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Appendix I: Answers to Selected Problems

  • Page ID
    23781
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     \( \newcommand{\R}{8.3145\units{J$\,$K$\per\,$mol$\per$}}     % gas constant value\)
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    3.3(b)
    \(q = -w = 1.00\timesten{5}\units{J}\)

    3.4(c)
    \(w=1.99\timesten{3}\units{J}\), \(q=-1.99\timesten{3}\units{J}\).

    3.5
    \(0.0079\%\)

    3.6(c)
    \(V_2 \ra nRV_1/(C_V+nR)\), \(T_2 \ra \infty\). For \(C_V=(3/2)nR\), \(V_2/V_1 \ra 0.4\).

    3.11
    \(9.58\timesten{3}\units{s}\) (\(2\units{hr}\) \(40\units{min}\))

    4.4
    \(\Del S=0.054\units{J K\(^{-1}\)}\)

    4.5
    \(\Del S = 549\units{J K\(^{-1}\)}\) for both processes; \(\int\!\dq/T\subs{ext} = 333\units{J K\(^{-1}\)}\) and \(0\).

    5.4(a)
    \( \D S = nR\ln\left[cT^{3/2}\left(\frac{V}{n}-b\right)\right] + \left(\frac{5}{2}\right)nR \)

    5.5(a)
    \(q=0\), \(w=1.50\timesten{4}\units{J}\), \(\Del U=1.50\timesten{4}\units{J}\), \(\Del H=2.00\timesten{4}\units{J}\)

    5.5(c)
    \(\Del S=66.7\units{J K\(^{-1}\)}\)

    6.1
    \(S\m \approx 151.6\units{J K\(^{-1}\) mol\(^{-1}\)}\)

    7.6(a)
    \(\alpha=8.519\timesten{-4}\units{K\(^{-1}\)}\)
    \(\kappa_t=4.671\timesten{-5}\units{bar\(^{-1}\)}\)
    \(\pd{p}{T}{V}=18.24\units{bar K\(^{-1}\)}\)
    \(\pd{U}{V}{T}=5437\br\)

    7.6(b)
    \(\Del p \approx 1.8\br\)

    7.7(b)
    \(\pd{\Cpm}{p}{T}=-4.210\timesten{-8}\units{J K\(^{-1}\) Pa\(^{-1}\) mol\(^{-1}\)}\)

    7.8(b)
    \(8\timesten{-4}\units{K\(^{-1}\)}\)

    7.11
    \(5.001\timesten{3}\units{J}\)

    7.12
    \(\Del H = 2.27\timesten{4}\units{J}\), \(\Del S = 43.6\units{J K\(^{-1}\)}\)

    7.13(a)
    \(\Cpm\st=42.3\units{J K\(^{-1}\) mol\(^{-1}\)}\)

    7.13(b)
    \(\Cpm \approx 52.0\units{J K\(^{-1}\) mol\(^{-1}\)}\)

    7.14(a)
    \(2.56\units{J K\(^{-1}\) g\(^{-1}\)}\)

    7.15(b)
    \(\fug = 17.4\br\)

    7.16(a)
    \(\phi=0.739\), \(\fug=148\br\)

    7.16(b)
    \(B = -7.28\timesten{-5}\units{m\(^3\) mol\(^{-1}\)}\)

    8.2(a)
    \(S\m\st\liquid =253.6\units{J K\(^{-1}\) mol\(^{-1}\)}\)

    8.2(b)
    \(\Delsub{vap}S\st=88.6\units{J K\(^{-1}\) mol\(^{-1}\)}\), \(\Delsub{vap}H\st=2.748\timesten{4}\units{J mol\(^{-1}\)}\)

    8.4
    \(4.5\timesten{-3}\br\)

    8.5
    \(19\units{J mol\(^{-1}\)}\)

    8.6(a)
    \(352.82\K\)

    8.6(b)
    \(3.4154\timesten{4}\units{J mol\(^{-1}\)}\)

    8.7(a)
    \(3.62\timesten{3}\units{Pa K\(^{-1}\)}\)

    8.7(b)
    \(3.56\timesten{3}\units{Pa K\(^{-1}\)}\)

    8.7(c)
    \(99.60\units{\(\degC\)}\)

    8.8(b)
    \(\Delsub{vap}H\st = 4.084\timesten{4}\units{J mol\(^{-1}\)}\)

    8.9
    \(0.93\units{mol}\)

    9.2(b)
    \(V\A(x\B=0.5) \approx 125.13\units{cm\(^3\) mol\(^{-1}\)}\)
    \(V\B(x\B=0.5)\approx 158.01\units{cm\(^3\) mol\(^{-1}\)}\)
    \(V\B^{\infty} \approx 157.15\units{cm\(^3\) mol\(^{-1}\)}\)

    9.4
    real gas: \(p=1.9743\br\)
    ideal gas: \(p=1.9832\br\)

    9.5(a)
    \(x\subs{N\(_2\)} = 8.83\timesten{-6}\)
    \(x\subs{O\(_2\)} = 4.65\timesten{-6}\)
    \(y\subs{N\(_2\)} = 0.763\)
    \(y\subs{O\(_2\)} = 0.205\)

    9.5(b)
    \(x\subs{N\(_2\)} = 9.85\timesten{-6}\)
    \(x\subs{O\(_2\)} = 2.65\timesten{-6}\)
    \(y\subs{N\(_2\)} = 0.851\)
    \(y\subs{O\(_2\)} = 0.117\)

    9.7(b)
    \(\fug\A=0.03167\br\), \(\fug\A=0.03040\br\)

    9.8(a)
    In the mixture of composition \(x\A=0.9782\), the activity coefficient is \(\g\B \approx 11.5\).

    9.9(d)
    \(k\subs{H,A} \approx 680\units{kPa}\)

    9.11
    Values for \(m\B/m\st=20\): \(\g\A=1.026\), \(\g\mbB=0.526\); the limiting slopes are \(\dif\g\A/\dif(m\B/m\st)=0\), \(\dif\g\mbB/\dif(m\B/m\st)=-0.09\)

    9.13
    \(p\subs{N\(_2\)} = 0.235\br\)
    \(y\subs{N\(_2\)} = 0.815\)
    \(p\subs{O\(_2\)} = 0.0532\br\)
    \(y\subs{O\(_2\)} = 0.185\)
    \(p=0.288\br\)

    9.14(b)
    \(h=1.2\units{m}\)

    9.15(a)
    \(p(7.20\units{cm})-p(6.95\units{cm})=1.2\br\)

    9.15(b)
    \(M\B=187\units{kg mol\(^{-1}\)}\)
    mass binding ratio \({} = 1.37\)

    10.2
    \( \g{\pm} = 0.392 \)

    11.1
    \(\Delsub{r}H\st = -63.94\units{kJ mol\(^{-1}\)}\)
    \(K=4.41\timesten{-2}\)

    11.2(b)
    \(\Delsub{f}H\st\): no change
    \(\Delsub{f}S\st\): subtract \(0.219\units{J K\(^{-1}\) mol\(^{-1}\)}\)
    \(\Delsub{f}G\st\): add \(65\units{J mol\(^{-1}\)}\)

    11.3
    \(p(298.15\K)=2.6\timesten{-6}\br\)
    \(p(273.15\K) = 2.7\timesten{-7}\br\)

    11.4(a)
    \(-240.34\units{kJ mol\(^{-1}\)}\), \(-470.36\units{kJ mol\(^{-1}\)}\), \(-230.02\units{kJ mol\(^{-1}\)}\)

    11.4(b)
    \(-465.43\units{kJ mol\(^{-1}\)}\)

    11.4(c)
    \(-39.82\units{kJ mol\(^{-1}\)}\)

    11.5
    \(\Del H = 0.92\units{kJ}\)

    11.6
    \(L\A=-0.405\units{J mol\(^{-1}\)}\)
    \(L\B=0.810\units{kJ mol\(^{-1}\)}\)

    11.7(a)
    State 1:
    \(n\subs{C\(_6\)H\(_{14}\)}=7.822\timesten{-3}\mol\)
    \(n\subs{H\(_2\)O}=0.05560\mol\)
    amount of O\(_2\) consumed: \(0.07431\mol\)
    State 2:
    \(n\subs{H\(_2\)O}=0.11035\mol\)
    \(n\subs{CO\(_2\)}=0.04693\mol\)
    \tx{mass of H\(_2\)O}=\(1.9880\units{g}\)

    11.7(b)
    \(V\m\tx{(C\(_6\)H\(_{14}\))} = 131.61\units{cm\(^3\) mol\(^{-1}\)}\)
    \(V\m\tx{(H\(_2\)O)} = 18.070\units{cm\(^3\) mol\(^{-1}\)}\)

    11.7(c)
    State 1: \(V\tx{(C\(_6\)H\(_{14}\))} = 1.029\units{cm\(^3\)}\)
    \(V\tx{(H\(_2\)O)} = 1.005\units{cm\(^3\)}\)
    \(V\sups{g} = 348.0\units{cm\(^3\)}\)
    State 2:
    \(V\tx{(H\(_2\)O)} = 1.994\units{cm\(^3\)}\)
    \(V\sups{g} = 348.0\units{cm\(^3\)}\)

    11.7(d)
    State 1:
    \(n\subs{O\(_2\)}=0.429\mol\)
    State 2:
    \(n\subs{O\(_2\)}=0.355\mol\)
    \(y\subs{O\(_2\)}=0.883\)
    \(y\subs{CO\(_2\)}=0.117\)

    11.7(e)
    State 2:
    \(p_2 = 27.9\br\)
    \(p\subs{O\(_2\)} = 24.6\br\)
    \(p\subs{CO\(_2\)} = 3.26\br\)

    11.7(f)
    \(\fug\subs{H\(_2\)O}(0.03169\br ) = 0.03164\br\)
    State 1: \(\fug\subs{H\(_2\)O} = 0.03234\br\)
    State 2: \(\fug\subs{H\(_2\)O} = 0.03229\br\)

    11.7(g)
    State 1:
    \(\phi\subs{H\(_2\)O}=0.925\)
    \(\phi\subs{O\(_2\)}=0.981\)
    \(\fug\subs{O\(_2\)}= 29.4\br\)
    State 2:
    \(\phi\subs{H\(_2\)O}=0.896\)
    \(\phi\subs{O\(_2\)}=0.983\)
    \(\phi\subs{CO\(_2\)}=0.910\)
    \(\fug\subs{O\(_2\)}=24.2\br\)
    \(\fug\subs{CO\(_2\)}=2.97\br\)

    11.7(h)
    State 1:
    \(n\subs{H\(_2\)O}\sups{g}=5.00\timesten{-4}\mol\)
    \(n\subs{H\(_2\)O}\sups{l} =0.05510\mol\)
    State 2:
    \(n\subs{H\(_2\)O}\sups{g}=5.19\timesten{-4}\mol\)
    \(n\subs{H\(_2\)O}\sups{l} =0.10983\mol\)

    11.7(i)
    State 1:
    \(k_{m,\tx{O\(_2\)}}= 825\units{bar kg mol\(^{-1}\)}\)
    \(n\subs{O\(_2\)} = 3.57\timesten{-5}\mol\)
    State 2:
    \(k_{m,\tx{O\(_2\)}}= 823\units{bar kg mol\(^{-1}\)}\)
    \(k_{m,\tx{CO\(_2\)}}= 30.8\units{bar kg mol\(^{-1}\)}\)
    \(n\subs{O\(_2\)} = 5.85\timesten{-5}\mol\)
    \(n\subs{CO\(_2\)} = 1.92\timesten{-4}\mol\)

    11.7(j)
    H\(_2\)O vaporization: \(\Del U = +20.8\units{J}\)
    H\(_2\)O condensation: \(\Del U = -21.6\units{J}\)

    11.7(k)
    O\(_2\) dissolution: \(\Del U = -0.35\units{J}\)
    O\(_2\) desolution: \(\Del U = 0.57\units{J}\)
    CO\(_2\) desolution: \(\Del U = 3.32\units{J}\)

    11.7(l)
    C\(_6\)H\(_{14}\)(l) compression: \(\Del U=-1.226\units{J}\)
    solution compression: \(\Del U=-0.225\units{J}\)
    solution decompression: \(\Del U=0.414\units{J}\)

    11.7(m)
    O\(_2\) compression: \(\Del U=-81\units{J}\)
    gas mixture: \(\dif B/\dif T = 0.26\timesten{-6}\units{m\(^3\)K\(^{-1}\) mol\(^{-1}\)}\)
    gas mixture expansion: \(\Del U=87\units{J}\)

    11.7(n)
    \(\Del U = 8\units{J}\)

    11.7(o)
    \(\Delsub{c}U\st = -4154.4\units{kJ mol\(^{-1}\)}\)

    11.7(p)
    \(\Delsub{c}H\st = -4163.1\units{kJ mol\(^{-1}\)}\)

    11.8
    \(\Delsub{f}H\st = -198.8\units{kJ mol\(^{-1}\)}\)

    11.9
    \(T_2=2272\K\)

    11.10
    \(p\tx{(O\(_2\))} =2.55\timesten{-5}\br\)

    11.11(a)
    \(K=3.5\timesten{41}\)

    11.11(b)
    \(p\subs{H\(_2\)}=2.8\timesten{-42}\br\)
    \(N\subs{H\(_2\)}=6.9\timesten{-17}\)

    11.11(c)
    \(t=22\units{s}\)

    11.12(b)
    \(p \approx 1.5\timesten{4}\br\)

    11.13(c)
    \(K=0.15\)

    12.1(b)
    \(T=1168\K\)
    \(\Delsub{r}H\st=1.64\timesten{5}\units{J mol\(^{-1}\)}\)

    12.4
    \(K\subs{f}=1.860\units{K kg mol\(^{-1}\)}\)
    \(K\bd=0.5118\units{K kg mol\(^{-1}\)}\)

    12.5
    \(M\B \approx 5.6\timesten{4}\units{g mol\(^{-1}\)}\)

    12.6
    \(\Delsub{sol,B}H\st/\tx{kJ mol\(^{-1}\)}=-3.06, 0, 6.35\)
    \(\Delsub{sol,B}S\st/\tx{J K\(^{-1}\) mol\(^{-1}\)} = -121.0, -110.2, -88.4\)

    12.7(a)
    \( m_+\aph = m_-\aph = 1.20\timesten{-3}\units{mol kg\(^{-1}\)} \)
    \( m_+\bph = 1.80\timesten{-3}\units{mol kg\(^{-1}\)} \)
    \( m_-\bph = 0.80\timesten{-3}\units{mol kg\(^{-1}\)} \)
    \( m\subs{P} = 2.00\timesten{-6}\units{mol kg\(^{-1}\)} \)

    12.8(a)
    \(p\sups{l} =2.44\br\)

    12.8(b)
    \(\fug(2.44\br)-\fug(1.00\br)=3.4\timesten{-5}\br\)

    12.10(a)
    \(x\B=1.8\timesten{-7}\)
    \(m\B = 1.0\timesten{-5}\units{mol kg\(^{-1}\)}\)

    12.10(b)
    \(\Delsub{sol,B}H\st = -1.99\timesten{4}\units{J mol\(^{-1}\)}\)

    12.10(c)
    \(K=4.4\timesten{-7}\)
    \(\Delsub{r}H\st=9.3\units{kJ mol\(^{-1}\)}\)

    12.13(a)
    \(p=92399.6\Pa\), \(y\B=0.965724\)

    12.13(b)
    \(\phi\A=0.995801\)

    12.13(c)
    \(\fug\A = 3164.47\Pa\)

    12.13(d)
    \(y\B = 0.965608\)

    12.13(e)
    \(Z = 0.999319\)

    12.13(f)
    \(p = 92347.7\Pa\)

    12.13(g)
    \(\kHB = 4.40890\timesten{9}\Pa\)

    12.15(a)
    \(\g\xbB=0.9826\)

    12.15(b)
    \(x\B=4.19\timesten{-4}\)

    12.16
    \(K=1.2\timesten{-6}\)

    12.17(a)
    \(\alpha=0.129\)
    \(m_+=1.29\timesten{-3}\units{mol kg\(^{-1}\)}\)

    12.17(b)
    \(\alpha=0.140\)

    12.18
    \(\Delsub{f}H\st(\tx{Cl\(^-\), aq}) = -167.15\units{kJ mol\(^{-1}\)}\)
    \(S\m\st(\tx{Cl\(^-\), aq}) = 56.46\units{J K\(^{-1}\) mol\(^{-1}\)}\)

    12.19(a)
    \(K\subs{s} = 1.783\timesten{-10}\)

    12.20(a)
    \(\Delsub{r}H\st=-65.769\units{kJ mol\(^{-1}\)}\)

    12.20(b)
    \(\Delsub{f}H\st\tx{(Ag\(^+\), aq)} =105.84\units{kJ mol\(^{-1}\)}\)

    13.1(a)
    \(F=4\)

    13.1(b)
    \(F=3\)

    13.1(c)
    \(F=2\)

    13.10(a)
    \(x\B\tx{(top)} =0.02\), \(x\B\tx{(bottom)} =0.31\)

    13.10(b)
    \(n\A = 2.1\mol\), \(n\B = 1.0 \mol\)

    14.3(a)
    \(\Delsub{r}G\st=-21.436\units{kJ mol\(^{-1}\)}\)
    \(\Delsub{r}S\st=-62.35\units{J K\(^{-1}\) mol\(^{-1}\)}\)
    \(\Delsub{r}H\st=-40.03\units{kJ mol\(^{-1}\)}\)

    14.3(b)
    \(\Delsub{f}H\st(\tx{AgCl, s})=-127.05\units{kJ mol\(^{-1}\)}\)

    14.3(c)
    \(S\m\st(\tx{AgCl, s})=96.16\units{J K\(^{-1}\) mol\(^{-1}\)}\)
    \(\Delsub{f}S\st(\tx{AgCl, s})=-57.93\)\units{J K\(^{-1}\) mol\(^{-1}\)}
    \(\Delsub{f}G\st(\tx{AgCl, s})=-109.78\units{kJ mol\(^{-1}\)}\)

    14.4(b)
    \(\Delsub{f}H\st(\tx{AgCl, s})=-126.81\units{kJ mol\(^{-1}\)}\)
    \(\Delsub{f}G\st(\tx{AgCl, s})=-109.59\units{kJ mol\(^{-1}\)}\)

    14.5
    \(K\subs{s} = 1.76\timesten{-10}\)

    14.6(b)
    \(\g_{\pm}=0.756\)

    14.7(b)
    \(\Delsub{f}G\st=-210.72\units{kJ mol\(^{-1}\)}\)

    14.7(c)
    \(K\subs{s}=1.4\timesten{-18}\)

    14.8
    \(E\st = 0.071\V\)

    14.9(c)
    \(\Eeq\st=1.36\V\)

    14.9(d)
    In the cell:
    \(\dq/\dif\xi = 2.27\units{kJ mol\(^{-1}\)}\)
    In a reaction vessel:
    \(\dq/\dif\xi = -259.67\units{kJ mol\(^{-1}\)}\)

    14.9(e)
    \(\dif\Eeq\st/\dif T = 3.9\timesten{-5}\units{V K\(^{-1}\)}\)

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