# 15.9: Appendix I- Answers to Selected Problems

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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}$$}\)

This page titled 15.9: Appendix I- Answers to Selected Problems is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Howard DeVoe via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.