Answer:
The molar mass of the gas is approximately 32.0 g/mol.
Step -by-step explanation:
To calculate the molar mass of the gas, we need to use the ideal gas law, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas:
PV = nRT
where R is the gas constant.
To solve for the number of moles, we can rearrange this equation as:
n = PV/RT
We are given the density (ρ) of the gas, which is related to the molar mass (M) and the volume by:
ρ = PM/RT
Rearranging this equation, we can solve for the molar mass:
M = ρRT/P
Now we can substitute in the given values:
ρ = 1.02 g/L
T = 37°C + 273.15 = 310.15 K
P = 0.990 atm
We also need to convert the density from g/L to kg/m³:
ρ = 1020 g/m³
Using the gas constant R = 0.08206 L atm/mol K, we get:
M = (1020 g/m³) (0.08206 L atm/mol K) (310.15 K) / (0.990 atm)
M ≈ 32.0 g/mol
Therefore, the molar mass of the gas is approximately 32.0 g/mol.