As shown in Table 15.2, the equilibrium constant for the reaction N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g) is K_p = 4.34 × 10^-3 at 300°C. Pure NH₃ is placed in a 1.00-L flask and allowed to reach equilibrium at this temperature. There are 1.05 g NH₃ in the equilibrium mixture. (b) What was the initial mass of ammonia placed in the vessel?

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Convert the mass of NH_3 at equilibrium (1.05 g) to moles using its molar mass (17.03 g/mol).

Use the stoichiometry of the reaction N_2(g) + 3 H_2(g) ⇌ 2 NH_3(g) to express the changes in moles of N_2, H_2, and NH_3 in terms of a variable 'x', which represents the change in moles of NH_3 from the initial state to equilibrium.

Write the expression for the equilibrium constant K_p in terms of partial pressures: K_p = (P_{NH_3}^2) / (P_{N_2} * P_{H_2}^3).

Relate the partial pressures to the moles of gases at equilibrium using the ideal gas law: P = (nRT)/V, where n is the number of moles, R is the gas constant, T is the temperature in Kelvin, and V is the volume of the flask.

Solve the equilibrium expression for 'x' using the known value of K_p and the calculated moles of NH_3 at equilibrium, then use 'x' to find the initial moles and mass of NH_3.

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Key Concepts

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

Equilibrium Constant (Kp)

The equilibrium constant (Kp) 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 N2(g) + 3 H2(g) ⇌ 2 NH3(g), Kp indicates how far the reaction favors the formation of ammonia (NH3) compared to the reactants. A small Kp value, like 4.34×10−3, suggests that at equilibrium, the concentration of reactants is much higher than that of the products.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the relationships between the amounts of substances involved. In this case, knowing the stoichiometric coefficients from the balanced equation helps in calculating the initial mass of ammonia needed to reach the equilibrium state, given the final mass and the equilibrium constant.

Molar Mass and Mass-Volume Relationships

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. To find the initial mass of ammonia, we can use the molar mass of NH3 (approximately 17.03 g/mol) to convert the mass of ammonia at equilibrium into moles. This conversion is essential for applying stoichiometry and determining how much ammonia was initially present before the reaction reached equilibrium.