9.9: Chapter 9 Problems
An underlined problem number or problem-part letter indicates that the numerical answer appears in Appendix I.
9.1 For a binary solution, find expressions for the mole fractions \(x_{\mathrm{B}}\) and \(x_{\mathrm{A}}\) as functions of the solute molality \(m_{\mathrm{B}}\).
9.2 Consider a binary mixture of two liquids, \(\mathrm{A}\) and \(\mathrm{B}\). The molar volume of mixing, \(\Delta V(\mathrm{mix}) / n\), is given by Eq. 9.2.19.
(a) Find a formula for calculating the value of \(\Delta V(\mathrm{mix}) / n\) of a binary mixture from values of \(x_{\mathrm{A}}, x_{\mathrm{B}}, M_{\mathrm{A}}, M_{\mathrm{B}}, \rho, \rho_{\mathrm{A}}^{*}\), and \(\rho_{\mathrm{B}}^{*} .\)
Table \(9.7\) Molar volumes of mixing of binary mixtures of 1-hexanol (A) and 1 -octene \((\mathrm{B})\) at \(25^{\circ} \mathrm{C} .^{a}\)
\begin{tabular}{lccc}
\hline\(x_{\mathrm{B}}\) & {\([\Delta V(\mathrm{mix}) / n] / \mathrm{cm}^{3} \mathrm{~mol}^{-1}\)} & \(x_{\mathrm{B}}\) & {\([\Delta V(\mathrm{mix}) / n] / \mathrm{cm}^{3} \mathrm{~mol}^{-1}\)} \\
\hline 0 & 0 & \(0.555\) & \(0.005\) \\
\(0.049\) & \(-0.027\) & \(0.597\) & \(0.011\) \\
\(0.097\) & \(-0.050\) & \(0.702\) & \(0.029\) \\
\(0.146\) & \(-0.063\) & \(0.716\) & \(0.035\) \\
\(0.199\) & \(-0.077\) & \(0.751\) & \(0.048\) \\
\(0.235\) & \(-0.073\) & \(0.803\) & \(0.056\) \\
\(0.284\) & \(-0.074\) & \(0.846\) & \(0.058\) \\
\(0.343\) & \(-0.065\) & \(0.897\) & \(0.057\) \\
\(0.388\) & \(-0.053\) & \(0.944\) & \(0.049\) \\
\(0.448\) & \(-0.032\) & 1 & 0 \\
\(0.491\) & \(-0.016\) & & \\
\hline
\end{tabular}
\({ }^{a}\) Ref. [170].
(b) The molar volumes of mixing for liquid binary mixtures of 1-hexanol (A) and 1-octene (B) at \(25^{\circ} \mathrm{C}\) have been calculated from their measured densities. The data are in Table 9.7. The molar volumes of the pure constituents are \(V_{\mathrm{A}}^{*}=125.31 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\) and \(V_{\mathrm{B}}^{*}=\) \(157.85 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\). Use the method of intercepts to estimate the partial molar volumes of both constituents in an equimolar mixture \(\left(x_{\mathrm{A}}=x_{\mathrm{B}}=0.5\right)\), and the partial molar volume \(V_{\mathrm{B}}^{\infty}\) of B at infinite dilution.
9.3 Extend the derivation of Prob. 8.1, concerning a liquid droplet of radius \(r\) suspended in a gas, to the case in which the liquid and gas are both mixtures. Show that the equilibrium conditions are \(T^{\mathrm{g}}=T^{\mathrm{l}}, \mu_{i}^{\mathrm{g}}=\mu_{i}^{1}\) (for each species \(i\) that can equilibrate between the two phases), and \(p^{1}=p^{g}+2 \gamma / r\), where \(\gamma\) is the surface tension. (As in Prob. 8.1, the last relation is the Laplace equation.)
9.4 Consider a gaseous mixture of \(4.0000 \times 10^{-2} \mathrm{~mol}\) of \(\mathrm{N}_{2}\) (A) and \(4.0000 \times 10^{-2} \mathrm{~mol}\) of \(\mathrm{CO}_{2}\) (B) in a volume of \(1.0000 \times 10^{-3} \mathrm{~m}^{3}\) at a temperature of \(298.15 \mathrm{~K}\). The second virial coefficients at this temperature have the values \({ }^{14}\)
\[
\begin{aligned}
B_{\mathrm{AA}} &=-4.8 \times 10^{-6} \mathrm{~m}^{3} \mathrm{~mol}^{-1} \\
B_{\mathrm{BB}} &=-124.5 \times 10^{-6} \mathrm{~m}^{3} \mathrm{~mol}^{-1} \\
B_{\mathrm{AB}} &=-47.5 \times 10^{-6} \mathrm{~m}^{3} \mathrm{~mol}^{-1}
\end{aligned}
\]
Compare the pressure of the real gas mixture with that predicted by the ideal gas equation. See Eqs. 9.3.20 and 9.3.23.
\({ }^{14}\) Refs. [3], [49], and [50].
9.5 At \(25^{\circ} \mathrm{C}\) and 1 bar, the Henry's law constants of nitrogen and oxygen dissolved in water are \(k_{\mathrm{H}, \mathrm{N}_{2}}=8.64 \times 10^{4}\) bar and \(k_{\mathrm{H}, \mathrm{O}_{2}}=4.41 \times 10^{4}\) bar. \({ }^{15}\) The vapor pressure of water at this temperature and pressure is \(p_{\mathrm{H}_{2} \mathrm{O}}=0.032\) bar. Assume that dry air contains only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) at mole fractions \(y_{\mathrm{N}_{2}}=0.788\) and \(y_{\mathrm{O}_{2}}=0.212\). Consider liquid-gas systems formed by equilibrating liquid water and air at \(25^{\circ} \mathrm{C}\) and \(1.000 \mathrm{bar}\), and assume that the gas phase behaves as an ideal gas mixture.
Hint: The sum of the partial pressures of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) must be \((1.000-0.032)\) bar \(=0.968\) bar. If the volume of one of the phases is much larger than that of the other, then almost all of the \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) will be in the predominant phase and the ratio of their amounts in this phase must be practically the same as in dry air.
Determine the mole fractions of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) in both phases in the following limiting cases:
(a) A large volume of air is equilibrated with just enough water to leave a small drop of liquid.
(b) A large volume of water is equilibrated with just enough air to leave a small bubble of gas.
9.6 Derive the expression for \(\gamma_{m, \mathrm{~B}}\) given in Table 9.4, starting with Eq. 9.5.18.
9.7 Consider a nonideal binary gas mixture with the simple equation of state \(V=n R T / p+n B\) (Eq. \(9.3 .21\) ).
(a) The rule of Lewis and Randall states that the value of the mixed second virial coefficient \(B_{\mathrm{AB}}\) is the average of \(B_{\mathrm{AA}}\) and \(B_{\mathrm{BB}}\). Show that when this rule holds, the fugacity coefficient of \(\mathrm{A}\) in a binary gas mixture of any composition is given by \(\ln \phi_{\mathrm{A}}=B_{\mathrm{AA}} p / R T\). By comparing this expression with Eq. \(7.8 .18\) for a pure gas, express the fugacity of \(\mathrm{A}\) in the mixture as a function of the fugacity of pure \(A\) at the same temperature and pressure as the mixture.
(b) The rule of Lewis and Randall is not accurately obeyed when constituents A and B are chemically dissimilar. For example, at \(298.15 \mathrm{~K}\), the second virial coefficients of \(\mathrm{H}_{2} \mathrm{O}\) (A) and \(\mathrm{N}_{2}\) (B) are \(B_{\mathrm{AA}}=-1158 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\) and \(B_{\mathrm{BB}}=-5 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\), respectively, whereas the mixed second virial coefficient is \(B_{\mathrm{AB}}=-40 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\).
When liquid water is equilibrated with nitrogen at \(298.15 \mathrm{~K}\) and 1 bar, the partial pressure of \(\mathrm{H}_{2} \mathrm{O}\) in the gas phase is \(p_{\mathrm{A}}=0.03185\) bar. Use the given values of \(B_{\mathrm{AA}}, B_{\mathrm{BB}}\), and \(B_{\mathrm{AB}}\) to calculate the fugacity of the gaseous \(\mathrm{H}_{2} \mathrm{O}\) in this binary mixture. Compare this fugacity with the fugacity calculated with the value of \(B_{\mathrm{AB}}\) predicted by the rule of Lewis and Randall.
Table \(9.8\) Activity coefficient of benzene (A) in mixtures of benzene and 1 -octanol at \(20^{\circ} \mathrm{C}\). The reference state
is the pure liquid.
\begin{tabular}{lccc}
\hline\(x_{\mathrm{A}}\) & \(\gamma_{\mathrm{A}}\) & \(x_{\mathrm{A}}\) & \(\gamma_{\mathrm{A}}\) \\
\hline 0 & \(2.0^{a}\) & \(0.7631\) & \(1.183\) \\
\(0.1334\) & \(1.915\) & \(0.8474\) & \(1.101\) \\
\(0.2381\) & \(1.809\) & \(0.9174\) & \(1.046\) \\
\(0.4131\) & \(1.594\) & \(0.9782\) & \(1.005\) \\
\(0.5805\) & \(1.370\) & & \\
\hline \multicolumn{3}{l}{\(a_{\text {extrapolated }}\)}
\end{tabular}
\({ }^{15}\) Ref. [184].
9.8 Benzene and 1-octanol are two liquids that mix in all proportions. Benzene has a measurable vapor pressure, whereas 1-octanol is practically nonvolatile. The data in Table \(9.8\) on the preceding page were obtained by Platford \({ }^{16}\) using the isopiestic vapor pressure method.
(a) Use numerical integration to evaluate the integral on the right side of Eq. \(9.6 .10\) at each of the values of \(x_{\mathrm{A}}\) listed in the table, and thus find \(\gamma_{\mathrm{B}}\) at these compositions.
(b) Draw two curves on the same graph showing the effective mole fractions \(\gamma_{\mathrm{A}} x_{\mathrm{A}}\) and \(\gamma_{\mathrm{B}} x_{\mathrm{B}}\) as functions of \(x_{\mathrm{A}}\). Are the deviations from ideal-mixture behavior positive or negative?
Table \(9.9\) Liquid and gas compositions in the two-phase system of methanol (A) and benzene (B) at \(45^{\circ} \mathrm{C}^{a}\)
\begin{tabular}{llllll}
\hline\(x_{\mathrm{A}}\) & \(y_{\mathrm{A}}\) & \(p / \mathrm{kPa}\) & \(x_{\mathrm{A}}\) & \(y_{\mathrm{A}}\) & \(p / \mathrm{kPa}\) \\
\hline 0 & 0 & \(29.894\) & \(0.4201\) & \(0.5590\) & \(60.015\) \\
\(0.0207\) & \(0.2794\) & \(40.962\) & \(0.5420\) & \(0.5783\) & \(60.416\) \\
\(0.0314\) & \(0.3391\) & \(44.231\) & \(0.6164\) & \(0.5908\) & \(60.416\) \\
\(0.0431\) & \(0.3794\) & \(46.832\) & \(0.7259\) & \(0.6216\) & \(59.868\) \\
\(0.0613\) & \(0.4306\) & \(50.488\) & \(0.8171\) & \(0.6681\) & \(58.321\) \\
\(0.0854\) & \(0.4642\) & \(53.224\) & \(0.9033\) & \(0.7525\) & \(54.692\) \\
\(0.1811\) & \(0.5171\) & \(57.454\) & \(0.9497\) & \(0.8368\) & \(51.009\) \\
\(0.3217\) & \(0.5450\) & \(59.402\) & 1 & 1 & \(44.608\) \\
\hline
\end{tabular}
\({ }^{a}\) Ref. [169].
9.9 Table \(9.9\) lists measured values of gas-phase composition and total pressure for the binary two-phase methanol-benzene system at constant temperature and varied liquid-phase composition. \(x_{\mathrm{A}}\) is the mole fraction of methanol in the liquid mixture, and \(y_{\mathrm{A}}\) is the mole fraction of methanol in the equilibrated gas phase.
(a) For each of the 16 different liquid-phase compositions, tabulate the partial pressures of \(\mathrm{A}\) and \(\mathrm{B}\) in the equilibrated gas phase.
(b) Plot \(p_{\mathrm{A}}\) and \(p_{\mathrm{B}}\) versus \(x_{\mathrm{A}}\) on the same graph. Notice that the behavior of the mixture is far from that of an ideal mixture. Are the deviations from Raoult's law positive or negative?
(c) Tabulate and plot the activity coefficient \(\gamma_{\mathrm{B}}\) of the benzene as a function of \(x_{\mathrm{A}}\) using a pure-liquid reference state. Assume that the fugacity \(f_{\mathrm{B}}\) is equal to \(p_{\mathrm{B}}\), and ignore the effects of variable pressure.
(d) Estimate the Henry's law constant \(k_{\mathrm{H}, \mathrm{A}}\) of methanol in the benzene environment at \(45^{\circ} \mathrm{C}\) by the graphical method suggested in Fig. 9.7(b). Again assume that \(f_{\mathrm{A}}\) and \(p_{\mathrm{A}}\) are equal, and ignore the effects of variable pressure.
9.10 Consider a dilute binary nonelectrolyte solution in which the dependence of the chemical potential of solute B on composition is given by
\[
\mu_{\mathrm{B}}=\mu_{m, \mathrm{~B}}^{\mathrm{ref}}+R T \ln \frac{m_{\mathrm{B}}}{m^{\circ}}+k_{m} m_{\mathrm{B}}
\]
where \(\mu_{m, \mathrm{~B}}^{\mathrm{ref}}\) and \(k_{m}\) are constants at a given \(T\) and \(p\). (The derivation of this equation is sketched in Sec. 9.5.4.) Use the Gibbs-Duhem equation in the form \(\mathrm{d} \mu_{\mathrm{A}}=-\left(n_{\mathrm{B}} / n_{\mathrm{A}}\right) \mathrm{d} \mu_{\mathrm{B}}\) to obtain an expression for \(\mu_{\mathrm{A}}-\mu_{\mathrm{A}}^{*}\) as a function of \(m_{\mathrm{B}}\) in this solution.
\({ }^{16}\) Ref. [145].
9.11 By means of the isopiestic vapor pressure technique, the osmotic coefficients of aqueous solutions of urea at \(25^{\circ} \mathrm{C}\) have been measured at molalities up to the saturation limit of about \(20 \mathrm{~mol} \mathrm{~kg}^{-1} .{ }^{17}\) The experimental values are closely approximated by the function
\[
\phi_{m}=1.00-\frac{0.050 m_{\mathrm{B}} / m^{\circ}}{1.00+0.179 m_{\mathrm{B}} / m^{\circ}}
\]
where \(m^{\circ}\) is \(1 \mathrm{~mol} \mathrm{~kg}^{-1}\). Calculate values of the solvent and solute activity coefficients \(\gamma_{\mathrm{A}}\) and \(\gamma_{m, \mathrm{~B}}\) at various molalities in the range \(0-20 \mathrm{~mol} \mathrm{~kg}^{-1}\), and plot them versus \(m_{\mathrm{B}} / m^{\circ}\). Use enough points to be able to see the shapes of the curves. What are the limiting slopes of these curves as \(m_{\mathrm{B}}\) approaches zero?
9.12 Use Eq. \(9.2 .49\) to derive an expression for the rate at which the logarithm of the activity coefficient of component \(i\) of a liquid mixture changes with pressure at constant temperature and composition: \(\left(\partial \ln \gamma_{i} / \partial p\right)_{T,\left\{n_{i}\right\}}=\) ?
9.13 Assume that at sea level the atmosphere has a pressure of \(1.00\) bar and a composition given by \(y_{\mathrm{N}_{2}}=0.788\) and \(y_{\mathrm{O}_{2}}=0.212\). Find the partial pressures and mole fractions of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), and the total pressure, at an altitude of \(10.0 \mathrm{~km}\), making the (drastic) approximation that the atmosphere is an ideal gas mixture in an equilibrium state at \(0^{\circ} \mathrm{C}\). For \(g\) use the value of the standard acceleration of free fall listed in Appendix B.
9.14 Consider a tall column of a dilute binary liquid solution at equilibrium in a gravitational field.
(a) Derive an expression for \(\ln \left[c_{\mathrm{B}}(h) / c_{\mathrm{B}}(0)\right]\), where \(c_{\mathrm{B}}(h)\) and \(c_{\mathrm{B}}(0)\) are the solute concentrations at elevations \(h\) and 0 . Your expression should be a function of \(h, M_{\mathrm{B}}, T, \rho\), and the partial specific volume of the solute at infinite dilution, \(v_{\mathrm{B}}^{\infty}\). For the dependence of pressure on elevation, you may use the hydrostatic formula \(\mathrm{d} p=-\rho g \mathrm{~d} h\) (Eq. \(8.1 .14\) on page 200) and assume the solution density \(\rho\) is the same at all elevations. Hint: use the derivation leading to Eq. \(9.8 .22\) as a guide.
(b) Suppose you have a tall vessel containing a dilute solution of a macromolecule solute of molar mass \(M_{\mathrm{B}}=10.0 \mathrm{~kg} \mathrm{~mol}^{-1}\) and partial specific volume \(v_{\mathrm{B}}^{\infty}=0.78 \mathrm{~cm}^{3} \mathrm{~g}^{-1}\). The solution density is \(\rho=1.00 \mathrm{~g} \mathrm{~cm}^{-3}\) and the temperature is \(T=300 \mathrm{~K}\). Find the height \(h\) from the bottom of the vessel at which, in the equilibrium state, the concentration \(c_{\mathrm{B}}\) has decreased to 99 percent of the concentration at the bottom.
9.15 FhuA is a protein found in the outer membrane of the Escherichia coli bacterium. From the known amino acid sequence, its molar mass is calculated to be \(78.804 \mathrm{~kg} \mathrm{~mol}^{-1}\). In aqueous solution, molecules of the detergent dodecyl maltoside bind to a FhuA molecule to form an aggregate that behaves as a single solute species. Figure \(9.13\) on the next page shows data collected in a sedimentation equilibrium experiment with a dilute solution of the aggregate. \({ }^{18}\) In the graph, \(A\) is the absorbance measured at a wavelength of \(280 \mathrm{~nm}\) (a property that is a linear function of the aggregate concentration) and \(r\) is the radial distance from the axis of rotation of the centrifuge rotor. The experimental points fall very close to the straight line shown in the graph. The sedimentation conditions were \(\omega=838 \mathrm{~s}^{-1}\) and \(T=293 \mathrm{~K}\). The authors used the values \(v_{\mathrm{B}}^{\infty}=0.776 \mathrm{~cm}^{3} \mathrm{~g}^{-1}\) and \(\rho=1.004 \mathrm{~g} \mathrm{~cm}^{-3}\).
(a) The values of \(r\) at which the absorbance was measured range from \(6.95 \mathrm{~cm}\) to \(7.20 \mathrm{~cm}\). Find the difference of pressure in the solution between these two positions.
(b) Find the molar mass of the aggregate solute species, and use it to estimate the mass binding ratio (the mass of bound detergent divided by the mass of protein).
\({ }^{17}\) Ref. [160]. \({ }^{18}\) Ref. [18].


1.6: Week 6 - Pathos (Emotions, Values)
Pathos is an important tool of persuasion in arguments. Pathos is a method of convincing people with an argument drawn out through an emotional response. Analyzing examples of pathos, one would come to the conclusion that it differs from other “ingredients of persuasion,” namely “ethos” and “logos,” in that it requires us to try to quantify subjective, emotional and values-based assumptions in our quest to understand and evaluate academic arguments. The use of pathos is called a “pathetic appeal.” Note that this is very different from our usual understanding of the word “pathetic.” “Pathos” is used to describe the rhetor’s attempt to appeal to “an audience’s sense of identity, their self-interest, and their emotions.”  “Pathos” most often refers to an attempt to engage an audience’s emotions. Think about the different emotions people are capable of feeling: they include love, pity, sorrow, affection, anger, fear, greed, lust, and hatred. If a rhetor tries to make an audience feel emotions in response to what is being said or written, then they are using pathos.
Common Examples of Pathos
For a better understanding of the subject, let us examine a few pathos examples from daily conversations:
- “If we don’t leave this place soon, we’ll be yelling for help. There’s no one to help us here, let’s get out of here and live.” – This statement evokes emotions of fear.
- The “Made in America” label on various products sold in America tries to enhance sales by appealing to customers’ sense of patriotism.
- Ads encouraging charitable donations show small children living in pathetic conditions, to evoke pity in people.
- Referring to a country as “the motherland” stirs up patriotic feelings in individuals living in that country or state.
- A soft, instrumental symphony may arouse people emotionally.
Resources for studying and using Pathos in Arguments
- View the video: What is Pathos? , https://www.youtube.com/watch?v=W6JQkXwgMVk&feature=youtu.be
- View the video: Four Ways to Persuade with Emotion (Pathos) , https://www.youtube.com/watch?v=f5k5Fkn8eAw&feature=youtu.be
- View the handout: Pathos
- View the handout: Using Logos, Pathos & Ethos
Using Pathos Correctly
Whether we are making arguments or analyzing them, it is important that we use Pathos carefully. Often, our emotions can get in the way or clear and critical thinking on an issue. Pathos can and should be used to clarify how a well-supported position relates to our values and beliefs but should never be used to manipulate, confuse or inflate an issue beyond what the evidence is capable of supporting.
The Science of Emotions
The following three TED Talks each address the science and growing body of research that explores the biological origins of our emotional states and what we can learn about ourselves from carefully studying our feelings. While not addressing the techniques of argument analysis and critical thinking directly, we can learn a great deal from these talks about the way Pathos is used to influence our choices, our perceptions, our thoughts, values and beliefs by understanding how emotions work and how, possibly, to better control them.
- View the video: Why What We Feel Matters More Than What We Think , https://www.youtube.com/watch?v=DsDVCQnqcy4&feature=youtu.be
- View the video: Why You Feel What You Feel , https://www.youtube.com/watch?v=h-rRgpPbR5w&feature=youtu.be
- View the video: The Science of Emotions , https://www.youtube.com/watch?v=65e2qScV_K8&feature=youtu.be
These TED Talks give us a great deal of information on the science of emotions and how we can use that data to better understand and work with our feelings. Some things to consider in summary:
- Humans are very complex emotional creatures who use their feelings as much as, or even more than, their thoughts to make decisions in the world.
- Even though scientists have graphed close to 35,000 distinct emotions, most people only feel around 10-12 of them with any regularity.
- Of those top 12, the overwhelming majority of people make most of their decisions based on just three: love, hatred and fear.
- We make, on average, around 33,000 individual choices a day. If the data is correct, most of those decisions are governed, at least in part, by our reactions to our internal states of love, hatred and/or fear.
- So if we are not aware of (and at least somewhat in control of) how we process these emotions, anyone who wishes to manipulate us (politicians, advertisers, abusive partners, incompetent writing professors, etc.) can misuse Pathos in manipulative ways to trigger states of love, hatred or fear in us to make us more susceptible to accepting or rejecting a given argument without fully considering the merits of its evidence.


Exercise \(\PageIndex{1}\)
Given the following:
Profits of falsely claiming high quality with no signal are 120.
Profits of truthfully claiming high quality with no signal are 100.
Profits of truthfully claiming low quality are 80.
The cost of a true signal of high quality is 16.
The cost of a false signal of high quality is 38.
(1) Is truthful access to the high-quality market profitable given the signal?
(2) Does the signal remove the incentive of high-quality firms to cheat?
(3) Does the signal remove the incentive of low-quality firms to deceive?
(4) Is there a separating equilibrium that corrects the lemons market?
-
Answer
-
Answer for (1): Yes
Answer for (2): Yes
Answer for (3): No
There is a separating equilibrium if all answers are 'Yes'


9.7: Evaluation- Rhetorical Analysis
By the end of this section, you will be able to:
- Evaluate the elements of a rhetorical analysis.
- Identify and correct errors involving mixed sentence structures.
- Evaluate an essay for clarity, coherence, and language.
At various points in your writing, especially after you complete the first draft, check the rubric provided here. Your instructor is likely to use a similar rubric to evaluate your rhetorical analysis. Aligning your writing to applicable points in the rubric—especially to those reflecting a score of 5— will keep you focused and guide you in your work.
Rubric
| Score | Critical Language Awareness | Clarity and Coherence | Rhetorical Choices |
|
5 Skillful |
The text always adheres to the “Editing Focus” of this chapter—mixed sentence constructions, as discussed in Section \(9.6\)—and maintains consistency in constructing the grammatical paths of sentences. The text also shows ample evidence of the writer’s intent to consciously meet or challenge conventional expectations in rhetorically effective ways. | The essay presents all information clearly and logically. Well-chosen transitions connect paragraphs and sections, and the essay focuses consistently on its thesis statement. Claims are fully supported with quoted or paraphrased evidence. | The writer skillfully identifies rhetorical strategies and writes with precision and insight. The writer maintains a consistent voice and an awareness of the rhetorical situation. |
|
4 Accomplished |
The text usually adheres to the “Editing Focus” of this chapter—mixed sentence constructions, as discussed in Section \(9.6\)—and maintains consistency in constructing the grammatical paths of sentences. The text also shows some evidence of the writer’s intent to consciously meet or challenge conventional expectations in rhetorically effective ways. | The essay presents most information clearly and logically. Well-chosen transitions connect most paragraphs and sections, and the essay focuses on its thesis statement. Claims are well supported with quoted or paraphrased evidence. | The writer identifies rhetorical strategies and writes with precision and insight. The writer maintains a consistent voice and an awareness of the rhetorical situation, although there may be an occasional slip. |
|
3 Capable |
The text generally adheres to the “Editing Focus” of this chapter—mixed sentence constructions, as discussed in Section \(9.6\)—and maintains consistency in constructing the grammatical paths of sentences. The text also shows limited evidence of the writer’s intent to consciously meet or challenge conventional expectations in rhetorically effective ways. | The essay presents most information clearly and logically. Transitions connect most paragraphs and sections, but the essay may stray occasionally from its thesis statement. Claims are generally supported with quoted or paraphrased evidence. | The writer identifies most, if not all, rhetorical strategies and writes with some insight. The writer maintains a fairly consistent voice and an awareness of the rhetorical situation, although there may be slips. |
|
2 Developing |
The text occasionally adheres to the “Editing Focus” of this chapter—mixed sentence constructions, as discussed in Section \(9.6\)—and maintains consistency in constructing the grammatical paths of sentences. The text also shows emerging evidence of the writer’s intent to consciously meet or challenge conventional expectations in rhetorically effective ways. | The essay presents some information clearly, but the organization is confusing and/or illogical. Transitions connect some paragraphs and sections, but the transitions may be confusing or misleading. The essay may stray from its thesis statement and is either too short or too long. Claims often lack the support of additional quoted or paraphrased evidence. | The writer identifies some rhetorical strategies but neglects to elaborate on them sufficiently. The writer maintains an inconsistent voice and awareness of the rhetorical situation. |
|
1 Beginning |
The text does not adhere to the “Editing Focus” of this chapter—mixed sentence constructions, as discussed in Section \(9.6\)—and does not maintain consistency in constructing the grammatical paths of sentences. The text also shows little to no evidence of the writer’s intent to consciously meet or challenge conventional expectations in rhetorically effective ways. |
The essay lacks clarity, and the organization is confusing and/or illogical. Transitions connect some paragraphs and sections, but the transitions may be too few, confusing, or misleading. The essay often strays from its thesis statement, if it has one, and is either too short or too long. Claims that do appear are not effectively supported. |
The writer identifies few if any rhetorical strategies and neglects to elaborate on them. The writer maintains an inconsistent voice and shows little, if any, awareness of the rhetorical situation. |


16.1: Introduction to Blood
Chapter Learning Objectives:
After studying this chapter, you will be able to:
- Identify the primary functions of blood, its fluid and cellular components, and its physical characteristics
- Identify the most important proteins and other solutes present in blood plasma
- Describe the formation of the formed element components of blood
- Discuss the structure and function of red blood cells and hemoglobin
- Classify and characterize white blood cells
- Describe the structure and function of platelets
- Explain the significance of ABO and Rh blood groups in blood transfusions
- Discuss a variety of blood disorders
Single-celled organisms do not need blood. They obtain nutrients directly from and excrete wastes directly into their environment. The human organism cannot do that. Our large, complex bodies need blood to deliver nutrients to and remove wastes from our trillions of cells. The heart pumps blood throughout the body in a network of blood vessels. Together, these three components—blood, heart, and vessels—make up the cardiovascular system. This chapter focuses on the fluid connective tissue that serves as a medium of transport: blood.
Contributors and Attributions
-
OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


9: Comprehension Last updated Save as PDF Page ID 91966 Wikipedia 9.1: Introduction 9.2: Historical Review on Psycholinguistics and Neurolinguistics 9.3: Characteristic Features 9.4: Physiological Approach 9.5: Behavioristic Approach – Parsing a Sentence 9.6: The Interactionist Approach of Parsing 9.7: Situation Model 9.8: Using Language 9.9: Language, Culture and Cognition 9.10: Culture and Language 9.11: What is the Connection between Language and Cognition? 9.12: Is Thought Dependent on, or even caused by Language? 9.13: Language as a Cognitive Ability 9.14: Non-Human Language - Animal Communication 9.15: Language Comprehension and Production 9.16: Using Language 9.17: Language, Culture and Cognition 9.18: References


20.4: Vanishing Area and Subdivisions
Any one-point set as well as any segment in the Euclidean plane have vanishing area.
- Proof
-
Fix a line segment \([AB]\) . Consider a sold square \(\blacksquare ABCD\) .
Note that given a positive integer \(n\) , there are \(n\) disjoint segments \([A_1B_1],\dots,[A_nB_n]\) in \(\blacksquare ABCD\) , such that each \([A_iB_i]\) is congruent to \([AB]\) in the sense of the Definition 20.1.1 .
Applying invariance, additivity, and monotonicity of the area function, we get that
\(\begin{aligned} n\cdot \text{area }[AB] &=\text{area }\left([A_1B_1]\cup\dots\cup[A_nB_n]\right)\le \\ &\le \text{area }(\blacksquare ABCD) \end{aligned}\)
That is,
\(\text{area }[AB]\le \tfrac1n\cdot\text{area }(\blacksquare ABCD)\)
for any positive integer \(n\) . Therefore, \(\text{area }[AB]\le 0\) . On the other hand, by definition of area, \(\text{area }[AB]\ge 0\) , hence
\(\text{area }[AB]= 0.\)
For any one-point set \(\{A\}\) we have that \(\{A\}\subset [AB]\) . Therefore,
\(0\le \text{area }\{A\}\le \text{area }[AB]=0.\)
Whence \(\text{area }\{A\}=0\) .
Any degenerate polygonal set has vanishing area.
- Proof
-
Let \(\mathcal P\) be a degenerate set, say
Since area is nonnegative by definition, applying additivity several times, we get that
\(\begin{aligned} \text{area }\mathcal{P}\le & \text{area }[A_1B_1]+\dots+\text{area }[A_nB_n]+ \\ &+\text{area }\{C_1\}+\dots+\text{area }\{C_k\}.\end{aligned}\)
By Proposition \(\PageIndex{1}\), the right hand side vanishes.
On the other hand, \(\text{area }\mathcal{P}\ge 0\) , hence the result.
We say that polygonal set \(\mathcal{P}\) is subdivided into two polygonal sets \(\mathcal{Q}_1,\dots,\mathcal{Q}_n\) if \(\mathcal{P}=\mathcal{Q}_1\cup\dots\cup \mathcal{Q}_n\) and the intersection \(\mathcal{Q}_i\cap\mathcal{Q}_j\) is degenerate for any pair \(i\) and \(j\) . (Recall that according to Claim20.3.1 , the intersections \(\mathcal{Q}_i\cap\mathcal{Q}_j\) are polygonal.)
Assume polygonal sets \(\mathcal{P}\) is subdivided into polygonal sets \(\mathcal{Q}_1, \dots, \mathcal{Q}_n\) . Then
\(\text{area }\mathcal{P}=\text{area }\mathcal{Q}_1+\dots+\text{area }\mathcal{Q}_n.\)
- Proof
-
Assume \(n=2\) ; by additivity of area,
\(\text{area }\mathcal{P}=\text{area }\mathcal{Q}_1+\text{area }\mathcal{Q}_2-\text{area }(\mathcal{Q}_1 \cap\mathcal{Q}_2).\)
Since \(\mathcal{Q}_1\cap\mathcal{Q}_2\) is degenerate, by Corollary \(\PageIndex{1}\),
\(\text{area }(\mathcal{Q}_1\cap\mathcal{Q}_2)=0.\)
Applying this formula a few times we get the general case. Indeed, if \(\mathcal{P}\) is subdivided into \(\mathcal{Q}_1,\dots,\mathcal{Q}_n\) , then
\(\begin{aligned} \text{area }\mathcal{P}&=\text{area }\mathcal{Q}_1+\text{area }(\mathcal{Q}_2\cup\dots\cup\mathcal{Q}_n)= \\ &=\text{area }\mathcal{Q}_1+\text{area } \mathcal{Q}_2+\text{area }( \mathcal{Q}_3\cup\dots\cup\mathcal{Q}_n)= \\ &\ \ \ \vdots \\ &=\text{area }\mathcal{Q}_1+\text{area } \mathcal{Q}_2+\dots+\text{area }\mathcal{Q}_n.\end{aligned}\)
Two polygonal sets \(\mathcal{P}\) and \(\mathcal{P}'\) are called equidecomposable if they admit subdivisions into polygonal sets \(\mathcal{Q}_1,\dots,\mathcal{Q}_n\) and \(\mathcal{Q}'_1,\dots,\mathcal{Q}'_n\) such that \(\mathcal{Q}_i\cong\mathcal{Q}'_i\) for each \(i\) .
According to the proposition, if \(\mathcal{P}\) and \(\mathcal{P}\) are equidecomposable, then \(\text{area } \mathcal{P}=\text{area }\mathcal{P}'\) . A converse to this statement also holds; namely if two nondegenerate polygonal sets have equal area, then they are equidecomposable.
The last statement was proved by William Wallace, Farkas Bolyai and Paul Gerwien. The analogous statement in three dimensions, known as Hilbert’s third problem , is false; it was proved by Max Dehn.


1.3: Social Norms- Folkways, Mores, Taboo, and Laws
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- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
Social Control Exercise
Assignment : We rely on informal social control to influence people’s behavior, such as giving the stink eye, cold shoulder, or correcting someone’s behavior in order to ensure people conform. Think about a time when a parent, guardian, coach, employer, or teacher (agents of social control) used informal social control to respond to your behavior. What did the agent of informal social control do? Provide an example when informal social control was applied to another person. What were they doing and how was their behavior controlled through informal social control?
Example : Talking on the phone with a work-related matter and kids start bickering over slime. I am unable to put the phone down, so I relied on hand motions to show them it was unacceptable. There was no need to hang up or say anything at all. The eye actions indicated they were acting inappropriate and their behavior changed
Norms can be internalized, which would make an individual conform without external rewards or punishments. There are four types of social norms that can help inform people about behavior that is considered acceptable: folkways, mores, taboos, and law. Further, social norms can vary across time, cultures, place, and even sub-group. [1]
Think back to your first experiences in school and surely you can identify some folkways and mores learned. Folkways are behaviors that are learned and shared by a social group that we often refer to as “customs” in a group that are not morally significant, but they can be important for social acceptance. [2] Each group can develop different customs, but there can be customs that embraced at a larger, societal level.
Folkway Example
Imagine sitting in the college classroom with sixty other people around. As a professor who teaches early morning classes, it is always encouraged to eat if hungry. However, everyone must be considerate of those around them. You should not chew loudly. That would be considered rude, and it is against class ‘customs’ to do so. To make it worse, imagine burping without saying ‘excuse me.’ These would be folkway violations. Remember, this may not be disrespectful in all cultures, and it is very subjective.
Perhaps stricter than folkways are more because they can lead to a violation of what we view as moral and ethical behavior. Mores are norms of morality, or right and wrong, and if you break one it is often considered offensive to most people of a culture. [3] Sometimes a more violation can also be illegal, but other times it can just be offensive. If a more is not written down in legislation, it cannot get sanctioned by the criminal justice system. Other times it can be both illegal and morally wrong.
More Example
If one attended a funeral for a family member, no one would expect to see someone in bright pink clothes or a bikini. Most people are encouraged to wear black clothing out of respect. Although there may not be specific rules or laws that state expected attire to wear to a funeral, it would be against what most of American society views as right and wrong to attend a funeral in a bikini or be in hot pink leotards. It would be disrespectful to the individual people are mourning. Both mores and folkways are taught through socialization with various sources: family, friends, peers, schools, and more.
A taboo goes a step farther and is a very negative norm that should not get violated because people will be upset. Additionally, one may get excluded from the group or society. The nature and the degree of the taboo are in the mores. [4]
Taboo Example
A student once gave the example of a man in their neighborhood in Colorado that had multiple wives and also had ten different children from the women. In most of American culture, it is seen as unacceptable to have more than one spouse/partner. However, there are instances where having children with multiple people would not be seen as taboo. Specifically, if a man or woman remarries and then has another child with their new partner. However, again, this is more acceptable today than in the past because of the greater societal acceptance of divorce and remarriage.
If one is religious think of something taboo in that specific religion? How about a sports team in college? Band? Any ideas?
Lastly, and most important to the study of crime and criminal justice, our laws. Remember, a social norm is an obligation to society that can lead to sanctions if one violates them. Therefore, laws are social norms that have become formally inscribed at the state or federal level and can laws can result in formal punishment for violations, such as fines, incarceration, or even death. Laws are a form of social control that outlines rules, habits, and customs a society uses to enforce conformity to its norms.
Law Example
Let us go back to our example of having multiple wives for a moment. It is illegal, a violation of law, to have multiple wives in American culture. It has not always been this way, and it is not true in every country, but in the United States, it was viewed as so taboo, morally and ethically wrong, that there are laws that can punish people for marrying more than one person at a time. However, there may be some people that do not think it is wrong or some groups, but regardless, it is still illegal.
The following link is for Oregon statue ORS 163.515 Bigamy https://www.oregonlaws.org/ors/163.515
Remember our previous discussion on being the new person to Oregon and trying to figure out if it is allowed to be nude at an ultimate frisbee practice, but they do not feel morally or ethically wrong. The first thing one may do is go home and look up some rules and see if they are violating ultimate frisbee rules. Next, one may check out Oregon laws governing clothing to see if they are violating laws by being nude. In the end, one finds out that it is not ‘illegal,’ so you cannot call the cops, but you certainly did find a case in Eugene, Oregon that determined not wearing clothes can be a violation of rules on the college campus.
https://www.oregonlive.com/news/index.ssf/2009/04/uo_board_says_no_clothes_no_ul.html However, this is a recreational league, and it does not appear to have any formal rules established. Now one has to make a decision that is hard: Does one want to be part of a subculture that endorses nudity? Does this go against one’s morals and ethics? Alternatively, is one willing to be part of the team and encourage acceptance of a new norm? The criminal justice system cannot act for merely violating norms, but at times, what feels like a norm can lead to criminal justice involvement. For example, walk a town or city, and many may be found jaywalking because it may be safer, faster, or more accessible. A person can get a ticket for it in most communities because it is technically violating a law. That is the thing with the line between deviance, rule violations, and criminality—it does not allow mean we agree. There are many examples of laws that are not deviant and things that are deviant some subcultures may wish to be illegal. Most, but not all crimes are deviant, and not all deviant acts are criminal. The question then becomes: well, how then do we as a society decide who does and does not have the opportunity to make law?
Adam Ruins Everything: Why Jaywalking is a Crime? www.trutv.com/shows/adam-ruins-everything/videos/why-jaywalking-is-a-crime.html


16.3: Introduce Evidence
“Introduce Evidence” was written by Jennifer A. Yirinec.
Can the reader distinguish between your ideas and those of your sources?
You don’t want to take credit for the ideas of others (that would be plagiarism), and you certainly don’t want to give outside sources the credit for your own ideas (that would be a waste of your time and effort). So, as a writer, you should distinguish between your ideas and those of your sources before quoting, paraphrasing, or summarizing. In order to help the reader see who’s writing what, it’s important to introduce your evidence. Here are some helpful hints to consider when introducing your sourced material (note that while MLA style is used in these examples, you should use whatever formatting style is required by your instructor):
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When incorporating a source into your paper for the first time, reference not only the author’s full name (if provided) but also the title of the publication.
For instance, if I wanted to use a quote from Homi Bhabha’s The Location of Culture and I had not referenced this source yet in my paper, I would want to give it a full introduction:
In The Location of Culture , Homi Bhabha discusses the effect of mimicry upon the cultural hybrid, claiming that mimicry renders “the colonial subject . . . a ‘partial’ presence” (123).[1]
Before quoting, the author provides the reader with both the author (Homi Bhabha) and the title of the publication ( The Location of Culture ). That way, going forth, unless the author introduces a different book or article, the reader knows that all references to Bhabha come from The Location of Culture .
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When incorporating a source into your paper for the second time (or any other time following the initial introduction of that source), provide the reader with only the author’s last name.
For instance, if I’m still working with Bhabha’s The Location of Culture , I might do something like this:
As Bhabha writes, “[Mimicry] is a form of colonial discourse that . . . [exists] at the crossroads of what is known and permissible and that which though known must be kept concealed” (128).
Since you’ve already provided the reader with Bhabha’s full name (Homi Bhabha), there’s no need to give it again. All later references thus only require Bhabha’s last name. If pulling material from a different work of Bhabha’s, though, you’ll need to introduce the quote (or paraphrase or summary) by specifying this new title (though you’ll still only need to provide Bhabha’s last name).
Side note: Never refer to an author by his or her first name. Either reference the author by his or her full name or by his or her last name, depending upon whether or not you’ve previously mentioned the author’s full name in your piece of writing.
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When incorporating a source into your paper for the second time (or any other time following the initial introduction of that source), you may want to place the idea or direct quote within one of your sentences; if so, provide the author’s last name and a page number or page range for the referenced material in an in-text citation.
This method can be quite tricky, because you don’t want your quote to appear “dropped in.” Here are a few ideas about how to effectively incorporate quotes into sentences:
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You may choose to use a dash (two hyphens) or a colon to introduce the quoted material:
The child crosses this bar when he enters into language, as he can never again access the Real—a realm that now may “only [be] approach[ed] through language” (Price Herndl 53).
This can be tricky, depending upon the excerpt you’re using, because you may have to rework the wording within the quote to suit the sentence structure.
Side note: Whenever you change or add/delete anything—anything at all, even a capitalization—within a quote, you must bracket [ ] the change, addition, or deletion.
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You may choose to change the wording within a quote (and bracket accordingly) so that it works within your sentence structure:
The child crosses this bar when he enters into language, as he can never again access the Real, for “[he] can only approach it through language” (Price Herndl 53).
Note that the excerpted material must make sense within the context of your sentence, and the reader still must be able to distinguish between your ideas and those of your source.
[1] Bhabha, Homi.
The Location of Culture
. London: Routledge, 1994. Print.
[2] Price Herndl, Diane. “The Writing Cure: Charlotte Perkins Gilman, Anna O., and ‘Hysterical’ Writing.”
NWSA Journal
1.1 (1988): 52–74.
MLA International Bibliography
. Web. 30 April 2011.
- Introduce Evidence. Authored by : Jennifer A. Yirinec. Located at : http://writingcommons.org/index.php?option=com_content&view=article&id=440:introduce-evidence&catid=130:incorporate-evidence&Itemid=236 . Project : Writing Commons. License : CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives


12.13.4: Wearable
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The average smartphone user looks at his or her smartphone 150 times a day for functions such as messaging (23 times), phone calls (22), listening to music (13), and social media (9). [9] Many of these functions would be much better served if the technology was worn on, or even physically integrated into, our bodies. This technology is known as a “wearable.”
Wearables have been around for a long time, with technologies such as hearing aids and, later, bluetooth earpieces. But now, we are seeing an explosion of new wearable technologies. Perhaps the best known of these is Google Glass, an augmented reality device that you wear over your eyes like a pair of eyeglasses. Visible only to you, Google Glass will project images into your field of vision based on your context and voice commands. You can find out much more about Google Glass at http://www.google.com/glass/start/ .
Another class of wearables are those related to health care. The UP by Jawbone consists of a wristband and an app that tracks how you sleep, move, and eat, then helps you use that information to feel your best. [10] It can be used to track your sleep patterns, moods, eating patterns, and other aspects of daily life, and then report back to you via an app on your smartphone or tablet. As our population ages and technology continues to evolve, there will be a large increase in wearables like this.


10.3: Music in the Baroque Era
Introduction
The term b aroque is also used to designate the style of music composed during a period that overlaps with that of baroque art, but usually encompasses a slightly later period.
It is a still-debated question as to what extent baroque music shares aesthetic principles with the visual and literary arts of the baroque period. A fairly clear, shared element is a love of ornamentation, and it is perhaps significant that the role of ornament was greatly diminished in both music and architecture as the baroque gave way to the classical period.
The application of the term “baroque” to music is a relatively recent development, although it has recently been pointed out that the first use of the word “baroque” in criticism of any of the arts related to music, in an anonymous, satirical review of the première in October 1733 of Rameau’s Hippolyte et Aricie, printed in the Mercure de France in May 1734. The critic implied that the novelty in this opera was “du barocque,” complaining that the music lacked coherent melody, was filled with unremitting dissonances, constantly changed key and meter, and speedily ran through every compositional device.
However this was an isolated reference, and consistent use was only begun in 1919, by Curt Sachs, and it was not until 1940 that it was first used in English (in an article published by Manfred Bukofzer).
Many musical forms were born in that era, like the concerto and sinfonia. Forms such as the sonata, cantataand oratorio flourished. Also, opera was born out of the experimentation of the Florentine Camerata, the creators of monody, who attempted to recreate the theatrical arts of the Ancient Greeks. An important technique used in baroque music was the use of ground bass, a repeated bass line. Dido’s Lament by Henry Purcell is a famous example of this technique.
Baroque Composers and Their Well-Known Works
- Giovanni Gabrieli (c. 1554/1557–1612) Sonata pian’ e forte (1597), In Ecclesiis (from Symphoniae sacrae book 2, 1615)
- Claudio Monteverdi (1567–1643), L’Orfeo, favola in musica (1610)
- Heinrich Schütz (1585–1672), Musikalische Exequien (1629, 1647, 1650)
- Francesco Cavalli (1602–1676), L’Egisto (1643), Ercole amante (1662), Scipione affricano (1664)
- Jean-Baptiste Lully (1632–1687), Armide (1686)
- Marc-Antoine Charpentier (1643–1704), Te Deum (1688-1698)
- Heinrich Ignaz Franz Biber (1644–1704), Mystery Sonatas (1681)
- John Blow (1649–1708), Venus and Adonis (1680–1687)
- Johann Pachelbel (1653–1706), Canon in D (1680)
- Arcangelo Corelli (1653–1713), 12 concerti grossi, Op. 6 (1714)
- Marin Marais (1656–1728), Sonnerie de Ste-Geneviève du Mont-de-Paris (1723)
- Henry Purcell (1659–1695), Dido and Aeneas (1688)
- Alessandro Scarlatti (1660–1725), L’honestà negli amori (1680), Il Pompeo (1683), Mitridate Eupatore (1707)
- François Couperin (1668–1733), Les barricades mystérieuses (1717)
- Tomaso Albinoni (1671–1751), Didone abbandonata (1724)
- Antonio Vivaldi (1678–1741), The Four Seasons (1723)
- Jan Dismas Zelenka (1679-1745), Il Serpente di Bronzo (1730), Missa Sanctissimae Trinitatis (1736)
- Georg Philipp Telemann (1681–1767), Der Tag des Gerichts (1762)
- Johann David Heinichen (1683–1729)
- Jean-Philippe Rameau (1683–1764), Dardanus (1739)
- George Frideric Handel (1685–1759), Water Music (1717), Messiah (1741)
- Domenico Scarlatti (1685–1757), Sonatas for harpsichord
- Johann Sebastian Bach (1685–1750), Toccata and Fugue in D minor (1703–1707), Brandenburg Concertos (1721), St Matthew Passion (1727)
- Nicola Porpora (1686–1768), Semiramide riconosciuta (1729)
- Giovanni Battista Pergolesi (1710–1736), Stabat Mater (1736)
Contributors and Attributions
- Baroque. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Baroque . License : CC BY-SA: Attribution-ShareAlike


3.6: Viral Mediated Delivery of Genes to Neurons
There are a number of ways to deliver DNA (or other genetic information) to neurons including transfection, electroporation, biolistic delivery, and nanoparticles, but within an intact biological system like the brain is challenging. Luckily, neurons are very easily infected by viruses (see Unit 1). Neurobiologists will therefore package genetic material that they want to be expressed within specific groups of neurons inside different types of viruses (Figure \(\PageIndex{1}\).).
Figure \(\PageIndex{1}\).
Schematic overview of how viruses (i.e. adenovirus) can be used to deliver recombinant genetic material to neurons, or other cell types within the nervous system. Steps include viral binding to cell membrane, endosomal packaging and breakdown, delivery and integration of vector into host DNA, and ending with the expression of the desired protein.
In fact, as molecular neurobiologists, we often have a number of different viral vectors that we can use to our benefit. Some viruses for example package only a small amount of genetic material (AAV for example) while others like HSV will be able to package up to 150 kb worth of genetic material (and this is a lot) into the virus. Speed of expression and how long the expression of the recombinant genetic material will persist for, are often considerations on the choice of viral vector (see Table \(\PageIndex{1}\)).
| Table \(\PageIndex{1}\). Properties of recombinant viral vectors useful for gene delivery in the adult nervous system | |||
|---|---|---|---|
| Adeno-Associated Virus (AAV) | Lentivirus | Herpes Simplex Virus (HSV) Amplicon | |
| Genetic material | Single-stranded DNA | RNA | Double-stranded DNA |
| Capacity for genetic material | ~5 kilobases | ~8 kilobases | ~150 kilobases |
| Speed of expression | Weeks | Weeks | Days |
| Duration of expression | Years | Years | Weeks to months, but elements can be added for persistent expression |
One technical consideration that is often overlooked – how are viruses containing the gene of interest that we hope to express in neurons generated? Viruses aren’t truly alive so how does this work? We often use a cell line like the HEK293 cell which is a non-neuronal cell line. We transfect 3 separate plasmids into the HEK293 cells in culture. 2 of the plasmids are viral (pVSV-G and packaging plasmids for example for lentiviruses, and the last one is the construct that we want to specifically deliver. Figure \(\PageIndex{2}\). shows the workflow for production of lentiviruses (upper panel) and AAV viruses (lower panel). In both cases, viral particles are released from the transfected HEK293 cells and the virus is collected from the cells and spun on a gradient using ultracentrifugation and a final purification step. The purified fluid then contains live virus that can infect neurons.
Figure \(\PageIndex{2}\).
Lentivirus (upper panel) – Part of the retroviridae family (viral sizes are 80-100 nm diameter) derived from HIV-1 virus. To produce lentiviruses with the gene of interest as the lentiviral DNA construct, first transfect cells with a packaging plasmid and the envelope vector (VSVG).
Adeno Associated Virus (AAV)
(lower panel) – Member of the parvoviridae family (20 nm diameter). To produce AAV, package a gene of interest into the AAV-ITR vector and transfect cells with a Helper vector and the Rep/Cap DNA integration vector.


1.9.2: Entropy- Dependence on Temperature and Pressure
The volume of a given closed system at equilibrium prepared using \(\mathrm{n}_{1}\) moles of solvent (water) and \(\mathrm{n}_{j}\) moles of solute-\(j\) is defined by the set of independent variables shown in equation (a).
\[\mathrm{V}=\mathrm{V}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \mathrm{A}=0, \xi^{\mathrm{eq}}\right] \nonumber \]
The same set of independent variables defines the entropy \(\mathrm{S}\).
\[\mathrm{S}=\mathrm{S}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \mathrm{A}=0, \xi^{\mathrm{eq}}\right] \nonumber \]
We envisage that the system is displaced by a change in pressure along a path where the system remains at equilibrium (i.e. \(\mathrm{A} = 0\)) and the volume remains the same as defined by equation (a). In a plot of entropy against \(\mathrm{p}\), the gradient of the plot at the point defined by the independent variables, \(\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \mathrm{A}=0, \boldsymbol{\xi}^{\mathrm{eq}}\right]\) is given by equation (c).
Isochoric
\[\left(\frac{\partial S}{\partial p}\right)_{V, A=0} \nonumber \]
The set of derivatives is completed by the following partial derivatives.
Isothermal
\[\left(\frac{\partial \mathrm{S}}{\partial \mathrm{p}}\right)_{\mathrm{T}, \mathrm{A}=0} \nonumber \]
Isobaric
\[\left(\frac{\partial S}{\partial T}\right)_{p, A=0} \nonumber \]


3.4: Reliability of a measurement
- Explain the distinction between the mean value of a series of measurements and the population mean .
- What quantity besides the mean value do we need in order to evaluate the quality of a series of measurements?
- Explain the meaning and significance of the dispersion of the mean, and state what factor controls it.
- Explain the distinction between determinate and indeterminate error.
- Describe the purpose process of using a blank and control value when making a series of measurements. What principal assumption must be made in doing this?
In this day of pervasive media, we are continually being bombarded with data of all kinds— public opinion polls, advertising hype, government reports and statements by politicians. Very frequently, the purveyors of this information are hoping to “sell” us on a product, an idea, or a way of thinking about someone or something, and in doing so, they are all too often willing to take advantage of the average person’s inability to make informed judgments about the reliability of the data, especially when it is presented in a particular context (popularly known as “spin”.) In Science, we do not have this option: we collect data and make measurements in order to get closer to whatever “truth” we are seeking, but it's not really "science" until others can have confidence in the reliability of our measurements.
Attributes of a measurement
The kinds of measurements we will deal with here are those in which a number of separate observations are made on individual samples taken from a larger population .
Population , when used in a statistical context, does not necessarily refer to people, but rather to the set of all members of the group of objects under consideration.
For example, you might wish to determine the amount of nicotine in a manufacturing run of one million cigarettes. Because no two cigarettes are likely to be exactly identical, and even if they were, random error would cause each analysis to yield a different result, the best you can do would be to test a representative sample of, say, twenty to one hundred cigarettes. You take the average (mean) of these values, and are then faced with the need to estimate how closely this sample mean is likely to approximate the population mean. The latter is the “true value” we can never know; what we can do, however, is make a reasonable estimate of the likelihood that the sample mean does not differ from the population mean by more than a certain amount.
The attributes we can assign to an individual set of measurements of some quantity x within a population are listed below. It is important that you learn the meaning of these terms:
Number of measurements
This quantity is usually represented by n .
Mean
The mean value x m (commonly known as the average ), defined as
Median
The median value, which we will not deal with in this brief presentation, is essentially the one in the middle of the list resulting from writing the individual values in order of increasing or decreasing magnitude.
Range
The range is the difference between the largest and smallest value in the set.
Problem example:
Find the mean value and range of the set of measurements depicted here.
Solution:
This set contains 8 measurements. The range is
(10.7 – 10.3) = 0.4, and the mean value is
6 More than one answer: dispersion of the mean
"Dispersion" means "spread-outedness". If you make a few measurements and average them, you get a certain value for the mean. But if you make another set of measurements, the mean of these will likely be different. The greater the difference between the means, the greater is their dispersion .
Suppose that instead of taking the five measurements as in the above example, we had made only two observations which, by chance, yielded the values that are highlighted here. This would result in a sample mean of 10.45. Of course, any number of other pairs of values could equally well have been observed, including multiple occurances of any single value, such as 10.6.
Shown at the left are the results of two possible pairs of observations, each giving rise to its own sample mean. Assuming that all observations are subject only to random error, it is easy to see that successive pairs of experiments could yield many other sample means. The range of possible sample means is known as the dispersion of the mean.
It is clear that both of the two sample means cannot correspond to the population mean, whose value we are really trying to discover. In fact, it is quite likely that neither sample mean is the “correct” one in this sense. It is a fundamental principle of statistics, however, that the more observations we make in order to obtain a sample mean, the smaller will be the dispersion of the sample means that result from repeated sets of the same number of observations. (This is important; please read the preceding sentence at least three times to make sure you understand it!)
How the dispersion of the mean depends on the number of observations
The difference between the sample mean (blue) and the population mean (the "true value", green) is the error of the measurement. It is clear that this error diminishes as the number of observations is made larger.
What is stated above is just another way of saying what you probably already know: larger samples produce more reliable results. This is the same principle that tells us that flipping a coin 100 times will be more likely to yield a 50:50 ratio of heads to tails than will be found if only ten flips (observations) are made.
The reason for this inverse relation between the sample size and the dispersion of the mean is that if the factors giving rise to the different observed values are truly random, then the more samples we observe, the more likely will these errors cancel out. It turns out that if the errors are truly random, then as you plot the number of occurrences of each value, the results begin to trace out a very special kind of curve.
The significance of this is much greater than you might at first think, because the G aussian curve has special mathematical properties that we can exploit, through the methods of statistics, to obtain some very useful information about the reliability of our data. This will be the major topic of the next lesson in this set.
For now, however, we need to establish some important principles regarding measurement error.
7 Systematic error
The scatter in measured results that we have been discussing arises from random variations in the myriad of events that affect the observed value, and over which the experimenter has no or only limited control. If we are trying to determine the properties of a collection of objects (nicotine content of cigarettes or lifetimes of lamp bulbs), then random variations between individual members of the population are an ever-present factor. This type of error is called random or indeterminate error , and it is the only kind we can deal with directly by means of statistics.
There is, however, another type of error that can afflict the measuring process. It is known as systematic or determinate error , and its effect is to shift an entire set of data points by a constant amount. Systematic error, unlike random error, is not apparent in the data itself, and must be explicitly looked for in the design of the experiment.
One common source of systematic error is failure to use a reliable measuring scale, or to misread a scale. For example, you might be measuring the length of an object with a ruler whose left end is worn, or you could misread the volume of liquid in a burette by looking at the top of the meniscus rather than at its bottom, or not having your eye level with the object being viewed against the scale, thus introducing parallax error.
8 Blanks and controls
Many kinds of measurements are made by devices that produce a response of some kind (often an electric current) that is directly proportional to the quantity being measured. For example, you might determine the amount of dissolved iron in a solution by adding a reagent that reacts with the iron to give a red color, which you measure by observing the intensity of green light that passes through a fixed thickness of the solution. In a case such as this, it is common practice to make two additional kinds of measurements:
One measurement is done on a solution as similar to the unknowns as possible except that it contains no iron at all. This sample is called the blank . You adjust a control on the photometer to set its reading to zero when examining the blank.
The other measurement is made on a sample containing a known concentration of iron; this is usually called the control . You adjust the sensitivity of the photometer to produce a reading of some arbitrary value (50, say) with the control solution. Assuming the photometer reading is directly proportional to the concentration of iron in the sample (this might also have to be checked, in which case a calibration curve must be constructed), the photometer reading can then be converted into iron concentration by simple proportion.
9 The standard deviation
Consider the two pairs of observations depicted here:
Notice that the sample means happen to have the same value of “40” (pure luck!), but the difference in the precisions of the two measurements makes it obvious that the set shown on the right is more reliable. How can we express this fact in a succinct way? We might say that one experiment yields a value of 40 ±20, and the other 40 ±5. Although this information might be useful for some purposes, it is unable to provide an answer to such questions as "how likely would another independent set of measurements yield a mean value within a certain range of values?" The answer to this question is perhaps the most meaningful way of assessing the "quality" or reliability of experimental data, but obtaining such an answer requires that we employ some formal statistics.
Deviations from the mean
We begin by looking at the differences between the sample mean and the individual data values used to compute the mean. These differences are known as deviations from the mean , x i – x m . These values are depicted below; note that the only difference from the plots above is placement of the mean value at 0 on the horizontal axis.
The variance and its square root
Next, we need to find the average of these deviations. Taking a simple average, however, will not distinguish between these two particular sets of data, because both deviations average out to zero. We therefore take the average of the squares of the deviations (squaring makes the signs of the deviations disappear so they cannot cancel out). Also, we compute the average by dividing by one less than the number of measurements, that is, by n –1 rather than by n . The result, usually denoted by S 2 , is known as the variance :
Finally, we take the square root of the variance to obtain the standard deviation S :
Problem example: Calculate the variance and standard deviation for each of the two data sets shown above.
Solution: Substitution into the two formulas yields the following results:
| data values | 20, 60 | 35,45 |
| sample mean | 40 | 40 |
| variance S 2 | ||
| standard deviation | 28 | 7.1 |
Comment: Notice how the contrasting values of S reflect the difference in the precisions of the two data sets— something that is entirely lost if only the two means are considered.
Now that we have developed the very important concept of standard deviation, we can employ it in the next section to answer practical questions about how to interpret the results of a measurement.