   Chapter 18, Problem 64GQ

Chapter
Section
Textbook Problem

When calcium carbonate is heated strongly, CO2 gas is evolved. The equilibrium pressure of CO2 is 1.00 bar at 897 °C, and ΔrH° at 298 K is 179.0 kJ/mol-rxn.CaCO3(s) → CaO(s) + CO2(g)Estimate the value of ΔrS° at 897 °C for the reaction.

Interpretation Introduction

Interpretation:

The value of ΔrS° for the given reaction should be estimated.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔG. It is related to entropy and enthalpy by the following expression,

ΔGo=ΔHo-TΔSo

The value of change in entropy can be calculated if the ΔH and ΔS is known.

ΔG is also related to the equilibrium constant K by the equation,

ΔrGo=-RTlnKp

Here Kp is the equilibium constant and is equal to the partial pressure of gases in the product over the reactants.

Explanation

The value of ΔrS° for the given reaction of decomposition of calcium carbonate is calculated below.

The given reaction is,

CaCO3(s)CaO(s)+CO2(g)

The equilibrium pressure of CO2(g) is 1 bar at 897 °C.

The value of Kp is,

Kp=pco2(g)

Thus,

Kp=1 bar

ΔG is related to the equilibrium constant K by the equation,

ΔrG=RTlnKp

Substituting the values,

ΔrG=RTlnKp=(8

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