Consider the following reversible steps and their equilibrium constants: (1) (2) Find the numerical — Chemical Equilibrium Chemistry Question
Question
Consider the following reversible steps and their equilibrium constants: (1) $SO_2(g) + \frac{1}{2}O_2(g) \rightleftharpoons SO_3(g) \quad K_1 = 2.0$ (2) $NO(g) + \frac{1}{2}O_2(g) \rightleftharpoons NO_2(g) \quad K_2 = 0.5$ Find the numerical value of the equilibrium constant ($K_3$) for the overall reaction: $SO_2(g) + NO_2(g) \rightleftharpoons SO_3(g) + NO(g)$.
💡 Solution & Explanation
The overall reaction can be obtained by adding reaction (1) and the reverse of reaction (2). The reverse of (2) is $NO_2(g) \rightleftharpoons NO(g) + \frac{1}{2}O_2(g)$ with a new constant $1/K_2 = 1/0.5 = 2.0$. Adding this to (1) gives $SO_2 + \frac{1}{2}O_2 + NO_2 \rightleftharpoons SO_3 + NO + \frac{1}{2}O_2$, which simplifies to the target reaction. Thus, $K_3 = K_1 \times (1/K_2) = 2.0 \times 2.0 = 4.0$.