High School

Calculate the molar mass of a gas with the following properties:

- Mass: 3.15 g
- Pressure: 785 mmHg
- Temperature: 20°C
- Volume: 750 mL

A. 9.79 g/mol
B. 97.9 g/mol
C. 979 g/mol
D. 9790 g/mol

Answer :

Final answer:

The molar mass of the gas is calculated using the ideal gas law rearranged to solve for molar mass (M = mRT / PV). The given values for the mass of the gas, temperature, pressure, and volume are substituted in the formula, yielding a molar mass of approximately 9.79 g/mol (option a).

Explanation:

To calculate the molar mass of the gas, we can use the ideal gas law (PV = nRT) which, when rearranged to solve for molar mass (M), becomes M = mRT / PV, where:

  • m is the mass of the gas (3.15 g),
  • R is the ideal gas constant (0.0821 L.atm/K.mol)
  • ,
  • T is temperature in degrees Kelvin (20 + 273 = 293 K),
  • P is the Pressure of the gas (785 mmHg, to convert to atm, we divide by 760, to get approximately 1.03 atm),
  • V is the volume of the gas (750 ml, which is 0.75 L)

Now, plug in these values to get M = (3.15 g * 0.0821 L.atm/K.mol * 293 K) / (1.03 atm * 0.75 L) = approximately 9.79 g/mol. Therefore, the answer is a) 9.79 g/mol

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