A particular container holds 4.67 mol of neon gas. The volume of this container can be altered by sliding a piston in or out. The volume is changed from 8.90 L to 7.60 L while at the same time the temperature is changed from 344 K to 294 K. The molar heat capacity, CV, m, for neon is 12.47 J / (mol · K). Assume that this value will not change over the given temperature range. What is the change in entropy for the gas?

Question

Chemistry

Leblanc

29 March, 11:57

A particular container holds 4.67 mol of neon gas. The volume of this container can be altered by sliding a piston in or out. The volume is changed from 8.90 L to 7.60 L while at the same time the temperature is changed from 344 K to 294 K. The molar heat capacity, CV, m, for neon is 12.47 J / (mol · K). Assume that this value will not change over the given temperature range. What is the change in entropy for the gas?

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Alexandra Armstrong · Answer 1

15.24 J/K

Explanation:

First, let's write the expression to calculate the change in entropy:

ΔS = n*C*ln (T2/T1)

C is the heat capacity. It will be Cp if the heating is isobaric, and Cv if it is isochoric. (In this case is Cv)

Now, in order to do this, we need to calculate first the pressure of the gas at first, and then, after the chance:

P = nRT/V

P1 = 4.67 * ¨0.082 * 344 / 8.9 = 14.801 atm

P2 = 4.67 * 0.082 * 294 / 7.6 = 14.814 atm

Now, let's calculate the change in entropy:

ΔS = 4.67 * (12.47 + 8.314) ln (344/294)

ΔS = 15.24 J/K