Question

What is the molar mass of a gas if 0.281 g of the gas occupies a volume of 125 ml at a temperature 126 °c and a pressure of 777 torr?

Answer 1

Answer : 72.05 g/mol

Explanation :

Let's assume that the given gas is an ideal gas. Then we can use ideal gas equation,
PV = nRT

Where, 
P = Pressure of the gas (Pa)
V = volume of the gas (m³)
n = number of moles (mol)
R = Universal gas constant (8.314 J mol⁻¹ K⁻¹)
T = temperature in Kelvin (K)

The given data for the gas is,
P = 777 torr = 103591 Pa
V = 125 mL = 125 x 10⁻⁶ m³
T = (126 + 273) = 399 K
R = 8.314 J mol⁻¹ K⁻¹
n = ?

By applying the formula,
103591 Pa x  125 x 10⁻⁶ m³ = n x 8.314 J mol⁻¹ K⁻¹ x 399 K
                                          n = 3.90 x 10⁻³ mol

Moles (mol) = mass (g) / molar mass (g/mol)

Mass of the gas = 0.281 g
Moles of the gas = 3.90 x 10⁻³ mol
Hence,
   molar mass of the gas = mass / moles
                                          = 0.281 g / 3.90 x 10⁻³ mol
                                          = 72.05 g/mol

Answer 2

Answer:

The molar mass of gas is 72.03 g/mol.

Explanation:

Volume of the gas = V = 125 mL= 0.125 L

Pressure of the gas = P = 777 torr = 1.021 atm

(1 torr = 0.0013 atm)

Temperature of the gas = T= 126 °C = 399 K

Mass of the gas = 0.281 g

Number of moles of gas = n =$\frac{0.281 g}{M}$

Using Ideal gas equation:

$PV=nRT$

$1.021 atm\times 0.125 l=\frac{0.281 g}{M}\times 0.0820 L atm/ mol K\times 399 K$

M = 72.03 g/mol

The molar mass of gas is 72.03 g/mol.