Question

A sample of an unknown compound is vaporized at 180.°C. The gas produced has a volume of 2010.mL at a pressure of 1.00atm, and it weighs 2.73g. Assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. Round your answer to 3 significant digits.

Answer 1

Answer: The molar mass of the given unknown compound is 50.5 g/mol.

Explanation:

To calculate the volume of water, we use the equation given by ideal gas, which is:

$PV=nRT$

or,

$PV=\frac{m}{M}RT$

where,

P = pressure of sample = 1.00 atm

V = volume of sample = 2010 mL = 2.010 L   (Conversion factor: 1 L = 1000 mL)

m = Given mass of unknown compound = 2.73 g

M = Molar mass of unknown compound = ? g/mol

R = Gas constant = $0.0820\text{ L atm }mol^{-1}K^{-1}$

T = temperature of sample = $180^oC=[180+273]K=453K$

Putting values in above equation, we get:

$1.00atm\times 2.010L=\frac{2.73g}{M}\times 0.0820\text{ L atm }mol^{-1}K^{-1}\times 453K\\\\V=50.45g/mol$

Rounding off to 3 significant figures, we get the molar mass to be 50.5 g/mol.

Hence, the molar mass of the given unknown compound is 50.5 g/mol.