Question

The following reaction has K = 4.0: A(aq) + B(aq) ⇄ C(aq) + D(aq). What is the maximum percent yield of the reaction if the reaction initially starts with 1.0 M of each reactant? (1) 25% (2) 33% (3) 50% (4) 67% (5) 75%

Answer 1

Explanation:We can use the equilibrium constant (K) and the initial concentrations of the reactants to calculate the equilibrium concentrations of reactants and products using the following ICE table:

| I | C | E |

|-------|--------|--------|

| A | 1.0 -x | 1.0-x |

| B | 1.0 -x | 1.0-x |

| C | 0 +x | x |

| D | 0 +x | x |

At equilibrium, the expression for K is:

K = [C][D]/[A][B]

Substituting the equilibrium concentrations in this expression, we get:

4.0 = x^2/(1.0-x)^2

Solving for x using the quadratic equation, we get:

x = 0.67

Substituting this back in the ICE table, we get the equilibrium concentrations:

[A] = [B] = 0.33 M

[C] = [D] = 0.67 M

The maximum amount of C that can be produced is (1.0 M - 0.67 M) = 0.33 M. The theoretical maximum yield of C is the amount of C produced divided by the amount of C that would be produced if all of the reactants were converted to C and D, which is:

maximum yield of C = 0.33 M / (1.0 M + 0.33 M) = 0.25 = 25%

Therefore, the correct answer is (1) 25%.