   # Consider the following diagram of free energy ( G ) versus fraction of A reacted in terms of moles for the reaction 2A( g ) →B( g ). Before any A has reacted, P A = 3.0 atm and P B = 0. Determine the sign of ∆G° and the value of K p . for this reaction. ### 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 94AE
Textbook Problem
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## Consider the following diagram of free energy (G) versus fraction of A reacted in terms of moles for the reaction 2A(g) →B(g). Before any A has reacted, PA = 3.0 atm and PB = 0. Determine the sign of ∆G° and the value of Kp. for this reaction.

Interpretation Introduction

Interpretation: The diagram of free energy versus fraction of A and partial pressure of A and B before any A has reacted is given. The sign of ΔG° and the value of Kp is to be calculated.

Concept introduction: Equilibrium constant K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

If the partial pressure of reactant and product is given, then the equilibrium pressure is expressed as Kp . The expression for free energy change is,

ΔG°=RTln(Kp)

### Explanation of Solution

Given

Before any A has reacted, the partial pressure of A , PA , is 3.0atm .

Before any A has reacted, the partial pressure of B , PB , is 0atm .

The stated reaction is,

2A(g)B(g)

The given graph is,

Figure 1

The diagram shows that equilibrium is closer to the reactant. The pressure of reactant A is 0.33 times the original pressure. Hence, the total pressure of A is,

0.33(3.0atm)=0.99atm

If the partial pressure of reactant and product is given, then the equilibrium pressure is expressed as Kp and its expression is written as,

Kp=(Partialpressure of product)a(Partialpressure of reactant)b

Where,

• a is the number of moles of product

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