Chapter 6, Problem 47P

For each value, are the reactants or products favored at equilibrium?
a. $K=5.2\times {10}^3$
b. $\Delta H=-27\text{ kcal/mol}$
c. $K=0.002$
d. $\Delta H=+2\text{ kcal/mol}$

Interpretation Introduction

(a)

Interpretation:

Whether reactants or products are favored at equilibrium and equilibrium constant value $5.2\times {10}^3$ needs to be determined.

Concept introduction:

For a reversible reaction, equilibrium constant ( $K_{eq}$ ) is defined as follows,

  $\begin{array}{l}aA+bB\rightleftarrows cC+dD\\ \text{equilibrium constant = }{K}_{eq}=\frac{{\left[C\right]}^c\times {\left[D\right]}^d}{{\left[A\right]}^a\times {\left[B\right]}^b}\end{array}$

  $\Delta H$ (enthalpy) is defined as the difference between the energy of the products and the energy of the reactants (See the figure below).

  

When energy is absorbed, the reaction is endothermic and the value of $\Delta H$ is positive (+). This indicates that the energy of products is lower than the energy of reactants. Lower the energy higher the stability of a chemical compound. Therefore, in this case, the products are more stable than the reactants.

Similarly, when energy is released, the reaction is exothermic and $\Delta H$ value is negative (−). Now the reactants are lower in energy, thus are more stable than the products.

Answer to Problem 47P

Products are favored.

Explanation of Solution

The magnitude of $K_{eq}$ reveals information about the composition of the reaction mixture at equilibrium,

  $\begin{array}{l}\text{When }{K}_{eq}=1,\text{ both the reactants and products are present at equilibrium}\\ \text{When }{K}_{eq}\text{> 1, equilibrium favors the products}\\ \text{When }{K}_{eq}\text{< 1, equilibrium favors the reactants}\end{array}$

Accordingly,

  $\begin{array}{l}\text{When }K=5.2\times {10}^3,\\ K>K_{eq}\end{array}$

Therefore, products are favored at equilibrium.

Interpretation Introduction

(b)

Interpretation:

Whether reactants or products are favored at equilibrium and change in enthalpy -27 kcal/mol needs to be explained.

Concept introduction:

For a reversible reaction, equilibrium constant ( $K_{eq}$ ) is defined as follows,

  $\begin{array}{l}aA+bB\rightleftarrows cC+dD\\ \text{equilibrium constant = }{K}_{eq}=\frac{{\left[C\right]}^c\times {\left[D\right]}^d}{{\left[A\right]}^a\times {\left[B\right]}^b}\end{array}$

  $\Delta H$ (enthalpy) is defined as the difference between the energy of the products and the energy of the reactants (See the figure below).

  

When energy is absorbed, the reaction is endothermic and the value of $\Delta H$ is positive (+). This indicates that the energy of products is lower than the energy of reactants. Lower the energy higher the stability of a chemical compound. Therefore, in this case, the products are more stable than the reactants.

Similarly, when energy is released, the reaction is exothermic and $\Delta H$ value is negative (−). Now the reactants are lower in energy, thus are more stable than the products.

Answer to Problem 47P

Products are favored.

Explanation of Solution

The value of $\Delta H$ is negative ( $-27\text{ kcal/mol}$ ). This value indicates that the reaction is exothermic , and the energy of the products is lower than that of the reactants. Therefore, the products are more stable and favored at equilibrium.

Interpretation Introduction

(c)

Interpretation:

Whether reactants or products are favored at equilibrium and equilibrium constant value $0.002$ needs to be determined.

Concept introduction:

For a reversible reaction, equilibrium constant ( $K_{eq}$ ) is defined as follows,

  $\begin{array}{l}aA+bB\rightleftarrows cC+dD\\ \text{equilibrium constant = }{K}_{eq}=\frac{{\left[C\right]}^c\times {\left[D\right]}^d}{{\left[A\right]}^a\times {\left[B\right]}^b}\end{array}$

  $\Delta H$ (enthalpy) is defined as the difference between the energy of the products and the energy of the reactants (See the figure below).

  

When energy is absorbed, the reaction is endothermic and the value of $\Delta H$ is positive (+). This indicates that the energy of products is lower than the energy of reactants. Lower the energy higher the stability of a chemical compound. Therefore, in this case, the products are more stable than the reactants.

Similarly, when energy is released, the reaction is exothermic and $\Delta H$ value is negative (−). Now the reactants are lower in energy, thus are more stable than the products.

Answer to Problem 47P

Reactants are favored.

Explanation of Solution

The magnitude of $K_{eq}$ reveals information about the composition of the reaction mixture at equilibrium,

  $\begin{array}{l}\text{When }{K}_{eq}=1,\text{ both the reactants and products are present at equilibrium}\\ \text{When }{K}_{eq}\text{> 1, equilibrium favors the products}\\ \text{When }{K}_{eq}\text{< 1, equilibrium favors the reactants}\end{array}$

Accordingly,

  $\begin{array}{l}\text{When }K=0.002,\\ K<K_{eq}\end{array}$

Therefore, reactants are favored at equilibrium.

Interpretation Introduction

(d)

Interpretation:

Whether reactants or products are favored at equilibrium and change in enthalpy +2 kcal/mol needs to be explained.

Concept introduction:

For a reversible reaction, equilibrium constant ( $K_{eq}$ ) is defined as follows,

  $\begin{array}{l}aA+bB\rightleftarrows cC+dD\\ \text{equilibrium constant = }{K}_{eq}=\frac{{\left[C\right]}^c\times {\left[D\right]}^d}{{\left[A\right]}^a\times {\left[B\right]}^b}\end{array}$

  $\Delta H$ (enthalpy) is defined as the difference between the energy of the products and the energy of the reactants (See the figure below).

  

When energy is absorbed, the reaction is endothermic and the value of $\Delta H$ is positive (+). This indicates that the energy of products is lower than the energy of reactants. Lower the energy higher the stability of a chemical compound. Therefore, in this case, the products are more stable than the reactants.

Similarly, when energy is released, the reaction is exothermic and $\Delta H$ value is negative (−). Now the reactants are lower in energy, thus are more stable than the products.

Answer to Problem 47P

Reactants are favored

Explanation of Solution

The value of $\Delta H$ is positive ( $+2\text{ kcal/mol}$ ), indicating that the reaction is endothermic . Therefore, the energy of the products should be higher than that of the reactants. Low energy reactants are more stable than the products, thus are favored at equilibrium.