Final answer:
To calculate the molar mass of a gaseous compound with a given density, you first convert the temperature to Kelvin and use the ideal gas law to find the molar volume. Then, by rearranging the density equation, you multiply the density by molar volume to find the molar mass, which is approximately 28.095 g/mol for this compound.
Step-by-step explanation:
To find the molar mass of the gaseous compound, we can use the ideal gas law and rearrange it to solve for molar mass.
The ideal gas law is:
PV = nRT
Where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
The density (d) of a gas is the mass (m) divided by its volume (V), and can also be represented as molar mass (M) divided by molar volume (Vm), or:
d = m/V = M/Vm
Given that d = 1.50 g/L at P = 1.34 atm, and T = 27.1 °C, we first convert the temperature to Kelvin:
T(K) = 27.1 °C + 273.15 = 300.25 K
Next, we rearrange the ideal gas law to solve for molar volume (Vm):
Vm = RT/P
Next, we can use R = 0.0821 L atm / mol K, the given temperature and pressure:
Vm = (0.0821 L atm / mol K)(300.25 K) / 1.34 atm = 18.73 L/mol
Now we can find the molar mass by rearranging the density equation:
M = d × Vm
M = (1.50 g/L) × (18.73 L/mol) = 28.095 g/mol
Therefore, the molar mass of the compound is approximately 28.095 g/mol.