A sample of an unknown compound is vaporize at 180°C. The gas produce has a volume of 1020 mL at a pressure of one atmosphere, and it weighs 0.934 g assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound round to three significant digits.
Given:
Temperature (T) = 180°C = 180 + 273.15 = 453.15 K
Volume (V) = 1020 mL = 1020 cm³
Pressure (P) = 1 atm
Mass (m) = 0.934 g
The ideal gas law equation is:
PV = nRT
First, we need to convert the volume from cm³ to liters:
V = 1020 cm³ = 1020/1000 L = 1.02 L
Also, convert the pressure from atm to Pa:
P = 1 atm = 1.013 × 10^5 Pa
The gas constant, R, is 0.0821 L · atm/(mol · K)
Rearranging the ideal gas law equation to solve for the number of moles (n) gives:
n = PV/RT
Substituting the given values:
n = (1.013 × 10^5 Pa)(1.02 L) / (0.0821 L · atm/(mol · K))(453.15 K)
Simplifying:
n ≈ 0.0242 mol
The molar mass (M) can be calculated by dividing the mass (m) by the number of moles (n):
M = m/n
Substituting the values:
M = 0.934 g / 0.0242 mol
Calculating:
M ≈ 38.43 g/mol
Therefore, the molar mass of the unknown compound is approximately 38.43 g/mol.