A sample of nitrosyl bromide (NOBr) decomposes according to the equation 2 NOBr(g) ⇌ 2 NO(g) + Br2(g). An equilibrium mixture in a 5.00-L vessel at 100 _x001F_C contains 3.22 g of NOBr, 3.08 g of NO, and 4.19 g of Br2. (a) Calculate Kc.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

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First, convert the masses of NOBr, NO, and Br2 to moles using their respective molar masses. Use the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).

Next, calculate the concentrations of each species in the equilibrium mixture. Since the volume of the vessel is 5.00 L, use the formula: \( \text{concentration (M)} = \frac{\text{moles}}{\text{volume (L)}} \).

Write the expression for the equilibrium constant \( K_c \) for the reaction: \( K_c = \frac{[\text{NO}]^2[\text{Br}_2]}{[\text{NOBr}]^2} \).

Substitute the concentrations of NO, Br2, and NOBr into the \( K_c \) expression. Ensure that the concentrations are raised to the power of their stoichiometric coefficients.

Finally, solve the expression to find the value of \( K_c \). This will give you the equilibrium constant for the reaction at the given temperature.

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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 chemical reaction. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients], where the concentrations are in mol/L. A larger Kc indicates a greater concentration of products at equilibrium, while a smaller Kc suggests that reactants are favored.

Molar Mass and Conversion to Molarity

To calculate Kc, it is essential to convert the mass of each substance into moles using their molar masses. Molarity (M) is then determined by dividing the number of moles by the volume of the solution in liters. This step is crucial because Kc is based on concentrations, and accurate conversion ensures correct equilibrium calculations.

Stoichiometry of the Reaction

Understanding the stoichiometry of the reaction is vital for determining the correct coefficients when calculating Kc. In the given reaction, 2 moles of NOBr decompose to produce 2 moles of NO and 1 mole of Br2. The stoichiometric coefficients directly influence the equilibrium expression, as they dictate how the concentrations of each species are related in the Kc calculation.