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Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases

An open container of volume 50 cc holds air (mean molecular weight = 28.8 g ) and is exposed to the atmosphere where the pressure is 100 kPa . The container is placed in a bath containing melting ice ( 0^ C ). Determine the mass of the air in the container when thermal equilibrium is established.

Options

  1. A0.0580 g
  2. B0.0464 g
  3. C0.0634 g
  4. D0.0721 g

Correct answer

C. 0.0634 g

Step-by-step solution

Given parameters: Volume of the container, V = 50 cc = 50 10⁻⁶ m ^3 Pressure, P = 100 kPa = 10^5 Pa Temperature, T = 0^ C = 273.15 K Mean molecular weight of air, M = 28.8 g/mol Universal gas constant, R = 8.314 J/(mol K) Using the ideal gas equation: PV = nRT Since the number of moles n = m M , we can write: PV = m M RT Rearranging for mass m : m = PVM RT Substituting the given values: m = 10^5 50 10⁻⁶ 28.8 8.314 273.15 m = 5 28.8 2270.97 m = 144 2270.97 0.0634 g

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