Question

The density of a gas is 1.78g/l at stp.the weight of one mole of gas is

Answer 1

Molar gas volume at stp is :

1 mole = 22400 cm³ = 22.4 litres

Density = mass / volume

Density = 1.78g/litre

Volume = 22.4 litres

Mass = volume × density

1.78 × 22.4 = 39.872 g

Answer 2

Answer: The weight of one mole of gas is 39.84 g.

Explanation:

To calculate the weight of one mole of gas, we use the equation given by ideal gas equation:

$PV=nRT$

Number of moles (n) can be written as: $n=\frac{m}{M}$

where, m = given mass

M = molar mass

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

where,

$\frac{m}{V}=d$ which is known as density of the gas

Evaluating the formula to calculate the weight of one mole of gas:

$M=\frac{dRT}{P}$      .....(1)

We are given:

d = 1.78 g/L

At STP conditions:

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

T = temperature of the gas = 273 K

P = pressure of the gas = 1 atm

Putting values in equation 1, we get:

$M=\frac{1.78g/L\times 0.0820\text{ L atm }mol^{-1}K^{-1}\times 273K}{1atm}\\\\M=39.84g/mol$

Hence, mass of the gas for 1 mole will be 39.84 grams.