Given the following equilibrium constants: (i) (ii) (iii) Which of the following represents the corr — Chemical Equilibrium Chemistry Question
Question
Given the following equilibrium constants: (i) $2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g) \quad K_1$ (ii) $NO_2(g) + SO_2(g) \rightleftharpoons SO_3(g) + NO(g) \quad K_2$ (iii) $2SO_3(g) \rightleftharpoons 2SO_2(g) + O_2(g) \quad K_3$ Which of the following represents the correct mathematical relationship between $K_1$, $K_2$, and $K_3$?
💡 Solution & Explanation
Reversing reaction (iii) gives $2SO_2 + O_2 \rightleftharpoons 2SO_3$ with constant $\frac{1}{K_3}$. We can construct this by taking reaction (i) and adding twice reaction (ii). $2 \times (\text{ii})$ gives $2NO_2 + 2SO_2 \rightleftharpoons 2SO_3 + 2NO$ with constant $(K_2)^2$. Adding (i): $(2NO + O_2) + (2NO_2 + 2SO_2) \rightleftharpoons 2NO_2 + (2SO_3 + 2NO)$, yielding $2SO_2 + O_2 \rightleftharpoons 2SO_3$. Therefore, $K_1 \cdot (K_2)^2 = \frac{1}{K_3}$, which implies $K_1 \cdot (K_2)^2 \cdot K_3 = 1$.