   Chapter 17, Problem 68E

Chapter
Section
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.

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.

ΔG=ΔG°+RTln(Q)

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

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