   Chapter 18.7, Problem 1.2ACP

Chapter
Section
Textbook Problem

Assume the reaction A(aq) + B(aq) → C(aq) + H3O+(aq) produces one hydronium ion. What is the mathematical relationship between ΔrG°’ and ΔrG° at 25 °C? (Hint: Use the equation ΔrG = ΔrG° + RT ln Q and substitute ΔrG°′ for ΔrG.)

Interpretation Introduction

Interpretation:

The mathematical relationship between ΔrG° and ΔrG°' for the given reaction should be identified.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

ΔrGo is related to ΔrG°' by the expression,

ΔrG=ΔrG°+RTlnQ

For a general reaction, aA + bBcC + dD

Q= [C]c[D]d[A]a[B]b

Explanation

The mathematical relationship between ΔrG° and ΔrG°' for the given reaction is calculated as follows,

Given:

The given reaction is,

A(aq)+ B(aq)C(aq)+ H3O+(aq)

ΔrG° is related to ΔrG°' by the expression,

ΔrG°'= ΔrG°+RTlnQ= ΔrG°+RT ln[C][H3O+

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