   # At 100°C and 1.00 atm, ∆H ° = 40.6 kJ/mol for the vaporization of water. Estimate ∆G ° for the vaporization of water at 90.°C and 110.°C. Assume ∆H ° and ∆S ° at 100.°C and 1.00 atm do not depend on temperature. ### 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 56E
Textbook Problem
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## At 100°C and 1.00 atm, ∆H° = 40.6 kJ/mol for the vaporization of water. Estimate ∆G° for the vaporization of water at 90.°C and 110.°C. Assume ∆H° and ∆S° at 100.°C and 1.00 atm do not depend on temperature.

Interpretation Introduction

Interpretation: The values of standard free energy change of the vaporization of water at the temperature 90°C and 110°C are to be calculated.

Concept Introduction: The standard free energy change of the given process is calculated by using the formula,

ΔG=ΔHTΔS

To determine: The standard free energy change of the process of vaporization of water at 90°C and 110°C .

### Explanation of Solution

Given

The standard enthalpy of vaporization at 100°C and 1atm is 40.6kJ/mol .

The conversion of enthalpy from kJ/mol into J/mol is done as,

1kJ/mol=103J/mol

Hence, the conversion of enthalpy from 40.6kJ/mol into J/mol is,

40.6kJ/mol=40.6×103J/mol

The conversion of temperature from °C into Kelvin is done as,

T(K)=T(°C)+273

Hence, the conversion of temperature from 100°C into Kelvin is,

T(K)=(100+273)K=373K

The conversion of temperature from 90°C into Kelvin is,

T(K)=(90+273)K=363K

The standard entropy change of the given process of vaporization of water is calculated by using the formula,

ΔS=ΔHT

Where,

• ΔS is the standard entropy change of the process.
• ΔH is the standard enthalpy change of the process.
• T is the temperature of the reaction.

Substitute the values of ΔH and ΔS in above equation.

ΔS=40.6×103J373K=108.85J/K

The standard free energy change of the given reaction is calculated by using the formula,

ΔG0=ΔH0TΔS0

Where,

• ΔG0 is the standard free energy change of the reaction.
• ΔH0 is the standard enthalpy change of the reaction.
• T is the temperature of the reaction.
• ΔS0 is the standard entropy change of the reaction

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