Hydrogen iodide is produced industrially by the equilibrium reaction A plant must not…

CHEMISTRY · Multi-part · A Level · Chemistry · Gaseous equilibria (Kp) · Gaseous equilibria (Kp)

Problem

Hydrogen iodide is produced industrially by the equilibrium reaction

H_2(g) + I_2(g) \rightleftharpoons 2\,\text{HI}(g)

\Delta H^\circ = +52\,\text{kJ mol}^{-1}

A plant must not exceed

5.0\,\text{atm}

total pressure for safety reasons. The reactor can operate at either

500\,\text{K}

700\,\text{K}

. Standard thermodynamic data at

298\,\text{K}

are provided below:

H_2

\Delta H_f^\circ = 0\,\text{kJ mol}^{-1}

S^\circ = 131\,\text{J mol}^{-1}\,\text{K}^{-1}

I_2

\Delta H_f^\circ = 0\,\text{kJ mol}^{-1}

S^\circ = 116\,\text{J mol}^{-1}\,\text{K}^{-1}

\text{HI}

\Delta H_f^\circ = 26\,\text{kJ mol}^{-1}

S^\circ = 206\,\text{J mol}^{-1}\,\text{K}^{-1}

Assume

\Delta H^\circ

and

\Delta S^\circ

are temperature-independent over the range

298

–

700\,\text{K}

and that all gases behave ideally. Answer the following. (a) Using the data above, calculate

\Delta G^\circ

298\,\text{K}

for the formation of

2\,\text{mol HI}

from its elements. (b) Determine the equilibrium constant

K_p

298\,\text{K}

. (c) Using the van ’t Hoff relationship and your result from part (b), estimate

K_p

700\,\text{K}

. (d) For an equimolar feed of

H_2

and

I_2

at an initial total pressure of

5.0\,\text{atm}

, qualitatively compare the equilibrium mole fraction of

HI

500\,\text{K}

versus

700\,\text{K}

. Explain how both temperature and the pressure limitation influence your conclusion. (e) Propose an operational strategy, other than increasing pressure, that the plant could implement to enhance

HI

production while remaining within the

5.0\,\text{atm}

safety limit. Justify your proposal based on equilibrium principles.

Related theory

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