For a specific ideal gaseous reaction, the equilibrium constants and are related such that . If the — Chemical Equilibrium Chemistry Question
Question
For a specific ideal gaseous reaction, the equilibrium constants $K_p$ and $K_c$ are related such that $\log_{10}(K_p / K_c) + \log_{10}(RT) = 0$. If the balanced reaction is strictly of the form $xA(g) + yB(g) \rightleftharpoons zC(g)$, what is the integer value of $(x + y - z)$?
Answer: 1
💡 Solution & Explanation
The standard relationship is $K_p = K_c(RT)^{\Delta n_g}$. Taking logs: $\log(K_p/K_c) = \Delta n_g \log(RT)$. The given equation is $\log(K_p/K_c) = -\log(RT)$. Comparing the two, we find $\Delta n_g = -1$. By definition, $\Delta n_g = \text{moles of products} - \text{moles of reactants} = z - (x + y) = -1$. Multiplying by $-1$ gives $(x + y) - z = 1$.
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