Five separate processes involving one or more ideal substances occur under the stated…

CHEMISTRY · Multi-part · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Five separate processes involving one or more ideal substances occur under the stated conditions. Process A:

2.0\,\text{mol}

Ar(g), initially at

298\,\text{K}

and

10.0\,\text{L}

, isothermally compressed to

5.0\,\text{L}

. Process B:

1.0\,\text{mol}

ethanol(l) vaporizes at its normal boiling point,

351\,\text{K}

;

\Delta H_{\text{vap}}=38.6\,\text{kJ mol}^{-1}

. Process C: A partition is removed to mix

1.0\,\text{mol}

Ne(g) with

1.0\,\text{mol}

Kr(g) in a rigid

20\,\text{L}

container at

298\,\text{K}

. Process D:

1.0\,\text{mol}

\mathrm{N}_2

(g) is cooled at constant volume from

400\,\text{K}

300\,\text{K}

. Process E:

1.0\,\text{mol}

\mathrm{CO}_2

(s) sublimes at

195\,\text{K}

and

1\,\text{atm}

;

\Delta H_{\text{sub}}=25.3\,\text{kJ mol}^{-1}

. (a) Without performing detailed calculations, rank the magnitude of the entropy change

|\Delta S|

for Processes A–E from smallest to largest. (b) Provide a thorough justification for the ranking in part (a), explicitly addressing how phase, volume, temperature, and mixing each influence matter and energy dispersal. (c) Derive an expression for

\Delta S

for an isothermal, reversible compression of an ideal gas and use it to calculate

\Delta S

for Process A. Then derive an expression for

\Delta S

for cooling an ideal gas at constant volume and use it to calculate

\Delta S

for Process D. Confirm that the numerical results are consistent with your qualitative ranking. (d) A student argues that Process C involves no entropy change because the total number of gas moles remains the same. Critically evaluate this claim, citing appropriate reasoning about microstate availability.

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