Question

14 multiple choice 2 points for the reaction a + b → c + d, δg° = -5.00 kcal/mol. what is the corresponding equilibrium constant at r = 1.987 cal/mol·k. 4648 0.4648 46.48 4.648 previous

Explanation:

Step1: Convert energy unit

First, convert $\Delta G^{\circ}$ from kcal/mol to cal/mol. Since 1 kcal = 1000 cal, $\Delta G^{\circ}=- 5.00\times1000\ cal/mol=-5000\ cal/mol$.

Step2: Use the formula $\Delta G^{\circ}=-RT\ln K$

At standard - state conditions (usually assumed $T = 298\ K$), and given $R = 1.987\ cal/mol\cdot K$. Rearrange the formula $\Delta G^{\circ}=-RT\ln K$ for $K$. We get $\ln K=-\frac{\Delta G^{\circ}}{RT}$. Substitute $\Delta G^{\circ}=-5000\ cal/mol$, $R = 1.987\ cal/mol\cdot K$ and $T = 298\ K$ into the formula: $\ln K=\frac{5000}{1.987\times298}$.

Step3: Calculate the value of $\ln K$

$1.987\times298 = 1.987\times(300 - 2)=1.987\times300-1.987\times2=596.1 - 3.974 = 592.126$. Then $\frac{5000}{592.126}\approx8.444$. So $\ln K\approx8.444$.

Step4: Solve for $K$

Since $\ln K\approx8.444$, then $K = e^{8.444}$. Using a calculator, $e^{8.444}\approx4648$.

Answer:

A. 4648