Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
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Chapter 2, Problem 2A.1ST
Interpretation Introduction

Interpretation: The expansion work done when 50 g of water is electrolysed under constant pressure at 25 οC has to be calculated.

Concept introduction: Thermodynamics address temperature and heat and their relationship to work, energy and matter.  Work is defined as the form of mechanical energy that is transferred from system to another.  The work done is calculated by the formula,

    w=nRT

Expert Solution & Answer
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Answer to Problem 2A.1ST

The expansion work done when 50 g of water is electrolysed under constant pressure at 25 οC is 10.33147 kJ_.

Explanation of Solution

It is given that the mass of water is 50 g.

The temperature is 25 οC.

Pressure is 1 atm.

The conversion of Celsius to Kelvin is done as,

    οC=273 K

Therefore, the conversion of 25 οC to Kelvin is done as,

    25 οC=25+273 K=298 K

The balanced chemical equation for the electrolysis of water is,

    2H2O(l)2H2(g)+O2(g)

First, the number of moles of oxygen and hydrogen are calculated by the formula,

    Number of moles=Mass(g)Molar mass(g mol1)                                                         (1)

The molar mass of water is 18 g mol1.

For oxygen,

    Moles of oxygen=50 g H2O×1 mol H2O18 g H2O×1 mol O22 mol H2O=1.39 mol O2

For hydrogen,

    Moles of oxygen=50 g H2O×1 mol H2O18 g H2O×2 mol H22 mol H2O=2.78 mol H2

Now, the initial volume of water is assumed to be negligible when compared to final volume of both hydrogen and oxygen gas.  Therefore,

    ΔV=Vfinal                                                                                                        (2)

The ideal gas equation is given by the expression,

    Vfinal=nRTPext                                                                                                    (3)

Now, the expansion work is calculated by the formula,

    w=Pext×Vfinal                                                                                               (4)

Substitute the value of Vfinal from equation (3) to equation (4).

    w=Pext×nRTPextw=nRT                                                                                              (5)

Substitute the values of number of moles of oxygen and hydrogen, universal gas constant and temperature in the above equation (5) to calculate the expansion work.

    w=(1.39 mol O2+2.78 mol H2)×8.314 J K1mol1×298 K=4.17 mol×2477.572 J mol1=10331.47 J

The conversion of joule into kJ is done as,

    1 kJ=1000 J1 J=103 kJ

Therefore, the conversion of 10331.47 J into kJ is done as,

    10331.47 J=103 ×10331.47 kJ=10.33147 kJ_

Hence, the expansion work done when 50 g of water is electrolysed under constant pressure at 25 οC is 10.33147 kJ_.

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Chapter 2 Solutions

Atkins' Physical Chemistry

Ch. 2 - Prob. 2A.4DQCh. 2 - Prob. 2A.5DQCh. 2 - Prob. 2A.1AECh. 2 - Prob. 2A.1BECh. 2 - Prob. 2A.2AECh. 2 - Prob. 2A.2BECh. 2 - Prob. 2A.3AECh. 2 - Prob. 2A.3BECh. 2 - Prob. 2A.4AECh. 2 - Prob. 2A.4BECh. 2 - Prob. 2A.5AECh. 2 - Prob. 2A.5BECh. 2 - Prob. 2A.6AECh. 2 - Prob. 2A.6BECh. 2 - Prob. 2A.1PCh. 2 - Prob. 2A.2PCh. 2 - Prob. 2A.3PCh. 2 - Prob. 2A.4PCh. 2 - Prob. 2A.5PCh. 2 - Prob. 2A.6PCh. 2 - Prob. 2A.7PCh. 2 - Prob. 2A.8PCh. 2 - Prob. 2A.9PCh. 2 - Prob. 2A.10PCh. 2 - Prob. 2B.1DQCh. 2 - Prob. 2B.2DQCh. 2 - Prob. 2B.1AECh. 2 - Prob. 2B.1BECh. 2 - Prob. 2B.2AECh. 2 - Prob. 2B.2BECh. 2 - Prob. 2B.3AECh. 2 - Prob. 2B.3BECh. 2 - Prob. 2B.4AECh. 2 - Prob. 2B.4BECh. 2 - Prob. 2B.1PCh. 2 - Prob. 2B.2PCh. 2 - Prob. 2B.3PCh. 2 - Prob. 2B.4PCh. 2 - Prob. 2B.5PCh. 2 - Prob. 2C.1DQCh. 2 - Prob. 2C.2DQCh. 2 - Prob. 2C.3DQCh. 2 - Prob. 2C.4DQCh. 2 - Prob. 2C.1AECh. 2 - Prob. 2C.1BECh. 2 - Prob. 2C.2AECh. 2 - Prob. 2C.2BECh. 2 - Prob. 2C.3AECh. 2 - Prob. 2C.3BECh. 2 - Prob. 2C.4AECh. 2 - Prob. 2C.4BECh. 2 - Prob. 2C.5AECh. 2 - Prob. 2C.5BECh. 2 - Prob. 2C.6AECh. 2 - Prob. 2C.6BECh. 2 - Prob. 2C.7AECh. 2 - Prob. 2C.7BECh. 2 - Prob. 2C.8AECh. 2 - Prob. 2C.8BECh. 2 - Prob. 2C.1PCh. 2 - Prob. 2C.2PCh. 2 - Prob. 2C.3PCh. 2 - Prob. 2C.4PCh. 2 - Prob. 2C.5PCh. 2 - Prob. 2C.6PCh. 2 - Prob. 2C.7PCh. 2 - Prob. 2C.8PCh. 2 - Prob. 2C.9PCh. 2 - Prob. 2C.10PCh. 2 - Prob. 2C.11PCh. 2 - Prob. 2D.1DQCh. 2 - Prob. 2D.2DQCh. 2 - Prob. 2D.1AECh. 2 - Prob. 2D.1BECh. 2 - Prob. 2D.2AECh. 2 - Prob. 2D.2BECh. 2 - Prob. 2D.3AECh. 2 - Prob. 2D.3BECh. 2 - Prob. 2D.4AECh. 2 - Prob. 2D.4BECh. 2 - Prob. 2D.5AECh. 2 - Prob. 2D.5BECh. 2 - Prob. 2D.1PCh. 2 - Prob. 2D.2PCh. 2 - Prob. 2D.3PCh. 2 - Prob. 2D.4PCh. 2 - Prob. 2D.5PCh. 2 - Prob. 2D.6PCh. 2 - Prob. 2D.7PCh. 2 - Prob. 2D.8PCh. 2 - Prob. 2D.9PCh. 2 - Prob. 2E.1DQCh. 2 - Prob. 2E.2DQCh. 2 - Prob. 2E.1AECh. 2 - Prob. 2E.1BECh. 2 - Prob. 2E.2AECh. 2 - Prob. 2E.2BECh. 2 - Prob. 2E.3AECh. 2 - Prob. 2E.3BECh. 2 - Prob. 2E.4AECh. 2 - Prob. 2E.4BECh. 2 - Prob. 2E.5AECh. 2 - Prob. 2E.5BECh. 2 - Prob. 2E.1PCh. 2 - Prob. 2E.2PCh. 2 - Prob. 2.1IACh. 2 - Prob. 2.3IACh. 2 - Prob. 2.4IACh. 2 - Prob. 2.5IACh. 2 - Prob. 2.6IACh. 2 - Prob. 2.7IA
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