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GATE 2024 ES – Question 34

Solid and Hazardous Waste Management · Municipal Solid Waste Management · 1 mark · Numerical answer

A digester produces1000 kg methane. Find storage volume in integer litres at 30°C and 3 atm. Use R=.082 L·atm/(mol·K),C12,H1.

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Correct answer: 517625 to 517885

Explanation

Methane molar mass is 16 g/mol. Moles are $1000(1000)/16=62500$. Use absolute temperature 303 K and ideal gas law: $V=nRT/P=62500(.082)(303)/3=\mathbf{517625}$ L. Kelvin, not degrees Celsius, must be used in this pressure-volume relation.

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