Which of the following reactions is a case where Kp equals Kc?

• A. S(s) + O2(g) ⇌ SO2(g)
• B. CaCO3(s) ⇌ CaO(s) + CO2(g)
• C. 2 HgO(s) ⇌ Hg(l) + O2(g)
• D. 2 H2O(l) ⇌ 2 H2(g) + O2(g)

Answer: (A)

Verified step by step guidance

1. Understand the relationship between Kp and Kc. Kp is the equilibrium constant for gases expressed in terms of partial pressures, while Kc is expressed in terms of concentrations. The relationship between Kp and Kc is given by the equation: $K{p}_{}=K{c}_{}\times \left(\mathrm{RT}\right){∆}^n$, where $R$ is the gas constant, $T$ is the temperature in Kelvin, and $∆n$ is the change in moles of gas.
2. Calculate $∆n$ for each reaction. This is done by subtracting the total moles of gaseous reactants from the total moles of gaseous products.
3. For the reaction $S\left(s\right)+O_2\left(g\right)\rightleftharpoons {\mathrm{SO}}_2\left(g\right)$, calculate $∆n$. The change in moles of gas is $1-1=0$.
4. For the reaction ${\mathrm{CaCO}}_3\left(s\right)\rightleftharpoons {\mathrm{CaO}}_{\left(}$, calculate $∆n$. The change in moles of gas is $1-0=1$.
5. Identify the reaction where $∆n$ equals zero, as this is the condition where $K{p}_{}=K{c}_{}$. The reaction $S\left(s\right)+O_2\left(g\right)\rightleftharpoons {\mathrm{SO}}_2\left(g\right)$ satisfies this condition.