A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 °C and a pressure of 886 torr. Find the molar mass of the gas.

4g/mol

Explanation:

Firstly, we can get the number of moles of the gas present using the ideal gas equation.

PV = nRT

Here:

P = 886 torr

V = 224ml = 224/1000 = 0.224L

T = 55 degrees celcius = 55 + 273.15 = 328.15K

R = molar gas constant = 62.36 L⋅Torr⋅K-1⋅mol-1

n = PV/RT

n = (886 * 0.224) / (62.36 * 328.15)

n = 0.009698469964 mole

Now to get the molar mass, this is mathematically equal to the mass divided by the number of moles. We have the mass and the number of moles, remaining only the molar mass.

First, we convert the mass to g and that is 38.8/1000 = 0.0388

The molar mass is thus 0.0388/0.009698469964 = 4g/mol