Sulfur dioxide reacts with oxygen in a step in the production of sulfuric acid. 2 SO2(g) + O2(g) ⇌ 2 SO3(g) Kc = 7.9 * 10^4 at 1800 K. For an equilibrium mixture in which [SO2] = 1.5 * 10^-3 M and [O2] = 3.0 * 10^-3 M, what is [SO3]?

Verified step by step guidance

1. Step 1: Write the expression for the equilibrium constant (Kc) for the reaction: \( K_c = \frac{[\text{SO}_3]^2}{[\text{SO}_2]^2[\text{O}_2]} \).
2. Step 2: Substitute the given values into the Kc expression: \( 7.9 \times 10^4 = \frac{[\text{SO}_3]^2}{(1.5 \times 10^{-3})^2 (3.0 \times 10^{-3})} \).
3. Step 3: Rearrange the equation to solve for \([\text{SO}_3]^2\): \([\text{SO}_3]^2 = 7.9 \times 10^4 \times (1.5 \times 10^{-3})^2 \times (3.0 \times 10^{-3})\).
4. Step 4: Calculate the value of \([\text{SO}_3]^2\) using the values from Step 3.
5. Step 5: Take the square root of \([\text{SO}_3]^2\) to find \([\text{SO}_3]\).

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction 2 SO2(g) + O2(g) ⇌ 2 SO3(g), Kc = [SO3]^2 / ([SO2]^2 * [O2]). A higher Kc value indicates that the products are favored at equilibrium.

Concentration and Molarity

Concentration refers to the amount of a substance in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. In this question, the concentrations of SO2 and O2 are given in molarity, which is essential for calculating the concentration of SO3 at equilibrium using the equilibrium constant.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In the context of this reaction, if the concentrations of SO2 or O2 change, the equilibrium will shift to either the left or right to re-establish balance, affecting the concentration of SO3.