GATE 2023 AE – Question 65
A cryogenic expander-cycle rocket burns hydrogen at 32 kg/s and oxygen with $\dot m_{O_2}/\dot m_{H_2}=8$. At stoichiometry with negligible reverse reaction, water formation rate (nearest integer kmol/s) is _____.
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Correct answer: 16
Explanation
**Stoichiometric reaction:** $2H_2+O_2\to2H_2O$.
The oxygen-to-hydrogen mass ratio of 8 is exactly the stoichiometric value: 32 kg of $O_2$ per 4 kg of $H_2$, which is 8. So the mixture is stoichiometric and with negligible reverse reaction all the hydrogen burns.
**Moles of hydrogen** per second (molar mass 2 kg/kmol):
$$\dot n_{H_2}=\frac{32}{2}=16\ \text{kmol/s}.$$
From the reaction, 2 mol of $H_2$ make 2 mol of $H_2O$, so
$$\dot n_{H_2O}=\dot n_{H_2}=\mathbf{16\ kmol/s}.$$