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NEET
Exam
NEET
Subject
Physics
Chapter
Kinetic Theory of Gases

NEET · Physics · Kinetic Theory of Gases

A graph displays straight lines passing through the origin,...

A graph displays straight lines passing through the origin, representing the Volume (VV) versus Mass (mm) at STP for four different gases: O2\text{O}_2, N2\text{N}_2, He\text{He}, and H2\text{H}_2. It is assumed that the intermolecular forces in all these gases vanish completely. The lines are labeled 1, 2, 3, and 4 in decreasing order of their slopes (i.e., line 1 is the steepest). Which of the following correctly identifies the gases corresponding to lines 1, 2, 3, and 4 respectively?

Options

  1. AO2\text{O}_2, N2\text{N}_2, He\text{He}, H2\text{H}_2
  2. BHe\text{He}, H2\text{H}_2, N2\text{N}_2, O2\text{O}_2
  3. CH2\text{H}_2, O2\text{O}_2, N2\text{N}_2, \text{He
  4. DH2\text{H}_2, He\text{He}, N2\text{N}_2, O2\text{O}_2

Correct answer

D. H2\text{H}_2, He\text{He}, N2\text{N}_2, O2\text{O}_2

Step-by-step solution

According to the ideal gas equation, the volume VV of a gas of mass mm and molar mass MM at STP is given by:

V=mM×22.4 LV = \dfrac{m}{M} \times 22.4\text{ L}

The slope of the VV versus mm graph is Vm=22.4M\dfrac{V}{m} = \dfrac{22.4}{M}.

Thus, the slope is inversely proportional to the molar mass MM. The gas with the smallest molar mass will have the steepest slope (line 1).

The molar masses of the given gases are:
H2=2 g mol−1\text{H}_2 = 2\text{ g mol}^{-1}
He=4 g mol−1\text{He} = 4\text{ g mol}^{-1}
N2=28 g mol−1\text{N}_2 = 28\text{ g mol}^{-1}
O2=32 g mol−1\text{O}_2 = 32\text{ g mol}^{-1}

Since MH2<MHe<MN2<MO2M_{\text{H}_2} < M_{\text{He}} < M_{\text{N}_2} < M_{\text{O}_2}, the order of decreasing slopes is H2>He>N2>O2\text{H}_2 > \text{He} > \text{N}_2 > \text{O}_2. Therefore, lines 1, 2, 3, and 4 correspond to H2\text{H}_2, He\text{He}, N2\text{N}_2, and O2\text{O}_2 respectively.

Answer: H2\text{H}_2, He\text{He}, N2\text{N}_2, O2\text{O}_2
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