Even gods needed to perform good acts such as penance or meditation to transcend to a higher plane of existence. Belief in reincarnation supported the idea that a person’s status in the present life came about not by chance, but rather as a consequence of past lives. Thus the authority of elites such as the Brahmans was sanctified as reflecting the divine will of the cosmos.
In this way, the Vedic religion of the Aryans religion produced the varna , a strictly hierarchical society based on inherited status. At the highest level were the Brahmans, who exerted authority by virtue of their knowledge of the sacrificial rituals and their role as guardians of the poems, hymns, and later texts that carried on the Vedic traditions. Below them were aristocratic warriors, Kshatriya , members of noble families who fought in small but effective armies to protect their kingdoms and carry conquest into new areas. Members of the third class living in the upper half of society were merchants and Aryan commoners, Vaishya , who along with the other two enjoyed privileges based on the idea that in their late childhood they underwent a rebirth.
The fourth major group were the Shudras , non-Aryan servants and peasants who were denied the opportunity to read or listen to Vedic hymns and accounted for more than half the population. At the bottom of society were the Dalits , a class of “untouchables,” who were likely the descendants of the populations that lived in parts of south India before the arrival of the Aryans. They were effectively outside and hierarchically below the four-tiered caste system. Prohibitions against marrying Indians from another caste were just one element of a constellation of provisions designed to keep everyone locked in their inherited class from birth to death. Taxes on the lower classes ensured that wealth remained at the top. In truth, the Indian subcaste system was quite complex. Distinctions between groups within each caste mattered a great deal as well, creating sub-castes that came with separate privileges, obligations, and social circles that fixed where people lived and who they could marry.
The caste system reflected Hindu religious beliefs by ensuring that people performed their proper role in this life based on their actions in the past. The laws preventing upward mobility and protecting the privilege of elites were seen as guaranteeing order. They kept the low-born from escaping the divine plan and the cosmic justice that allowed for a slow, steady advancement up the spiritual scale over a series of lives. The ultimate goal was release from the wheel of life, the never-ending transmission of the soul to ultimate peace. Thus the arrival of Aryans and the gradual emergence of Brahmanism created a new social blueprint for India.
Buddhism
Indian culture, religion, and art were forever transformed with the life of Buddha Sakyamuni around 563 BCE.  He came to be called the Buddha, meaning “enlightened,” because his teachings offered an alternative to the then-dominant Brahmanist values.
Buddhism explores the depths of human suffering, desire, envy, decadence, and death, offering adherents a way out of an eternal cycle of misery if they adopt the Four Noble Truths leading to the Eightfold Path . The Four Noble Truths acknowledge that pain and disappointment are an unavoidable part of life and that by focusing on spiritual matters via the Eightfold Path, pain and suffering can be overcome. By adopting Buddha’s teachings about how to think, speak, and act with respect for all life, and many other practices, followers eventually arrive at an enlightened salvation called nirvana . Nirvana is a state of ultimate peace found in the extinction of all desire and transcendence of the person’s very being. Without nirvana , upon death the soul is reincarnated into a new life that will again run the gamut of suffering, misery, and the search for enlightenment.
The teachings of Buddha and his followers issued a direct challenge to the status quo in ancient India . In his time, Buddha relished criticizing the Brahmans, questioning their authority and their dependence on ritualism. Continued generations of teachers, missionaries, and lay Buddhists used his teachings to assail the Brahmanist-based caste system. Female Buddhists were attracted by ideas promoting the opportunity for women to achieve enlightenment on an equal basis with men.
Before Buddhism, Brahmanist teachings had supported a system of gender that in the first centuries of the common era pronounced women’s genitalia foul, leading women to be excluded from public rituals and worship. Buddhism protected women from being seen as spiritually unclean, promising them an elevated status and greater participation in the community’s spiritual life. The same was true for members of the lower castes despite their inherited class. Both women and lower castes were drawn to Buddhism by the greater independence and freedom they found in it. But women adopting Buddhism often found the religion just as patriarchal: Buddhist monasteries were segregated into spheres for male monks and female nuns, and women were given lower positions and fewer privileges.
Buddhism never supplanted Brahmanism as the dominant religion in India. In later centuries, Buddhist thought and institutions were influenced by Brahmanism, incorporating deities such as Shiva and concepts such as karma. Boundaries between the two religions became blurred, a development that helped followers of Brahmanism and Buddhists find a means for coexistence and even cooperation. Buddhism arose in a historical context dominated by a Brahmanist society, and many Buddhist teachings and practices such as meditation reflect the influence of Brahmanism. Likewise, Brahmanism was greatly influenced by Buddhism and its popularity with certain classes in India. As a result, over several centuries between around 400 BCE and 200 CE, Brahmanism evolved into more of a devotional religion, allowing individual practitioners to communicate directly with the gods, not just through the Brahman priests. Worship became more personalized and private, centered on prayer and songs within the home. In this way, Brahmanism emerged as Hinduism , which retained the caste system and belief in the Vedas while also offering a prescription for common followers seeking to live a moral and fulfilling life. What emerged as the central text of Hinduism was called the Bhagavad Gita . Finished around 300 CE, it taught that commoners, not just Brahmans, could lead exemplary moral lives by abandoning bodily desires and seeking inner peace.
Both Buddhism and Hinduism were and remained diverse, branching into hundreds of schools of thought and sects that were each quite adaptable to local contexts. As it became institutionalized, however, Buddhism lost some of its early character as a means for liberation of the lowly of India. Instead it attracted the patronage of elites, who elevated it into Asia’s most influential source of inspiration for monumental architecture and high art. Buddhism made inroads across all of Asia , coming to be adopted by millions in China, Korea, Thailand, Japan, and many other communities in Southeast Asia.
Dueling Voices
Hinduism and Buddhism in Ancient India
The first excerpt, concerning the Hindu tradition, is from the Bhagavad Gita , titled “Perform Action, Free from Attachment.” The second, “Basic Teachings of the Buddha,” includes a version of Buddhism’s teachings on the Four Noble Truths and the Eightfold Path. Notice how each spiritual system conceived of immorality, the proper way to demonstrate right conduct and living, and the purpose of life.
8. Perform thou action that is (religiously) required;
For action is better than inaction.
And even the maintenance of the body for thee
Can not succeed without action.
9. Except action for the purpose of worship,
This world is bound by actions;
Action for that purpose, son of Kunti,
Perform thou, free from attachment (to its fruits)
10. Therefore unattached ever
Perform action that must be done;
For performing action without attachment
Man attains the highest. . . .
21. Whatsoever the noblest does,
Just that in every case other folk (do);
What he makes his standard,
That the world follows.
35. Better one’s own duty, (tho) imperfect,
Than another’s duty well performed;
Better death in (doing) one’s own duty;
Another’s duty brings danger.— Bhagavad Gita , translated by Franklin Edgerton
What, now, is the Noble Truth of Suffering? Birth is suffering; Decay is suffering; Death is suffering; Sorrow, Lamentation, Pain, Grief, and Despair, are suffering; not to get what one desires, is suffering. . . .
What, now, is the Noble Truth of the Origin of Suffering? It is that craving which gives rise to fresh rebirth, and, bound up with pleasure and lust, now here, now there, finds ever fresh delight.
What, now, is the Noble Truth of the Extinction of Suffering? It is the complete fading away and extinction of this desire, its forsaking and giving up, the liberation and detachment from it. . . .
It is the Noble Eightfold Path, the way that leads to the extinction of suffering, namely: 1. Right Understanding, 2. Right Mindedness, which together are Wisdom. 3. Right Speech, 4. Right Action, 5. Right Living, which together are Morality. 6. Right Effort, 7. Right Attentiveness, 8. Right Concentration, which together are Concentration. This is the Middle Path which the Perfect One has found out, which makes one both to see and to know, which leads to peace, to discernment, to enlightenment, to Nirvana. . . .
— Buddha, the Word , edited by Nyanatiloka
- Based on these excerpts, what does it mean for one to lead a moral life in each of these distinct traditions?
- How is the Eightfold Path in the Buddhist excerpt similar to or different from the call for action in the Hindu excerpt?
The Mauryan Empire
The initial spur to Buddhism’s migration across Asia occurred with the rise of the Mauryan Empire (326–184 BCE). This entity grew out of the smaller Indian kingdom of Magahda once its ruler, Chandragupta Maurya , managed to unify much of north India from a capital near the city of Patna and pass it on to his descendants, founding the Maurya dynasty. A Greek historian named Megasthenes visited the seat of Chandragupta’s power around the end of the fourth century BCE, marveling at its palaces replete with grottoes, bathing pools, and gardens filled with jasmine, hibiscus, and lotus.
Ruling over a population nearing fifty million, Chandragupta’s successors conquered all but the southern tip of the subcontinent in a series of military campaigns. The Mauryan Empire’s political structure employed a large and well-run army, administered by a war office with branches for a navy and for raising horses and elephants for cavalry warfare. A civilian bureaucracy ran the ministries overseeing industries such as weaving, mining, and shipbuilding as well as organizing irrigation, road construction, and tax collection. The Mauryan rulers lived in constant fear of assassination and intrigue against their rule, however, which forced them to rely on an elaborate network of spies to monitor officials throughout the empire.
The high point of Mauryan greatness came with the ascension of Emperor Ashoka in approximately 268 BCE, opening a period of monumental architecture that left its mark on the ancient world. Ashoka’s personal grandeur came from the story of his transformation from a ruthless warrior general to a devout man of peace with a universal mission (Figure 5.22). As the head of the Mauryan army laying siege to the kingdom of Kalinga , he won a great battle that caused an estimated 100,000 deaths. The carnage brought an awakening that led Ashoka to Buddhism and to reforms intended to promote harmony and compassionate rule throughout India. To that end, he supported missionary efforts to spread Buddhism to Burma and Sri Lanka. His new law code gave protections to the vulnerable—the ill and diseased, the poor and powerless, and travelers making their way across the empire. His ministers put their sovereign’s will into action by building hospitals, digging wells, setting up rest-houses along India’s roads, and sending out traveling magistrates to resolve disputes and bring justice to remote areas.
Ashoka also had a lasting influence on the world of art. He decreed that his sayings and teachings on morality be inscribed on stone pillars erected throughout India (Figure 5.23). The Pillars of Ashoka demonstrate the Indian empire’s character as a spiritual and political system. Through Buddhism, patronage of the arts, and monumental architecture, the Mauryans wished to demonstrate morality and benevolence to their subjects and exercise less direct rule. Leaders such as Ashoka hoped the people’s loyalty and duty in turn would be motivated by admiration of their achievements, if not by the money and other gifts given to reward the virtuous and charm supporters. The Pillars of Ashoka also demonstrate the flexibility of the Mauryan system of rule. Those closest to the capital were inscribed with detailed summaries of the Mauryan codes for behavior and an orderly society. Farther away, in newly won territories, the pillars promoted very simple teachings, a mark of the ruler’s intent to allow room for local autonomy and customs to prevail as long as his subjects met certain universal norms and tax obligations.
At the end of Ashoka’s reign, the Mauryans left a legacy for future generations of Indian rulers to try to emulate so as to rule a diverse society. When the Mauryan Empire finally collapsed in 185 BCE, India entered another period of fragmentation and rule by small competing states and autonomous cities and villages. By the early centuries of the common era, it was a multitude of smaller regional kingdoms that shared with each other a common culture linked by Hinduism , Buddhism , a canon of Sanskrit texts, and the caste system .
The Gupta Dynasty
From the fourth to the seventh centuries, an empire founded by the Gupta dynasty (320–600 CE) ruled over northern India. As revealed by the name he took, Chandragupta, the founder, emulated the Mauryans and its famous founder, Chandragupta Maurya . He hired scribes working in Sanskrit to promote learning and the arts, and during this age, Sanskrit became the basis for a classical literature that influenced generations of Indians and the world. Texts such as the Mahabharata and Ramayana glorified ideas about duty, valor, and performing a proper role in society (Figure 5.24). The first was a collection of thrilling poems featuring feuding rulers and powerful families, the other an epic tale of a warrior prince’s journey to recover his honor.
In Ramayana , Rama, an avatar for the Hindu deity Vishnu, triumphs over the demon Ravana on the island of Sri Lanka and rescues his wife Sita before going on to found a perfect Indian society from his capital of Ayudha. His noble virtues and ideal society became models for Hindus to aspire to as rulers and aristocrats, while his exploits were retold for centuries in countless paintings, sculptures, carnivals, plays, and shadow theatres.
The Sanskrit classics Mahabharata and Ramayana soon spread far and wide in Southeast Asia, where they became part of the cultural fabric for a multitude of non-Indians as well. Other intellectuals of the Gupta era proved themselves in the field of mathematics by using decimals and a mark to denote the concept of zero for precise measurements and recordkeeping. Among the more notable was the astronomer Brahmagupta , who in the seventh century CE pioneered the use of multiplication and division and the idea of negative numbers .
Link to Learning
You can read a brief synopsis of the Ramayana and a description of the epic’s major characters at the British Library website.
An animated English-language version of the epic is also available.
In politics the Guptas were innovators as well. In return for their loyalty, rulers granted tracts of land as gifts to powerful families, Brahmans, and temple complexes, guaranteeing these followers a share of the harvest and consolidating their own control. In return, the Brahmans elevated the Gupta rulers to new heights in rituals honoring Vishnu and Shiva. Yet as these deities became more important, worship among the commoners turned more personal and private; singing as a form of prayer and ritualism inside the home became essential to daily lives. Many Indians began to believe in the sanctity of bhakti , a direct personal relationship between a follower and the deity. This idea bypassed the role of Brahmans as intermediaries, displeasing the Brahmans but gaining popularity in southern India, where poems written in the Tamil language became foundational to the new practice of personalized worship among Hindus.
The Gupta’s dynasty marked a flourishing of art and religion and the heyday of Buddhism in India. Painted caves with beautiful sculptures found in the Ajanta caves illustrate the sophistication of the artists patronized by the dynasty. While Hinduism remained the official religion of the state and the Guptas, Buddhist universities such as Nalanda were among the first of their kind in the ancient world and attracted throngs of students and pilgrims from China . India ’s educated classes ranked among the most learned and knowledgeable of the ancient world, and at times they turned their attention from math and morality to explore the depths of passion, love, and eroticism. During this period, the Kama Sutra , a treatise on courtship and sexuality, became a seminal piece of Indian literature, inspiring and titillating generations worldwide ever since.
The opulence and stability provided by the Guptas dissipated under the threat of invaders from the north known as the Huns . While northern India fractured into smaller states after this point, southern India’s ties and trade with South Asia deepened and matured. By the eleventh century, the region’s profitable exports of goods such as ivory, pepper, spices, Roman coins, and even animals like the peacock had led to the formation of notable southern kingdoms, such as the Tamil Chola dynasty. But the most influential exports from India to the rest of South Asia—Hinduism, Buddhism, and the art and learning each inspired—long outlived these states.


10.2: Structure Maps
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Structure maps, which plot structures against properties such electronegativity, are more consistent than radius ratio rules in correctly predicting coordination numbers and crystal structures. One of the early examples of this approach was published by Mooser and Pearson in 1959. [3]
A Mooser-Pearson diagram maps crystal structures according to the average principal quantum numbers of the atoms and their electronegativity difference. The basic ideas behind such a plot are:
The lines in the Mooser-Pearson diagram separate MX compounds with CsCl, NaCl, and tetrahedral (wurtzite and zincblende) structures. Note that wurtzite has higher ionicity than zincblende in the plot, consistent with our discussion of the "boat" and "chair" ring structures in Chapter 8. Diamorphic compounds tend to fall on the boundaries. On the whole, the Mooser-Pearson diagram makes far fewer errors in predicting structures than the radius ratio rule. There are similar diagrams for MX 2 structures, in which the order of ionicity is CaF 2 (8:4 coordination) > rutile (6:3) > silica structures (4:2).


3.4: Graphing Data
Examine the graph below
a. As temperature increases, what happens to the solubility of oxygen in water?
b. Water in a particular stream varies from 8 - 13 mg/liter. What temperature range does this reflect?
Fish require oxygen to live. As water passes through gills, dissolved oxygen (DO) is transferred to blood. Dissolved oxygen in water is affected by:
Photosynthesis: During light hours, aquatic plants produce oxygen. Mixing: Waves and waterfalls aerate water and increase oxygen concentration.
Decomposition: As organic material decays, bacteria consume oxygen. Salinity: As water becomes more salty, its ability to hold oxygen decreases.
Examine the graph below:
a. At which temperature is dissolved oxygen highest?
b. A trout requires more DO when the water temperature is 24 o C (75 o F) as compared to when the water temperature is 4 o C. (to support an increase in metabolic activities). How do the DO levels compare at these two temperatures?
c. A power plant discharges warm water into a river. Why would this have a detrimental effect on fish that live in the river? Be specific in your answer and relate it to this lab.
High levels of CO2 have been implicated in global warming and as a causative factor in mass extinctions.
a. Construct a line graph of the 1970–2018 data by decade from 1970 and ending with to 2010.
b. State a conclusion as to the change in CO2 levels over time.