Question

An unknown gas at 73.1 °C and 1.10 atm has a molar mass of 28.01 g/mol. Assuming ideal behavior, what is the density of the gas? density

Answer 1

Density = 1.08 g/L

Explanation:

The Ideal Gas Law states that 

PV = nRT 

n is the number of moles, which can be translated as

PV = (m/M)RT

Where m = mass and M = molar mass.

The equation for solving for density is mass divided by volume (m/V). So rearrange the equation now to substitute density.

PM = (m/V)RT OR PM = (D)RT

Now, rearrange it once again to solve for density.

D = PM/RT 

(Where D = Density (g/L), P = Pressure (atm), M = Molar mass (g/mol), R = Ideal Gas Constant (0.08206 L*atm/(mol*K)), and T = Temperature (K).

Since the temperature is given in Celsius, convert it to Kelvin by adding 273.15.

73.1 + 273.15 = 346.25

Now substitute all of the values given into the equation.

D = (1.1 atm)(28.01 g/mol)/(0.08206)(346.25)

D = 30.811/28.413275

D = 1.08438749 OR 1.08

And you're done!