Use your answer from Problem 7.53 to calculate the following:[N2O4] at equilibrium when [NO2] = 0.0250 mol/L

Verified step by step guidance

1. Identify the chemical equilibrium reaction: \( \text{N}_2\text{O}_4 (g) \rightleftharpoons 2\text{NO}_2 (g) \).
2. Write the expression for the equilibrium constant \( K_c \) using the concentrations of the products and reactants: \( K_c = \frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]} \).
3. Use the given concentration of \([\text{NO}_2] = 0.0250 \text{ mol/L}\) and the value of \( K_c \) from Problem 7.53 to set up the equation: \( K_c = \frac{(0.0250)^2}{[\text{N}_2\text{O}_4]} \).
4. Rearrange the equation to solve for \([\text{N}_2\text{O}_4]\): \([\text{N}_2\text{O}_4] = \frac{(0.0250)^2}{K_c} \).
5. Substitute the value of \( K_c \) from Problem 7.53 into the equation to find \([\text{N}_2\text{O}_4]\).

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in concentration. Understanding equilibrium is crucial for predicting how changes in concentration, temperature, or pressure will affect the system.

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For the reaction involving N2O4 and NO2, K can be used to relate the concentrations of these species at equilibrium. Knowing K allows for the calculation of unknown concentrations when some are provided.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction. It is based on the balanced chemical equation, which provides the mole ratios needed to convert between moles of different substances. In this context, stoichiometry is essential for determining the concentration of N2O4 at equilibrium based on the given concentration of NO2.