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NEETPhysicsKinetic Theory of Gases

A rigid container is initially filled with oxygen gas. A student plots a pressure-temperature ( P-T ) graph for the gas. The initial state of the gas is represented by point A at coordinates (T₀, P₀) . After some gas is allowed to leak out, the container is resealed and the gas reaches a new state represented by point B at coordinates (2T₀, 1.2P₀) . What percentage of the initial mass of the gas was released from the

Options

  1. A60 %
  2. B20 %
  3. C40 %
  4. D80 %

Correct answer

C. 40 %

Step-by-step solution

From the ideal gas equation, PV = nRT n = PV RT . For the initial state A, the number of moles is n_A = P₀ V R T₀ . For the final state B, the number of moles is n_B = 1.2 P₀ V R (2T₀) = 0.6 ( P₀ V R T₀ ) = 0.6 n_A . Since the mass of the gas is directly proportional to the number of moles, the remaining mass in the container is 60 % of the initial mass. Therefore, the percentage of the initial mass that leaked out is 100 % - 60 % = 40 % . Answer: 40 %

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