Question

In a chemical reaction, substrate molecule A is broken down to form one molecule of product B and one molecule of product C. The equilibrium constant, K, for this reaction is 0.5. If we start with a mixture containing only substrate A at a concentration of 1 M, what will be the concentration of A when the reaction reaches equilibrium?a. 0.125 Mb. 0.25 Mc. 0.333 Md. 0.5 Me. 0.667 M

Answer 1

Answer:

The answer to your question is d. 0.5 M

Explanation:

Data

[A] = 1M

K = 0.5

Concentration of B and C at equilibrium = x

Concentration of A at equilibrium = 1 - x

Equation of equilibrium

                                       k = $\frac{[B][C]}{A}$

Substitution

                                       $0.5 = \frac{[x][x]}{1 - x}$

Simplification

                                       0.5 = $\frac{x^{2}}{1 - x}$

Solve for x

                                      0.5(1 - x) = x²

                                      0.5 - 0.5x = x²

                                       x² + 0.5x - 0.5 = 0

Find the roots             x₁ = 0.5     x₂ = -1

There are no negative concentrations so the concentration of A at equilibrium is  

                       [A] = 1 - 0.5

                             = 0.5 M