the equilibrium constant $k_p$ for the reaction $co(g)+cl_2(g)\rightleftharpoons cocl_2(g)$ is $5.62\times…

the equilibrium constant $k_p$ for the reaction $co(g)+cl_2(g)\rightleftharpoons cocl_2(g)$ is $5.62\times 10^{35}$ at $25^{circ}c$. calculate $delta g_f^{circ}$ for $cocl_2$ at $25^{circ}c$. round your answer to 4 significant digits.
Answer
Explanation:
Step1: Recall the relationship between $\Delta G^{\circ}$ and $K_p$
The equation is $\Delta G^{\circ}=-RT\ln K_p$. The gas - constant $R = 8.314\ J/(mol\cdot K)$ and the temperature $T=(25 + 273.15)\ K=298.15\ K$, and $K_p = 5.62\times 10^{35}$.
Step2: Calculate $\Delta G^{\circ}$
First, calculate $\ln K_p=\ln(5.62\times 10^{35})=\ln5.62+\ln(10^{35})\approx1.726+35\times\ln10\approx1.726 + 80.55 = 82.276$. Then, $\Delta G^{\circ}=-8.314\ J/(mol\cdot K)\times298.15\ K\times82.276$. $\Delta G^{\circ}=-8.314\times298.15\times82.276\ J/mol\approx - 2.040\times10^{5}\ J/mol=-204.0\ kJ/mol$.
Answer:
$-204.0\ kJ/mol$