Question

A 13.5 g sample of an unknown gas occupies 5.10 L at 149.83 kPa and 301 K. What is the molar mass of the gas ?

Answer 1

The molar mass of the gas is 44.19 g/mol

Step-by-step explanation:

Amount of sample of gas = m = 13.5 g

Volume occupied by the gas = V = 5.10 L

Pressure of the gas = P = 149.83 KPa

1 KPa = 0.00986 atm

P =
`149.83 \textrm{ KPa} * 0.00986 \textrm{ atm/KPa} = 1.48 \textrm{ atm}`

Assuming M g/mol to be the molar mass of the gas

Assuming the gas is behaving as an ideal gas

`\textrm{PV} =\textrm{nRT} \\\textrm{PV} = \displaystyle (m)/(M)\textrm{ RT } \\1.48 \textrm{ atm}* 5.10 \textrm{ L} = \displaystyle \frac{13.5 \textrm{ g}}{M}* 0.0821 \textrm{ L.atm.mol}^(-1).K^(-1)* 301\textrm{K} \\M = 44.19 \textrm{ g/mol}`

The molar mass of gas is 44.19 g/mol