At 1285 _x001F_C, the equilibrium constant for the reaction Br2(g) ⇌ 2 Br(g) is Kc = 1.04 * 10^-3. A 0.200-L vessel containing an equilibrium mixture of the gases has 0.245 g of Br2(g) in it. What is the mass of Br(g) in the vessel?

Verified step by step guidance

Step 1: Calculate the number of moles of Br2 using its mass and molar mass. The molar mass of Br2 is approximately 159.808 g/mol.

Step 2: Determine the concentration of Br2 in the vessel by dividing the number of moles of Br2 by the volume of the vessel in liters.

Step 3: Set up the expression for the equilibrium constant Kc for the reaction Br2(g) ⇌ 2 Br(g), which is Kc = [Br]^2 / [Br2].

Step 4: Use the equilibrium constant expression to solve for the concentration of Br(g) at equilibrium. Substitute the known values of Kc and [Br2] into the equation.

Step 5: Calculate the mass of Br(g) by first finding the number of moles of Br(g) using its concentration and the volume of the vessel, then multiply by the molar mass of Br (approximately 79.904 g/mol).

Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction Br2(g) ⇌ 2 Br(g), Kc = [Br]^2 / [Br2]. A low Kc value, such as 1.04 * 10^-3, indicates that at equilibrium, the concentration of reactants (Br2) is much higher than that of the products (Br).

Molar Mass and Mass to Moles Conversion

To find the number of moles from a given mass, the molar mass of the substance is used. For Br2, the molar mass is approximately 159.8 g/mol. By dividing the mass of Br2 (0.245 g) by its molar mass, we can determine the number of moles of Br2 present in the vessel, which is essential for calculating the moles of Br produced at equilibrium.

Stoichiometry in Chemical Reactions

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In the reaction Br2(g) ⇌ 2 Br(g), the stoichiometric coefficients indicate that one mole of Br2 produces two moles of Br. This relationship is crucial for determining the amount of Br(g) formed based on the amount of Br2(g) present at equilibrium.