Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
9th Edition
ISBN: 9781133949640
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Textbook Question
Chapter 15, Problem 63GQ

A sample of N2O4 gas with a pressure of 1.00 atm is placed in a flask. When equilibrium is achieved, 20.0% of the N2O4 has been convened to NO2 gas.

  1. (a) Calculate Kp.

If the original pressure of N2O4 is 0.10 atm, what is the percent dissociation of the gas? Is the result in agreement with Le Chatelier’s principle?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The KP for the dissociation reaction of N2O4 to NO2 with a pressure of 1atm has to be calculated.

Concept Introduction:

  • Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
  • Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
  • Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

    xa=nantotal

  • pa=xa×Ptotal

    Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

  • Ideal gas equation:PV=nRT

Equilibrium constant in terms of pressure[Kp]: Equilibrium constant can be expressed in terms of partial pressures in atmospheres.

  • aA(g)+bB(g)cC(g)+dD(g)KP=PCc×PDdPAa×PBb

Le Chatelier’s principle: If an equilibrium is disturbed by changing conditions, the system will moves the equilibrium to reverse the change.

Answer to Problem 63GQ

The KP for the given reaction is 0.2.

Explanation of Solution

Given:

N2O42NO2Pressure=1atmAtequilibrium,20%N2O4convertstoNO2

Given that initial pressure is 1atm

Given the reaction:

N2O42NO2Initialpressure1atm0Change-x+2xAtequilibrium1-x2x

At equilibrium 20% N2O4 decomposed and 80% remains. Thus we can write

1-x=0.8atm[80%]

x=0.2atm

KP=P[NO2]2P[N2O4]=[2×0.2]21-0.2=0.160.8=0.2

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The percent of dissociation of gas if the original pressure of N2O4 is 0.10atm has to be given.

Concept Introduction:

  • Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
  • Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
  • Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

    xa=nantotal

  • pa=xa×Ptotal

    Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

  • Ideal gas equation:PV=nRT

Equilibrium constant in terms of pressure[Kp]: Equilibrium constant can be expressed in terms of partial pressures in atmospheres.

  • aA(g)+bB(g)cC(g)+dD(g)KP=PCc×PDdPAa×PBb

Le Chatelier’s principle: If an equilibrium is disturbed by changing conditions, the system will moves the equilibrium to reverse the change.

Answer to Problem 63GQ

The percent dissociation of the gas is 50%.

Explanation of Solution

Given:

N2O42NO2Pressure=0.10atm

Given the reaction:

N2O42NO2Initialpressure0.1atm0Change-x+2xAtequilibrium0.1-x2x

KP=P[NO2]2P[N2O4]0.2=[2x]20.1-x4x2+0.2x-0.02=0

Solving the quadratic equation we get x=0.05

Therefore the percent of dissociation at equilibrium =[0.05atm0.1atm]×100=50%

Here we can see that when the pressure decreases from 1atmto0.1atm, the percent of dissociation increases and more amount of product is formed.

According to Le Chatelier’s principle, if an equilibrium is disturbed by changing conditions, the system will moves the equilibrium to reverse the change.

If pressure of the system decreases, system will shift to the direction which having more number of molecules. Here product side has more number of molecules and thus the dissociation percent increases.

The result is in agreement with Le Chatelier’s principle.

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Chapter 15 Solutions

Chemistry & Chemical Reactivity

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