The following reaction, which has Kc = 0.145 at 298 K, takes place in carbon tetrachloride solution:2 BrCl1soln2 ∆ Br21soln2 + Cl21soln2 A measurement of the concentrations shows 3BrCl4 =0.050 M, 3Br24 = 0.035 M, and 3Cl24 = 0.030 M. (b) Determine the equilibrium concentrations of BrCl, Br1, and Cl2.
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Step 1: Write down the balanced chemical equation. In this case, it is 2 BrCl ⇌ Br2 + Cl2.
Step 2: Write down the expression for the equilibrium constant (Kc) for this reaction. Kc = [Br2][Cl2] / [BrCl]^2.
Step 3: Substitute the given values into the equilibrium constant expression. 0.145 = [0.035][0.030] / [0.050]^2.
Step 4: Solve the equation for the unknown, which in this case is the equilibrium concentration of BrCl. You can do this by rearranging the equation and then performing the necessary calculations.
Step 5: Once you have found the equilibrium concentration of BrCl, you can use the stoichiometry of the reaction to find the equilibrium concentrations of Br2 and Cl2. Remember that for every 2 moles of BrCl that react, 1 mole of Br2 and 1 mole of Cl2 are produced.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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] / [reactants], where the concentrations are raised to the power of their coefficients in the balanced chemical equation. A Kc value less than 1 indicates that reactants are favored, while a value greater than 1 suggests that products are favored.
An ICE table is a tool used to organize the initial concentrations, the changes in concentrations as the reaction proceeds, and the equilibrium concentrations of reactants and products. By setting up an ICE table, one can systematically determine how the concentrations of each species change from the initial state to equilibrium, allowing for the calculation of unknown concentrations using the equilibrium constant.
Stoichiometry refers to the quantitative relationship between the reactants and products in a chemical reaction, as dictated by the balanced chemical equation. In this case, the stoichiometry indicates that two moles of BrCl produce one mole of Br2 and one mole of Cl2. Understanding the stoichiometric ratios is essential for calculating the changes in concentrations of each species during the reaction and for applying the equilibrium constant correctly.
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