Consider the reaction and the associated equilibrium constant: aA(g) + bB(g) ⇌ cC(g) with Kc = 5.0. Find the equilibrium concentrations of A, B, and C for the given values of a, b, and c. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction. Calculate the equations for x without solving them for the following cases: a) a=1, b=1, c=2; b) a=1, b=1, c=1; c) a=2, b=1, c=1.

Verified step by step guidance

Identify the balanced chemical equation for each case and write the expression for the equilibrium constant Kc.

Set up an ICE (Initial, Change, Equilibrium) table for each case to track the changes in concentrations of A, B, and C.

Express the equilibrium concentrations in terms of the change variable x, where x is the amount of A and B that reacts.

Substitute the equilibrium concentrations into the Kc expression for each case.

Solve the resulting equation for x, but do not calculate the final value.

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 = [C]^c / ([A]^a * [B]^b), where [A], [B], and [C] are the molar concentrations of the reactants and products. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests that reactants are favored.

ICE Table

An ICE table (Initial, Change, Equilibrium) is a tool used to organize the concentrations of reactants and products in a chemical reaction at different stages. It helps in determining the changes in concentration as the reaction progresses towards equilibrium. By filling in the initial concentrations, the changes that occur as the reaction shifts, and the equilibrium concentrations, one can derive expressions for the unknowns in the reaction.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction, based on the balanced chemical equation. It allows for the calculation of how much of each substance is consumed or produced during the reaction. Understanding stoichiometry is essential for setting up the equations for equilibrium concentrations, as it dictates the proportions in which reactants and products interact.

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