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Q12.3: NCERT Physics - Part 2 KINETIC THEORY 12.3 Solution: Figure 12.8 shows plot of PV/T versus P for kg of oxygen gas at …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently treat the PV/T value where the curves meet as a universal constant for any gas, forgetting that $PV/T=nR$ depends on the number of moles, not the mass. Always convert the given mass to moles using the correct molecular weight before using $PV/T=nR$, otherwise the calculated intersection value will be wrong.

Figure 12.8 shows plot of PV/T versus P for 1.00×10−31.00 \times 10^{-3} kg of oxygen gas at two different temperatures. (a) What does the dotted plot signify? (b) Which is true: T1>T2T_1 > T_2 or T1<T2T_1 < T_2? (c) What is the value of PV/T where the curves meet on the y-axis? (d) If we obtained similar plots for 1.00×10−31.00 \times 10^{-3} kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot)? (Molecular mass of H_ = 2.02 u, of O_ = 32.0 u, R = 8.31 J mol__ K__.)

Step-by-Step Verified Solution

**Answer:** (a) Ideal gas behaviour (b) T1>T2T_1 > T_2 (c) PV/T=0.26 J K−1PV/T = 0.26 \text{ J K}^{-1} (d) No; mass of hydrogen = 6.3×10−56.3 \times 10^{-5} kg **Step-by-Step Explanation:** (a) The dotted plot is parallel to the P-axis, signifying that PV/TPV/T is constant and independent of pressure. This represents ideal gas behaviour. (b) The curve at T1T_1 is closer to the ideal dotted line than the curve at T2T_2. A real gas approaches ideal behaviour at higher temperatures. Hence, T1>T2T_1 > T_2. (c) Where the curves meet on the y-axis:
PV=nRT  ⟹  PVT=nRPV = nRT \implies \frac{PV}{T} = nR
For oxygen, mass m=1.00×10−3m = 1.00 \times 10^{-3} kg =1.00= 1.00 g, M=32M = 32 g/mol.
n=1.0032=0.03125 moln = \frac{1.00}{32} = 0.03125 \text{ mol}
PVT=nR=0.03125×8.31=0.26 J K−1\frac{PV}{T} = nR = 0.03125 \times 8.31 = 0.26 \text{ J K}^{-1}
(d) For hydrogen, M=2.02M = 2.02 g/mol. To get the same PV/TPV/T, we need the same number of moles:
n=0.03125 moln = 0.03125 \text{ mol}
mH2=n×M=0.03125×2.02=0.063 g=6.3×10−5 kgm_{H_2} = n \times M = 0.03125 \times 2.02 = 0.063 \text{ g} = 6.3 \times 10^{-5} \text{ kg}
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All Questions in this Chapter

Q12.1 Q12.2 Q12.3 Q12.4 Q12.5 Q12.6 Q12.7 Q12.8 Q12.9 Q12.10

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