GATE 2021 BT – Question 20

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 1 mark · Multiple choice

Under standard T and P, 128 g of ideal gas A occupies 1 L and obeys $RT=0.25PV$. R is the universal gas constant. A is

$CO_2$
$H_2$
$N_2$
$O_2$

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Correct answer: (D) $O_2$

Explanation

**Ideal gas law:** $PV=nRT$.

**Step 1: use the given relation.** The problem gives $RT=0.25\,PV$. Substitute it into $PV=nRT$:
$$PV=n\,(0.25\,PV)\;\Rightarrow\;n=\frac1{0.25}=4\text{ mol}.$$

**Step 2: molar mass.** 128 g of the gas is 4 mol, so
$$M=\frac{128}{4}=32\text{ g/mol}.$$

CO₂ = 44, H₂ = 2, N₂ = 28, **O₂ = 32**. ✓

Answer **O₂** (D).