15.9: Apéndice I- Respuestas a problemas seleccionados

Template:DeVoeMathJax

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

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\(^{-1}\)}\) para ambos procesos;\(\int\!\dq/T\subs{ext} = 333\units{J K\(^{-1}\)}\) y\(0\).

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

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)
En la mezcla de composición\(x\A=0.9782\), el coeficiente de actividad es\(\g\B \approx 11.5\).

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

9.11
Los valores para\(m\B/m\st=20\):\(\g\A=1.026\),\(\g\mbB=0.526\); las pendientes limitantes son\(\dif\g\A/\dif(m\B/m\st)=0\),\(\dif\g\mbB/\dif(m\B/m\st)=-0.09\)

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\(^{-1}\)}\) relación de unión
en masa\({} = 1.37\)

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)
\(\Delsub{f}H\st\): sin cambio
\(\Delsub{f}S\st\): restar\(0.219\units{J K\(^{-1}\) mol\(^{-1}\)}\)
\(\Delsub{f}G\st\): sumar\(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)
Estado 1:
\(n\subs{C\(_6\) H\(_{14}\)} =7.822\ timesten {-3}\ mol\)
\(n\subs{H\(_2\) O} =0.05560\ mol\)
cantidad de O\(_2\) consumida:\(0.07431\mol\)
Estado 2:
\(n\subs{H\(_2\) O} =0.11035\ mol\)
\(n\subs{CO\(_2\)} =0.04693\ mol\)
\ tx {masa de H\(_2\) O} =\(1.9880\units{g}\)

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

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

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

11.7 (e)
Estado 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\)
Estado 1:\(\fug\subs{H\(_2\) O} = 0.03234\ br\)
Estado 2:\(\fug\subs{H\(_2\) O} = 0.03229\ br\)

11.7 (g)
Estado 1:
\(\phi\subs{H\(_2\) O} =0.925\)
\(\phi\subs{O\(_2\)} =0.981\)
\(\fug\subs{O\(_2\)} = 29.4\ br\)
Estado 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)
Estado 1:
\(n\subs{H\(_2\) O}\ sups {g} =5.00\ timesten {-4}\ mol\)
\(n\subs{H\(_2\) O}\ sups {l} =0.05510\ mol\)
Estado 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)
Estado 1:
\(k_{m,\tx{O\(_2\)}} = 825\ unidades {bar kg mol\(^{-1}\)}\)
\(n\subs{O\(_2\)} = 3.57\ timesten {-5}\ mol\)
Estado 2:
\(k_{m,\tx{O\(_2\)}} = 823\ unidades {bar kg mol\(^{-1}\)}\)
\(k_{m,\tx{CO\(_2\)}} = 30.8\ unidades {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 vaporización:\(\Del U = +20.8\units{J}\)
H\(_2\) O condensación:\(\Del U = -21.6\units{J}\)

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

11.7 (l)
C\(_6\) H\(_{14}\) (l) compresión:\(\Del U=-1.226\units{J}\)
solución compresión:\(\Del U=-0.225\units{J}\)
solución descompresión:\(\Del U=0.414\units{J}\)

11.7 (m)
O\(_2\) compresión: mezcla de\(\Del U=-81\units{J}\)
gases:\(\dif B/\dif T = 0.26\timesten{-6}\units{m\(^3\) K\(^{-1}\) mol\(^{-1}\)}\) expansión de la mezcla de
gases:\(\Del U=87\units{J}\)

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\ unidades {kJ mol\(^{-1}\)}\)
\(S\m\st(\tx{Cl\(^-\), aq}) = 56.46\ unidades {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\ unidades {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\(^{-1}\)}\)
\(\Delsub{f}S\st(\tx{AgCl, s})=-57.93\)\ unidades {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)
En la celda:
\(\dq/\dif\xi = 2.27\units{kJ mol\(^{-1}\)}\)
En un recipiente de reacción:
\(\dq/\dif\xi = -259.67\units{kJ mol\(^{-1}\)}\)

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