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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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BuyFindarrow_forward

Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

Consider the following reaction:

N 2 ( g ) + 3 H 2 ( g ) 2 NH 3 ( g )

Calculate ∆G for this reaction under the following conditions (assume an uncertainty of ± 1 in all quantities):

a. T = 298 K , P N 2 = P H 2 = 200 atm , P NH 3 = 50 atm

b. T = 298 K , P N 2 = 200 atm , P H 2 = 600 atm,  P NH 3 = 200 atm

(a)

Interpretation Introduction

Interpretation: The reaction of N2 and 3H2 is given. The value of ΔG is to be calculated for given conditions.

Concept introduction: Reaction quotient, Q , is the measure of concentration or partial pressure of reactants and products of a system before the equilibrium point is reached.

The expression for free energy change is,

ΔG=ΔG°+RTln(Q)

To determine: The value of ΔG for the given values.

Explanation

Explanation

The reaction that takes place is,

N2(g)+3H2(g)2NH3(g)

Refer to Appendix 4 .

The value of ΔG°(kJ/mol) for the given reactant and product is,

Molecules ΔG°(kJ/mol)
H2(g) 0
N2(g) 0
NH3(g) 17

The formula of ΔG° is,

ΔG°=npΔG°(product)nfΔG°(reactant)

Where,

  • np is number of moles of each product.
  • nr is number of moles each reactant.
  • ΔG°(product) is free energy of product at a pressure of 1atm .
  • ΔG°(reactant) is free energy of reactant at a pressure of 1atm .

Substitute all values from the table in the above equation.

ΔG°=npΔG°(product)nfΔG°(reactant)=[2(17)1(0)3(0)]kJ=34kJ_

Given

Pressure of H2 , PH2 , is 200atm .

Pressure of N2 , PN2 , is 200atm .

Pressure of NH3 , PNH3 , is 50atm .

Formula

The reaction quotient, is expressed by the formula,

Q=PressureofproductsPressureofreactants

Where,

  • Q is the reaction quotient.

The reaction quotient expression for the given reaction is,

Q=(PNH3)2(PN2)(PH2)3

Substitute the values of PH2,PN2 and PNH3 in the above expression

(b)

Interpretation Introduction

Interpretation: The reaction of N2 and 3H2 is given. The value of ΔG is to be calculated for given conditions.

Concept introduction: Reaction quotient, Q , is the measure of concentration or partial pressure of reactants and products of a system before the equilibrium point is reached.

The expression for free energy change is,

ΔG=ΔG°+RTln(Q)

To determine: The value of ΔG for the given values.

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