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GATE 2021 CH – Question 13

Thermodynamics · Laws of thermodynamics, open and closed systems, entropy and chemical potential · 1 mark · Multiple choice

The heat of combustion of methane, carbon monoxide and hydrogen are $P,Q$ and $R$ respectively. For the reaction below, $\mathrm{CH_4+H_2O\to CO+3H_2}$, the heat of reaction is given by

  1. $P-Q-3R$
  2. $Q+3R-P$
  3. $P-Q-R$
  4. $Q+R-P$

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Correct answer: (A) $P-Q-3R$

Explanation

Apply Hess’s law using signed heats of combustion. Burning methane gives $\mathrm{CH_4+2O_2\to CO_2+2H_2O}$ with heat $P$. Burning the reformer products gives $\mathrm{CO+3H_2+2O_2\to CO_2+3H_2O}$ with heat $Q+3R$.

Subtract the second reaction from the first. The common oxygen and carbon dioxide cancel, leaving $\mathrm{CH_4+H_2O\to CO+3H_2}$. Consequently $\Delta H=P-(Q+3R)=\mathbf{P-Q-3R}$, **A**.