Question

A gas has a density of 1.43 g/L at a temperature of 23°C and a pressure of 0.789 atm. Calculate its molar mass.

a) 28.7 g/mol
b) 32.0 g/mol
c) 44.6 g/mol
d) 52.1 g/mol

Answer 1

To find the molar mass of the gas, use the ideal gas equation. Convert the given values and substitute them into the equation to calculate the molar mass. The molar mass is 32.0 g/mol, so the correct answer is b) 32.0 g/mol.

Step-by-step explanation:

To calculate the molar mass of the gas, we need to use the ideal gas equation:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

1. First, convert the given density from g/L to kg/m³. In this case, the density is 1.43 g/L.
2. Next, convert the pressure from atm to Pa. In this case, the pressure is 0.789 atm.
3. Convert the temperature from °C to K. In this case, the temperature is 23°C.
4. Now, rearrange the equation to solve for molar mass:

Molar mass = (density)(RT)/(P)

Substitute the given values into the equation to find the molar mass:

Molar mass = (1.43 g/L)(0.0821 L.atm.mol⁻¹K⁻¹)(273 K)/(0.789 atm) = 32.0 g/mol

Therefore, the molar mass of the gas is 32.0 g/mol, so the correct answer is b) 32.0 g/mol.