Chemistry

Problem

Methanol can be synthesized from synthesis gas according to

\mathrm{CO(g)+2\,H_2(g)}\;\longleftrightarrow\;\mathrm{CH_3OH(g)}

At 500 K the equilibrium constant is

K_p = 14.0

. A reactor is charged to 500 K with the following partial pressures:

P_{\mathrm{CO}} = 3.0\,\text{atm}

P_{\mathrm{H_2}} = 6.0\,\text{atm}

, and

P_{\mathrm{CH_3OH}} = 1.0\,\text{atm}

. (a) Calculate the reaction quotient

Q_p

for the initial mixture. Show your work. (b) Based on the value of

Q_p

relative to

K_p

, state the direction in which the system will shift to reach equilibrium and briefly explain your reasoning. (c) Process operators can instantly raise the partial pressure of only one species while keeping temperature constant. Determine which single change—doubling

P_{\mathrm{CO}}

, doubling

P_{\mathrm{H_2}}

, or halving

P_{\mathrm{CH_3OH}}

—will most effectively drive the reaction toward additional methanol formation. Support your choice with quantitative or logical justification.

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