A Haber-Bosch facility is evaluating two possible operating pressures for ammonia…

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

Problem

A Haber-Bosch facility is evaluating two possible operating pressures for ammonia production at

500\,\text{K}

100\,\text{atm}

and

200\,\text{atm}

. The feed stream enters each reactor with the stoichiometric ratio of

1\,\text{mol}

_2

3\,\text{mol}

_2

and negligible NH

_3

. At

500\,\text{K}

, the equilibrium constant for the reaction

\mathrm{N_2(g)} + 3\,\mathrm{H_2(g)} \leftrightarrow 2\,\mathrm{NH_3(g)}

K_\mathrm{p} = 4.34 \times 10^{-3}

. Assume ideal-gas behavior and that the total pressure inside the reactor equals the chosen operating pressure throughout. The estimated additional compression cost is

0.15

energy units per mole of gas per atmosphere above

100\,\text{atm}

. Use the information provided to analyze the two pressure options. (a) Determine the equilibrium mole fraction of NH

_3

when the total pressure is

200\,\text{atm}

. (b) Repeat the calculation in part (a) for a total pressure of

100\,\text{atm}

. (c) For each pressure, calculate the number of moles of NH

_3

produced per mole of N

_2

fed and the corresponding compression cost per mole of NH

_3

formed (assume the feed is compressed from

1\,\text{atm}

to the reactor pressure). (d) Based on your results, recommend which operating pressure offers the better economic trade-off between equilibrium yield and compression cost. Support your recommendation with quantitative reasoning.

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