Question

What is the density (in g/L) of a gas with a molar mass of 122.7 g/mol at a pressure of 2.07 atm and a temperature of 52.39 °C?

Answer 1

We know ideal gas law equation

PV = nRT

Where we have

P = Pressure of gas = 2.07 atm

V = Volume it occupies

R = gas constant = 0.0821 L.atm/mol.K

T = Absolute temperature = 52.39 ⁰C = 52.39 + 273.15 = 325.54 K

n = number of moles of gas

And Molar mass (M_M ) = 122.7 g/mol

We know the formula of mole and density

Mole (n) = mass in g (m) / Molar mass (M_M )

Density ($\rho$) = mass (m) / Volume (V)

Lets simplify the ideal gas law equation

PV = nRT

PV = (m/M_M ) RT

by rearranging

P $\times$ M_M = ( m /V) $\times$ RT

P $\times$ M_M = $\rho$$\times$ RT

Then

Density = $\rho$ = P $\times$ M_M / RT

= 2.07 atm $\times$ 122.7 g/mol / ( 0.0821 L.atm/mol.K $\times$ 325.54 K)

= 9.50 g/L

So Our answer is 9.50 g/L