   # In the text, the equation Δ G = Δ G ° + R T In ( Q ) was derived for gaseous reactions where the quantities in Q were expressed in units of pressure. We also can use units of mol/L for the quantities in Q, specifical.ly for aqueous reactions. With this in mind, consider the reaction HF ( a q ) ⇌ H + ( a q ) + F - ( a q ) for which K a = 7.2 × 10 −4 at 25°C. Calculate ∆ G for the reaction under the following conditions at 25°C. a. [HF] = [H + ] = [F − ] = 1.0 M b. [HF] = 0.98 M, [H + ] = [F − ] = 2.7 × 10 −2 M c. [HF] = [H + ] = [F − ] = 1.0 × 10 −5 M d. [HF] = [F − ] = 0.27 M, [H + ] = 7.2 × 10 −4 M e. [HF] = 0.52 M , [ F − ] = 0.67 M, [H + ] = 1.0 × 10 −3 M Based on the calculated ∆G values, in what direction will the reaction shift to reach equilibrium for each of the five sets of conditions? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 16, Problem 90AE
Textbook Problem
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## In the text, the equation Δ G = Δ G ° + R T   In ( Q ) was derived for gaseous reactions where the quantities in Q were expressed in units of pressure. We also can use units of mol/L for the quantities in Q, specifical.ly for aqueous reactions. With this in mind, consider the reaction HF ( a q ) ⇌ H + ( a q ) + F - ( a q ) for which Ka = 7.2 × 10−4 at 25°C. Calculate ∆G for the reaction under the following conditions at 25°C.a. [HF] = [H+] = [F−] = 1.0 Mb. [HF] = 0.98 M, [H+] = [F−] = 2.7 × 10−2Mc. [HF] = [H+] = [F−] = 1.0 × 10−5 Md. [HF] = [F−] = 0.27 M, [H+] = 7.2 × 10−4Me. [HF] = 0.52 M, [F−] = 0.67 M, [H+] = 1.0 × 10−3MBased on the calculated ∆G values, in what direction will the reaction shift to reach equilibrium for each of the five sets of conditions?

(a)

Interpretation Introduction

Interpretation: The value of the Gibb’s free energy change is to be calculated for the given reaction under the given conditions. The direction in which the reaction shifts to reach the equilibrium is to be predicted.

Concept introduction: The Le Chatelier’s principle is basically an equilibrium law. According to which the equilibrium always shifts in the direction which nullify the outside effects. The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Under the standard conditions the change in Gibb’s free energy is called standard Gibb’s free energy change and is denoted by ΔGο .

To determine: The ΔGο value and the direction in which the reaction shifts to reach the equilibrium.

### Explanation of Solution

Given

The reaction is given as,

HF(aq)H+(aq)+F(aq)

Concentration values are given as,

[HF]=[H+]=[F]=1.0M

The given value of Ka is 7.2×104 .

For the given reaction the value of ΔG is calculated by t he formula,

ΔG=RTlnKa

Where,

• ΔG is the change in Gibb’s free energy.
• R is the gas constant.
• T is the temperature in Kelvin.
• Ka is the acid dissociation constant.

Substitute the value in the above equation.

ΔGο=RTlnKaΔGο=(8.314J/Kmol)(298K)ln(7.2×104)ΔGο=(2477.57)(7.23)ΔGο=17928.33J/mol_

The direction of equilibrium shift is depend upon the following conditions,

ΔGValuesEffectonequilibrium

(b)

Interpretation Introduction

Interpretation: The value of the Gibb’s free energy change is to be calculated for the given reaction under the given conditions. The direction in which the reaction shifts to reach the equilibrium is to be predicted.

Concept introduction: The Le Chatelier’s principle is basically an equilibrium law. According to which the equilibrium always shifts in the direction which nullify the outside effects. The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Under the standard conditions the change in Gibb’s free energy is called standard Gibb’s free energy change and is denoted by ΔGο .

To determine: The ΔGο value and the direction in which the reaction shifts to reach the equilibrium.

(c)

Interpretation Introduction

Interpretation: The value of the Gibb’s free energy change is to be calculated for the given reaction under the given conditions. The direction in which the reaction shifts to reach the equilibrium is to be predicted.

Concept introduction: The Le Chatelier’s principle is basically an equilibrium law. According to which the equilibrium always shifts in the direction which nullify the outside effects. The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Under the standard conditions the change in Gibb’s free energy is called standard Gibb’s free energy change and is denoted by ΔGο .

To determine: The direction in which the reaction shifts to reach the equilibrium.

(d)

Interpretation Introduction

Interpretation: The value of the Gibb’s free energy change is to be calculated for the given reaction under the given conditions. The direction in which the reaction shifts to reach the equilibrium is to be predicted.

Concept introduction: The Le Chatelier’s principle is basically an equilibrium law. According to which the equilibrium always shifts in the direction which nullify the outside effects. The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Under the standard conditions the change in Gibb’s free energy is called standard Gibb’s free energy change and is denoted by ΔGο .

To determine: The direction in which the reaction shifts to reach the equilibrium.

(e)

Interpretation Introduction

Interpretation: The value of the Gibb’s free energy change is to be calculated for the given reaction under the given conditions. The direction in which the reaction shifts to reach the equilibrium is to be predicted.

Concept introduction: The Le Chatelier’s principle is basically an equilibrium law. According to which the equilibrium always shifts in the direction which nullify the outside effects. The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Under the standard conditions the change in Gibb’s free energy is called standard Gibb’s free energy change and is denoted by ΔGο .

To determine: The direction in which the reaction shifts to reach the equilibrium.

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