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.

The molar mass of the gas is 4 g/mol.  

Based on the given information,  

•The mass of a sample of gas is 38.8 mg.

•The volume (V) of the gas is 224 ml at temperature 55 degree C or (273+55 = 328 K)

•The pressure (P) of the gas is 886 torr.  

Now to find the molar mass of the gas, there is a need to use the ideal gas law, that is,

PV = nRT

The value of R is 62.36 L.Torr/K/mol.

Mass is 38.8 mg or 0.0388 g.

Thus, the molar mass of the gas is 4 g/mol.

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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