# 10.7: Chapter 10 Problems

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$$\newcommand{\id}{^{\text{id}}} % ideal$$
$$\newcommand{\rf}{^{\text{ref}}} % reference state$$
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$$\newcommand{\K}{\units{K}} % kelvins$$
$$\newcommand{\degC}{^\circ\text{C}} % degrees Celsius$$
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$$\newcommand{\V}{\units{V}} % volts$$
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$$\newcommand{\m}{_{\text{m}}} % subscript m for molar quantity$$
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$$\newcommand{\Cpm}{C_{p,\text{m}}} % molar heat capacity at const.p$$
$$\newcommand{\kT}{\kappa_T} % isothermal compressibility$$
$$\newcommand{\A}{_{\text{A}}} % subscript A for solvent or state A$$
$$\newcommand{\B}{_{\text{B}}} % subscript B for solute or state B$$
$$\newcommand{\bd}{_{\text{b}}} % subscript b for boundary or boiling point$$
$$\newcommand{\C}{_{\text{C}}} % subscript C$$
$$\newcommand{\f}{_{\text{f}}} % subscript f for freezing point$$
$$\newcommand{\mA}{_{\text{m},\text{A}}} % subscript m,A (m=molar)$$
$$\newcommand{\mB}{_{\text{m},\text{B}}} % subscript m,B (m=molar)$$
$$\newcommand{\mi}{_{\text{m},i}} % subscript m,i (m=molar)$$
$$\newcommand{\fA}{_{\text{f},\text{A}}} % subscript f,A (for fr. pt.)$$
$$\newcommand{\fB}{_{\text{f},\text{B}}} % subscript f,B (for fr. pt.)$$
$$\newcommand{\xbB}{_{x,\text{B}}} % x basis, B$$
$$\newcommand{\xbC}{_{x,\text{C}}} % x basis, C$$
$$\newcommand{\cbB}{_{c,\text{B}}} % c basis, B$$
$$\newcommand{\mbB}{_{m,\text{B}}} % m basis, B$$
$$\newcommand{\kHi}{k_{\text{H},i}} % Henry's law constant, x basis, i$$
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$$\newcommand{\rev}{\subs{rev}} % reversible$$
$$\newcommand{\irr}{\subs{irr}} % irreversible$$
$$\newcommand{\fric}{\subs{fric}} % friction$$
$$\newcommand{\diss}{\subs{diss}} % dissipation$$
$$\newcommand{\el}{\subs{el}} % electrical$$
$$\newcommand{\cell}{\subs{cell}} % cell$$
$$\newcommand{\As}{A\subs{s}} % surface area$$
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$$\newcommand{\pha}{\alpha} % phase alpha$$
$$\newcommand{\phb}{\beta} % phase beta$$
$$\newcommand{\phg}{\gamma} % phase gamma$$
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$$\newcommand{\bph}{^{\beta}} % beta phase superscript$$
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$$\newcommand{\bpht}{\small\bph} % beta phase tiny superscript$$
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$$\newcommand{\dBar}{\mathop{}\!\mathrm{d}\hspace-.3em\raise1.05ex{\Rule{.8ex}{.125ex}{0ex}}} % inexact differential$$
$$\newcommand{\dq}{\dBar q} % heat differential$$
$$\newcommand{\dw}{\dBar w} % work differential$$
$$\newcommand{\dQ}{\dBar Q} % infinitesimal charge$$
$$\newcommand{\dx}{\dif\hspace{0.05em} x} % dx$$
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$$\newcommand{\G}{\varGamma} % activity coefficient of a reference state (pressure factor)$$
$$\newcommand{\ecp}{\widetilde{\mu}} % electrochemical or total potential$$
$$\newcommand{\Eeq}{E\subs{cell, eq}} % equilibrium cell potential$$
$$\newcommand{\Ej}{E\subs{j}} % liquid junction potential$$
$$\newcommand{\mue}{\mu\subs{e}} % electron chemical potential$$
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$$\newcommand{\R}{8.3145\units{J\,K\per\,mol\per}} % gas constant value$$
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An underlined problem number or problem-part letter indicates that the numerical answer appears in Appendix I.

10.1
The mean ionic activity coefficient of NaCl in a 0.100 molal aqueous solution at $$298.15\K$$ has been evaluated with measurements of equilibrium cell potentials, with the result $$\ln\g_{\pm}=-0.2505$$ (R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 2nd edition, Butterworths, London, 1959, Table 9.3). Use this value in Eq. 10.6.9, together with the values of osmotic coefficients in Table 10.1, to evaluate $$\g_{\pm}$$ at each of the molalities shown in the table; then plot $$\g_{\pm}$$ as a function of $$m\B$$.

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