Answered: Imagine 1.63 moles of NH3(g) undergo…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Imagine 1.63 moles of NH3(g) undergo reversible, adiabatic expansion from 1.6 L to 5.6
L at 333 K. The molar heat capacity at constant volume of NH3(g) is 28.05 J/molK at 333
K. You may assume perfect gas behavior. Calculate the work done.

Expert Solution

Step 1: Adiabatic process

For adiabatic process

$bold italic T subscript bold 1 bold V subscript bold 1 to the power of bold gamma bold minus bold 1 end exponent bold equals bold italic T subscript bold 2 bold V subscript bold 2 to the power of bold gamma bold minus bold 1 end exponent$ ----------- eq (1)

where,

T₁ = initial temperature,

T₂ = final temperature,

V₁ = initial volume

V₂ = final volume

$bold italic gamma bold equals bold c subscript bold p over bold c subscript bold v$ ----------eq (2)

where,

c_p = heat capacity at constant pressure,

c_v = heat capacity at constant volume

Relation between c_p and c_v(for an ideal gas)

_{$bold italic c subscript bold p bold minus bold italic c subscript bold v bold equals bold italic R$ -----------} eq(3)

where R is unversal gas constant ( 8.314 J K^-1mol^-1)

Work can be calculated for and adiabatic reversible process from equation,

$bold italic w bold equals bold italic n bold italic c subscript bold v bold increment bold italic T$ --------------- eq (4)

where n is number of moles

The above equation comes from the relation, $increment U equals q plus w$ (where U is internal energy and q is heat) for adiabatic process heat exchanged is zero, so work become equal to change in internal energy.

Given data,

V₁= 1.6 L

V₂= 5.6 L

T₁ = 333 K

T_{2 ---}we have to find

c_v = 28.05 J K^-1mol^-1

n = 1.63 moles

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