An equilibrium mixture of N2, H2, and NH3 at 700 K con- tains 0.036 M N2 and 0.15 M H2. At this temperature, Kc for the reaction N21g2 + 3 H21g2 ∆ 2 NH31g2 is 0.29. What is the concentration of NH3?

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Write the balanced chemical equation for the reaction: \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \).

Write the expression for the equilibrium constant \( K_c \) for the reaction: \( K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \).

Substitute the known values into the \( K_c \) expression: \( 0.29 = \frac{[\text{NH}_3]^2}{0.036 \times (0.15)^3} \).

Solve the equation for \([\text{NH}_3]^2\) by multiplying both sides by \(0.036 \times (0.15)^3\).

Take the square root of both sides to find \([\text{NH}_3]\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 this concept is crucial for analyzing equilibrium problems, as it allows us to apply the equilibrium constant (Kc) to find unknown concentrations.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) 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 N2(g) + 3 H2(g) ⇌ 2 NH3(g), Kc = [NH3]^2 / ([N2][H2]^3). This constant provides insight into the position of equilibrium and is essential for calculating unknown concentrations in equilibrium mixtures.

Concentration Calculations

Concentration calculations involve determining the molarity of substances in a solution, which is defined as the number of moles of solute per liter of solution. In equilibrium problems, knowing the concentrations of some species allows us to use the Kc expression to solve for unknown concentrations. This requires careful manipulation of the equilibrium expression and an understanding of stoichiometry to relate the concentrations of reactants and products.