Consider the reaction and the associated equilibrium constant: aA(g) ⇌ bB(g) Kc = 4.0 Find the equilibrium concentrations of A and B for each value of a and b. Assume that the initial concentration of A in each case is 1.0 M and that no B is present at the beginning of the reaction. c. a=1;b=2

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Step 1: Write down the equilibrium expression for the reaction. For the reaction aA(g) ⇌ bB(g), the equilibrium constant expression is Kc = [B]^b / [A]^a. In this case, a=1 and b=2, so the expression becomes Kc = [B]^2 / [A].

Step 2: Set up an ICE (Initial, Change, Equilibrium) table to keep track of the changes in concentrations of A and B. Initially, [A] = 1.0 M and [B] = 0. At equilibrium, [A] = 1.0 - x and [B] = 2x, where x is the change in concentration of A that reacts.

Step 3: Substitute the equilibrium concentrations into the equilibrium expression. This gives 4.0 = (2x)^2 / (1.0 - x).

Step 4: Solve the resulting equation for x. This will give you the change in concentration of A and, since the stoichiometry of the reaction is 1:2, twice this value will be the equilibrium concentration of B.

Step 5: Substitute the value of x back into the expressions for the equilibrium concentrations of A and B to find their actual values at equilibrium.

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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 = [B]^b / [A]^a, where [B] and [A] are the equilibrium concentrations of the products and reactants, respectively. A Kc value greater than 1 indicates that products are favored at equilibrium.

Initial Concentration and Changes at Equilibrium

In chemical reactions, the initial concentration of reactants and products influences the equilibrium position. For the reaction aA(g) ⇌ bB(g), if the initial concentration of A is 1.0 M and no B is present, the change in concentration as the system reaches equilibrium must be calculated. This involves determining how much A is converted to B based on the stoichiometric coefficients a and b.

Stoichiometry in Reactions

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction, defined by their coefficients in the balanced equation. In the context of the given reaction, the coefficients a and b indicate the molar ratios in which A and B react and are produced. Understanding stoichiometry is essential for calculating the changes in concentrations of A and B as the system reaches equilibrium.

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