Two different proteins X and Y are dissolved in aqueous solution at 37 _x001F_C. The proteins bind in a 1:1 ratio to form XY. A solution that is initially 1.00 mM in each protein is allowed to reach equilibrium. At equilibrium, 0.20 mM of free X and 0.20 mM of free Y remain. What is Kc for the reaction?

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Identify the initial concentrations of proteins X and Y, which are both 1.00 mM.

Determine the change in concentration for proteins X and Y as they form the complex XY. Since 0.20 mM of each remains, 0.80 mM of each has reacted to form XY.

Calculate the equilibrium concentration of the complex XY. Since the proteins bind in a 1:1 ratio, the concentration of XY formed is also 0.80 mM.

Write the expression for the equilibrium constant Kc for the reaction: \( K_c = \frac{[XY]}{[X][Y]} \).

Substitute the equilibrium concentrations into the Kc expression: \( K_c = \frac{0.80}{0.20 \times 0.20} \).

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 reversible chemical reaction. It is calculated using the formula Kc = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced equation. A higher Kc value indicates a greater extent of reaction towards products.

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution (mol/L). In this context, the initial concentrations of proteins X and Y are given as 1.00 mM, which means there are 1.00 millimoles of each protein in one liter of solution. Understanding how to convert between moles and molarity is essential for calculating equilibrium concentrations.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. In this case, the proteins X and Y bind in a 1:1 ratio to form the complex XY. Knowing the initial concentrations and the changes at equilibrium allows us to set up an expression to find the equilibrium concentrations of all species involved, which is crucial for calculating Kc.

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Textbook Question

A mixture of 0.2000 mol of CO₂, 0.1000 mol of H₂, and 0.1600 mol of H₂O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO₂(g) + H₂(g) ⇌ CO(g) + H₂O(g) (d) Calculate K_c for the reaction.

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Textbook Question

Indicate whether each of the following statements about the reaction quotient Q is true or false: (a) The expression for 𝑄_𝑐 looks the same as the expression for 𝐾_𝑐.

Textbook Question

Indicate whether each of the following statements about the reaction quotient Q is true or false: (b) If 𝑄_𝑐< 𝐾_𝑐, the reaction needs to proceed to the right to reach equilibrium.

Textbook Question

At 100°C, the equilibrium constant for the reaction COCl₂(𝑔) ⇌ CO(𝑔) + Cl₂(𝑔) has the value 𝐾_𝑐= 2.19×10⁻¹⁰. Are the following mixtures of COCl₂, CO, and Cl₂ at 100°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium.

(a) [COCl₂] = 2.00×10⁻³M, [CO] = 3.3×10⁻⁶M, [Cl₂] = 6.62×10⁻⁶ M

(b) [COCl₂] = 4.50×10⁻²M, [CO] = 1.1×10⁻⁷M, [Cl₂] = 2.25×10⁻⁶ M