Chapter 18, Problem 1KSP

Which of the following must be negative for a process to be spontaneous as written?

$\begin{array}{l}\text{(a)}\\ \Delta G°\\ \text{(b)}\\ \Delta G\\ \text{(c)}\\ K\\ \text{(d)}\\ Q\\ \text{(e)}\\ R\end{array}$

Interpretation Introduction

Interpretation:

The role of Gibbs free energy in a spontaneous reaction is to be explained.

Concept introduction:

Gibbs free energy is defined as the energy that is used to get the work done. The abbreviation for Gibbs free energy is $G$.

The standard Gibbs free energy, abbreviated as $\Delta G$, is defined as the change in free energy that occurs when a compound is formed from its elements in their most thermodynamically stable states under standard-state conditions. 

Answer to Problem 1KSP

Correct answer: Option(b)

Explanation of Solution

Reason for correct option:

The Gibbs energy is given by the expression as follows:

$\Delta G=\Delta H-T\Delta S$

Here, $\Delta G$ is the Gibbs energy change, $T$ is the absolute temperature, $\Delta S$ is the change in entropy, and $\Delta H$ is the change in enthalpy.

At constant temperature and pressure condition in a reaction, $\Delta G$ should be negative for the reaction to be spontaneous.

This is so, because for a spontaneous process, free energy of the system decreases and they do not need any external energy to carry out the process.

Hence, option (b) is the correct answer.

Reasons for incorrect options:

Option (a) is incorrect because the sign $\Delta G^o$ indicates the magnitude of the equilibrium constant (abbreviated as $\text{K}$).

Option (c) is incorrect because the equilibrium constant $\left(\text{K}\right)$ indicates the extent of the reaction that is the concentration of reactants and products. The higher the value of $\left(\text{K}\right)$, the smaller is the concentration of reactants, and the lower the value of $\left(\text{K}\right)$, the higher is the concentration of reactants in a reaction mixture.

Option (d) is incorrect because the reaction quotient $\left(Q\right)$ is defined as a numerical quantity that changes when the system reaches the end of the equilibrium. It defines whether the reaction will proceed in the forward or backward direction.

Option (e) is incorrect as $\text{R}$, whichis the universal gas constant, is constant for all ideal gases.

Hence, options(a), (c), (d), and (e) are incorrect.