A chemist studies the gas-phase decomposition of compound X described by the balanced…

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

Problem

A chemist studies the gas-phase decomposition of compound X described by the balanced equation X(g)

\rightarrow

Y(g) + Z(g) At 1.0 bar, the Gibbs free energy change of the reaction has been measured at several temperatures. A colleague summarizes the results in a report that includes a verbal description of a graph: • The plot of

\Delta G

(y-axis, in kJ mol

^{-1}

) versus

T

(x-axis, in K) is a straight line that crosses the temperature axis at

575\,\text{K}

. • When extrapolated to

T = 0\,\text{K}

, the line intersects the

\Delta G

axis at

+120\,\text{kJ mol}^{-1}

. • The slope of the line is

-0.21\,\text{kJ mol}^{-1}\,\text{K}^{-1}

. Use the information contained in this description to analyze the thermodynamic favorability of the reaction. (1) Part 1: (a) Identify the sign of

\Delta G

\Delta H

, and

\Delta S

298\,\text{K}

. Justify each sign qualitatively with reference to features of the graph. (2) Part 2: (b) Estimate the numerical values (including units) of

\Delta H

and

\Delta S

for the reaction, indicating clearly how each value is obtained from the graph description. (3) Part 3: (c) Determine whether the reaction is thermodynamically favored at

298\,\text{K}

. Support your answer with a calculation that uses the values from part (b). (4) Part 4: (d) Describe the temperature range in which the reaction is spontaneous. Explain how this range is represented on the

\Delta G

–

T

plot.

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