Chemistry

Problem

The two elementary processes below are studied under identical standard conditions. Process X:

\text{C}_{2}\text{H}_{6}(g) \longrightarrow 2\,\text{C}(s,\text{graphite})+3\,\text{H}_{2}(g)

Process Y:

6\,\text{C}(s,\text{graphite})+9\,\text{H}_{2}(g) \longrightarrow 3\,\text{C}_{2}\text{H}_{6}(g)

The magnitude of the standard entropy change for Process X is reported as

\lvert\Delta S^{\circ}_{X}\rvert = 254\,\text{J\,mol}^{-1}\,\text{K}^{-1}

. (a) Without performing any numerical calculation, state the sign (positive or negative) of

\Delta S^{\circ}_{X}

and justify your choice in terms of changes in the amount of gas. (b) Process Y is the reverse of Process X but carried out on a different stoichiometric scale. Describe how the magnitude and sign of

\Delta S^{\circ}_{Y}

are related to

\Delta S^{\circ}_{X}

. Provide a verbal explanation referencing the coefficients in the balanced equations. (c) Explain in a short paragraph why multiplying a balanced chemical equation by a factor other than Unity necessarily changes the numerical value of the associated standard entropy change even though the intensive thermodynamic state variables remain the same.

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