High School

A sample of gas has a mass of 38.6 mg. Its volume is 220 mL at a temperature of 55 °C and a pressure of 898 torr. Find the molar mass of the gas.

Answer :

The molar mass of the gas is calculated to be 3.94 g/mol.

To find the molar mass of the gas, we can use the Ideal Gas Law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

  1. First, convert the given information into appropriate units:
    • Mass = 38.6 mg = 0.0386 g
    • Volume = 220 mL = 0.220 L
    • Temperature = 55 °C = 55 + 273.15 = 328.15 K
    • Pressure = 898 torr = 898 / 760 = 1.18 atm
  2. Using the Ideal Gas Law formula and solving for n (moles of gas):
    n = PV / RT
    n = (1.18 atm) x (0.220 L) / (0.0821 L·atm/K·mol x 328.15 K)≈ 0.0098 mol
  3. Next, find the molar mass (M) using the formula:
    M = mass / moles
    M = 0.0386 g / 0.0098 mol ≈ 3.94 g/mol

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