Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Under standard temperature (T) and pressure (P) conditions, 128 g of an ideal gas molecule A occupies a volume of 1 L. The gas molecule A obeys the relationship RT = 0.25 PV, where R is the universal gas constant and V is ideal gas volume. The molecule A is:
Options:
(A) CO2
(B) H2
(C) N2
(D) O2
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.20)**
**1. Governing Concept**:
- **Topic**: Chemical Thermodynamics & Ideal Gas Equation
- Mass of gas $m = 128\text{ g}$, volume $V = 1\text{ L}$ at STP ($T_0 = 273.15\text{ K}, P_0 = 1\text{ atm}$).
- Given equation of state:
$RT = 0.25 PV \implies PV = 4 RT$
- Ideal gas equation relates moles $n$ by $PV = nRT$. Comparing coefficients:
$n = 4\text{ moles}$
- Molar mass of gas molecule $A$:
$M = \frac{m}{n} = \frac{128\text{ g}}{4\text{ mol}} = 32\text{ g/mol}$
- Molecular weight of candidates:
- $\text{CO}_2 = 44\text{ g/mol}$
- $\text{H}_2 = 2\text{ g/mol}$
- $\text{N}_2 = 28\text{ g/mol}$
- $\text{O}_2 = 32\text{ g/mol}$
- Thus, the molecule is **$\text{O}_2$**.
**2. Option Analysis**:
- **Option (A) [CO2] is INCORRECT**: Molar mass $44\text{ g/mol}$.
- **Option (B) [H2] is INCORRECT**: Molar mass $2\text{ g/mol}$.
- **Option (C) [N2] is INCORRECT**: Molar mass $28\text{ g/mol}$.
- **Option (D) [O2] is CORRECT**: Molar mass matches $128 / 4 = 32\text{ g/mol}$.
**3. Final Answer**:
- **Correct Choice**: **D**
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