JEE MAIN - Chemistry (2015 (Offline) - No. 5)
The following reaction is performed at 298 K
2NO(g) + O2 (g) $$\leftrightharpoons$$ 2NO2 (g)
The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO2(g) at 298 K? (KP = 1.6 × 1012)
2NO(g) + O2 (g) $$\leftrightharpoons$$ 2NO2 (g)
The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO2(g) at 298 K? (KP = 1.6 × 1012)
86600 + R(298) ln(1.6 $$\times$$ 1012)
86600 - $$ln (1.6 \times 10^{12}) \over R (298)$$
0.5[2×86,600 – R(298) ln(1.6×1012)]
R(298) ln(1.6×1012) – 86600
Explanation
$$\Delta {G^ \circ }_{NO\left( g \right)}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\, = 86.6kJ/mol = 86600J/mol;$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$$${G^ \circ }_{N{O_2}\left( g \right)} = x\,J/mol$$
$$T = 298,\,{K_p} = 1.6 \times {10^{12}}$$
$$\Delta {G^ \circ } = - RT\,\ln \,{K_p}$$
Given equation,
$$2NO\left( g \right) + {O_2}\left( g \right)\,\rightleftharpoons\,2N{O_2}\left( g \right)$$
$$2\Delta {G^ \circ }_{N{O_2}} - 2\Delta {G^ \circ }_{NO}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$2\Delta {G^ \circ }_{N{O_2}} - 2 \times 86600$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$2\Delta {G^ \circ }_{N{O_2}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = 2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$\Delta {G^ \circ }_{N{O_2}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = {1 \over 2}\left[ {2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)} \right]$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = 0.5\left[ {2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)} \right]$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\, = 86.6kJ/mol = 86600J/mol;$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$$${G^ \circ }_{N{O_2}\left( g \right)} = x\,J/mol$$
$$T = 298,\,{K_p} = 1.6 \times {10^{12}}$$
$$\Delta {G^ \circ } = - RT\,\ln \,{K_p}$$
Given equation,
$$2NO\left( g \right) + {O_2}\left( g \right)\,\rightleftharpoons\,2N{O_2}\left( g \right)$$
$$2\Delta {G^ \circ }_{N{O_2}} - 2\Delta {G^ \circ }_{NO}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$2\Delta {G^ \circ }_{N{O_2}} - 2 \times 86600$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$2\Delta {G^ \circ }_{N{O_2}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = 2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)$$
$$\Delta {G^ \circ }_{N{O_2}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = {1 \over 2}\left[ {2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)} \right]$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = 0.5\left[ {2 \times 86600 - R\left( {298} \right)\ln \left( {1.6 \times {{10}^{12}}} \right)} \right]$$
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