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

Verified step by step guidance

1. Identify the chemical equilibrium reaction involved. The reaction is typically: N₂O₄ ⇌ 2NO₂. This means dinitrogen tetroxide (N₂O₄) dissociates into nitrogen dioxide (NO₂).
2. Write the equilibrium constant expression for the reaction: Kc = ([NO₂]²) / [N₂O₄]. Here, [NO₂] and [N₂O₄] represent the equilibrium concentrations of NO₂ and N₂O₄, respectively.
3. Rearrange the equilibrium constant expression to solve for [N₂O₄]: [N₂O₄] = ([NO₂]²) / Kc. This step isolates the concentration of N₂O₄ at equilibrium.
4. Substitute the given value of [NO₂] = 0.0250 mol/L into the rearranged equation. You will also need the value of Kc, which should have been determined in Problem 7.53. Ensure the units of Kc are consistent with the concentration units (mol/L).
5. Perform the calculation by squaring the [NO₂] value, dividing it by the Kc value, and solving for [N₂O₄]. This will give you the equilibrium concentration of N₂O₄ in mol/L.

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. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. Understanding Kc is essential for predicting the concentrations of species in a chemical reaction at equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps in understanding how changes in concentration, pressure, or temperature affect the position of equilibrium in a chemical reaction.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It involves using mole ratios derived from the coefficients of the balanced equation to relate the amounts of different substances. Mastery of stoichiometry is crucial for determining the concentrations of reactants and products at equilibrium.