Chapter U6, Problem 20STP

Interpretation Introduction

Interpretation:

The correct equilibrium-constant expression for the following reaction should be determined:

${{\text{(NH}}_4\text{)}}_{\text{3}}{\text{PO}}_{\text{4}}\text{(s) }\to {\text{ 3NH}}_4^{+}{\text{(aq) + PO}}_4^{3-}\text{(aq)}$

Concept introduction:

The relationship between the concentration of products and reactants at equilibrium for a general reaction:

$\text{aA}\text{+}\text{bB}\rightleftarrows \text{cC}\text{+}\text{dD}$

Where A, B, C, and D represents chemical species and a, b, c, and d are the coefficients for balanced reaction.

The equilibrium expression, K_c for reversible reaction is determined by multiplying the concentrations of products together and divided by the concentrations of the reactants. Each concentration is raised to the power that is equal to the coefficient in the balanced reaction. So, the expression is:

${\text{K}}_{\text{c}}\text{=}\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

Square brackets represent the concentration.

Answer to Problem 20STP

The correct option is (b), ${\text{K = [NH}}_4^{+}{\text{]}}^3{\text{[PO}}_4^{3-}\text{]}$.

Explanation of Solution

The given reaction is:

${{\text{(NH}}_4\text{)}}_{\text{3}}{\text{PO}}_{\text{4}}\text{(s) }\to {\text{ 3NH}}_4^{+}{\text{(aq) + PO}}_4^{3-}\text{(aq)}$

For this reaction, the concentration of pure solid are constant that is they do not change. Thus, they are not included in the equilibrium expression.

Therefore, for the given reaction, the expression for the equilibrium constant is:

${\text{K}}_{\text{c}}{\text{ = [NH}}_4^{+}{\text{]}}^3{{\text{[PO}}_4^{3-}\text{]}}^1$

Since, the correct equilibrium-constant expression for the given reaction is, ${\text{K}}_{\text{c}}{\text{ = [NH}}_4^{+}{\text{]}}^3{{\text{[PO}}_4^{3-}\text{]}}^1$ so, the correct option is (b).