Chapter 6, Problem 6.22P

Interpretation Introduction

(a)

Interpretation: Whether the given statement is true for a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is to be stated. The false statement is to be corrected.

Concept introduction: The activation energy $\left(E_{\text{a}}\right)$ aids in determining the rate of the chemical reactions. The small value of $E_{\text{a}}$ exhibits that less energy is required to convert the reactants into products. It results in the increases of a rate of reaction.

The change in Gibbs free energy, enthalpy and entropy is represented by $\text{Δ}G°$, $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ respectively. They are state functions. The relation $\text{Δ}G°$ with $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ is shown as,

$\text{Δ}G\text{°}=\text{Δ}H\text{°}-T\text{Δ}S\text{°}$

The change in Gibbs free energy describes the spontaneity of the reaction. The change in enthalpy describes the relative bond strength in the substance, whereas the change in entropy describes the randomness in the system.

Answer to Problem 6.22P

The given statement is false. The true statement is, the rate of the reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is equal to a reaction with $K_{\text{eq}}=8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$.

Explanation of Solution

The given statement is “the reaction is faster than a reaction with $K_{\text{eq}}=8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$”.

The value of $K_{\text{eq}}$ does not have any affect on the rate of reaction, due to which the given statement is false.

Therefore, the correct statement is the rate of the given reaction is equal to a reaction with $K_{\text{eq}}=8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$.

Conclusion

The given statement is false. The true statement is, the rate of the reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is equal to a reaction with $K_{\text{eq}}=8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$.

Interpretation Introduction

(b)

Interpretation: Whether the given statement is true for a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is to be stated. The false statement is to be corrected.

Concept introduction: The activation energy $\left(E_{\text{a}}\right)$ aids in determining the rate of the chemical reactions. The small value of $E_{\text{a}}$ exhibits that less energy is required to convert the reactants into products. It results in the increases of a rate of reaction.

The change in Gibbs free energy, enthalpy and entropy is represented by $\text{Δ}G°$, $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ respectively. They are state functions. The relation $\text{Δ}G°$ with $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ is shown as,

$\text{Δ}G\text{°}=\text{Δ}H\text{°}-T\text{Δ}S\text{°}$

The change in Gibbs free energy describes the spontaneity of the reaction. The change in enthalpy describes the relative bond strength in the substance, whereas the change in entropy describes the randomness in the system.

Answer to Problem 6.22P

The true statement is, the rate of the reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is lower than a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=40\text{kJ}/\text{mol}$.

Explanation of Solution

The given statement is “the reaction is faster than a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=40\text{kJ}/\text{mol}$”.

The value of $E_{\text{a}}$ affects the rate of reaction. In the given statement $E_{\text{a}}$ has low value. The low value of $E_{\text{a}}$ increases the reaction rate. Hence, this statement is false.

Therefore, the correct statement is the rate of the given reaction is lower than the reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=40\text{kJ}/\text{mol}$.

Conclusion

The given statement is false. The true statement is, the rate of the reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is lower than a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=40\text{kJ}/\text{mol}$.

Interpretation Introduction

(c)

Interpretation: Whether the given statement is true for a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is to be stated. The false statement is to be corrected.

Concept introduction: The activation energy $\left(E_{\text{a}}\right)$ aids in determining the rate of the chemical reactions. The small value of $E_{\text{a}}$ exhibits that less energy is required to convert the reactants into products. It results in the increases of a rate of reaction.

The change in Gibbs free energy, enthalpy and entropy is represented by $\text{Δ}G°$, $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ respectively. They are state functions. The relation $\text{Δ}G°$ with $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ is shown as,

$\text{Δ}G\text{°}=\text{Δ}H\text{°}-T\text{Δ}S\text{°}$

The change in Gibbs free energy describes the spontaneity of the reaction. The change in enthalpy describes the relative bond strength in the substance, whereas the change in entropy describes the randomness in the system.

Answer to Problem 6.22P

The given statement, $\text{Δ}\text{G}°$ for the reaction is a positive value is true.

Explanation of Solution

The given statement is “$\text{Δ}\text{G}°$ for the reaction is a positive value”.

The value of $K_{\text{eq}}$ is $0.8$.

The relation of $\text{Δ}\text{G}°$ with $K_{\text{eq}}$ is shown below.

$\text{Δ}\text{G}°=-\text{R}T\ln K_{\text{eq}}$

Substitute the value of $K_{\text{eq}}$ in the above expression.

$\begin{array}{rll}\text{Δ}\text{G}°& =& -\text{R}T\ln 0.8\\ & =& -\text{R}T\left(-0.223\right)\\ & =& 0.223\text{R}T\end{array}$

Therefore, the given statement is true.

Conclusion

The given statement, $\text{Δ}\text{G}°$ for the reaction is a positive value is true.

Interpretation Introduction

(d)

Interpretation: Whether the given statement is true for a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is to be stated. The false statement is to be corrected.

Concept introduction: The activation energy $\left(E_{\text{a}}\right)$ aids in determining the rate of the chemical reactions. The small value of $E_{\text{a}}$ exhibits that less energy is required to convert the reactants into products. It results in the increases of a rate of reaction.

The change in Gibbs free energy, enthalpy and entropy is represented by $\text{Δ}G°$, $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ respectively. They are state functions. The relation $\text{Δ}G°$ with $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ is shown as,

$\text{Δ}G\text{°}=\text{Δ}H\text{°}-T\text{Δ}S\text{°}$

The change in Gibbs free energy describes the spontaneity of the reaction. The change in enthalpy describes the relative bond strength in the substance, whereas the change in entropy describes the randomness in the system.

Answer to Problem 6.22P

The given statement, the starting materials are lower in energy than the products of the reaction is true.

Explanation of Solution

The given statement is, “the starting materials are lower in energy than the products of the reaction”.

The given reaction has positive $\text{Δ}\text{G}°$ value, which implies that the reaction is not feasible and the reactants have lower energy than the products of the reaction.

Therefore, the given statement is true.

Conclusion

The given statement, the starting materials are lower in energy than the products of the reaction is true.

Interpretation Introduction

(e)

Interpretation: Whether the given statement is true for a reaction with $K_{\text{eq}}=0.8$ and $E_{\text{a}}=80\text{kJ}/\text{mol}$ is to be stated. The false statement is to be corrected.

Concept introduction: The activation energy $\left(E_{\text{a}}\right)$ aids in determining the rate of the chemical reactions. The small value of $E_{\text{a}}$ exhibits that less energy is required to convert the reactants into products. It results in the increases of a rate of reaction.

The change in Gibbs free energy, enthalpy and entropy is represented by $\text{Δ}G°$, $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ respectively. They are state functions. The relation $\text{Δ}G°$ with $\text{Δ}H\text{°}$ and $\text{Δ}S\text{°}$ is shown as,

$\text{Δ}G\text{°}=\text{Δ}H\text{°}-T\text{Δ}S\text{°}$

The change in Gibbs free energy describes the spontaneity of the reaction. The change in enthalpy describes the relative bond strength in the substance, whereas the change in entropy describes the randomness in the system.

Answer to Problem 6.22P

The given statement is false. The correct statement is, the reaction is exothermic.

Explanation of Solution

The given statement is, “the reaction is exothermic”.

The statement in part (d) states that the starting materials possess lower energy than the products of the reaction. It indicates that bonds of reactants are stronger due to which they absorb energy. Hence, the given statement is false.

Therefore, the correct statement is, the reaction is exothermic.

Conclusion

The given statement is false. The correct statement is, the reaction is exothermic.