Problem 2

Dissociating gas cycle. Dinitrogen tetroxide forms an equilibrium mixture with nitrogen dioxide:

\ce{N2O4(g) <=> 2 NO2(g)}

. 1.00 mol of

\ce{N2O4}

was placed in an empty vessel of fixed volume 24.44 dm

^3

. The equilibrium gas pressure at 298 K was 1.190 bar; when heated to 348 K the equilibrium pressure rose to 1.886 bar. (a) Calculate

\Delta G^{\circ}

of the reaction at 298 K, assuming ideal gases. (b) Calculate

\Delta H^{\circ}

and

\Delta S^{\circ}

, assuming they do not vary significantly with temperature. The reversible dissociation of

\ce{N2O4}

can be exploited in power cycles: in step

3 \to 4

the hot gas mixture expands reversibly and adiabatically through a turbine. (c) Give the equation for the work done by 1 mol of an inert gas (air) during the reversible adiabatic expansion

3 \to 4

, assuming constant

C_{V,m}

and a temperature drop from

T_3

T_4

Step 5 of 5: Work of adiabatic expansion

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w_{\text{air}} = \Delta U = C_{V,m}(\text{air})\,(T_3 - T_4)

Analysis

For a reversible adiabatic expansion $q = 0$ , so the work done by the gas equals its internal-energy decrease: $w_{\text{air}} = -\Delta U = C_{V,m}(T_3 - T_4)$ (taking work output as positive).

Common pitfall. Do not forget that

p_{ini}

must be recalculated at each temperature with the ideal-gas law — using 1.014 bar at 348 K gives the wrong

x