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NEETPhysicsKinetic Theory of Gases

An ideal gas is maintained at a pressure of 10^5 N/m ^2 and a temperature of 300 K . If its mass density is 1.2 kg/m ^3 , what is the molar mass of the gas? (Take the universal gas constant R = 25 3 J/(mol K) )

Options

  1. A0.03 g/mol
  2. B30 g/mol
  3. C3 g/mol
  4. D300 g/mol

Correct answer

B. 30 g/mol

Step-by-step solution

The ideal gas equation in terms of mass density is given by: P = R T M₀ Rearranging for molar mass M₀ : M₀ = R T P Substitute the given values: = 1.2 kg/m ^3 R = 25 3 J/(mol K) T = 300 K P = 10^5 N/m ^2 M₀ = 1.2 ( 25 3 ) 300 10^5 M₀ = 1.2 25 100 100000 M₀ = 3000 100000 = 0.03 kg/mol To convert to g/mol , multiply by 1000 : M₀ = 0.03 1000 = 30 g/mol . Answer: 30 g/mol

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