Chemistry

Problem

Three industrially important gas–phase reactions are carried out in separate reactors that can be operated at variable temperatures. To investigate temperature effects, a chemical engineer measures the equilibrium constants at two temperatures,

350\,\text{K}

and

600\,\text{K}

, as summarized in the table.

Reaction	Balanced equation	$K_{350\,\text{K}}$	$K_{600\,\text{K}}$
I	\ce{N2O4(g) <=> 2NO2(g)}	$1.1\times10^{-3}$	$4.5\times10^{-2}$
II	\ce{2SO2(g) + O2(g) <=> 2SO3(g)}	$5.5\times10^{4}$	$6.3\times10^{2}$
III	\ce{C2H4(g) + H2(g) <=> C2H6(g)}	$7.8\times10^{3}$	$6.0\times10^{0}$

Assume ideal-gas behavior. a. At each temperature, rank the three reactions in order of increasing extent of conversion of reactants to products at equilibrium. b. For Reaction I, calculate the factor by which the equilibrium mole fraction of \ce{NO2} increases when the temperature is raised from

350\,\text{K}

600\,\text{K}

, assuming the total pressure and initial amounts remain the same in both experiments. Clearly state any approximations used in your calculation. c. Using the data in the table, propose a thermodynamic explanation—based on the sign of

\Delta H^\circ

—for the observed temperature dependence of the equilibrium constant for each reaction. Support your explanation with appropriate reasoning.

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