Question

Mass of 22.4 L of a gas at STP is 20g. Find its molar mass

Answer 1

Answer:

20 g

Explanation:

22.4 L is 1 mole of the gas

so its molar mass is 20g

Answer 2

Concept:

According to the ideal gas law, the product of the absolute temperature of the gas and the universal gas constant is equal to the product of the pressure and volume of one gram of an ideal gas.

Given:

Mass of gas = 20 g

The volume of gas = 22.4 L

Find:

Find the molar mass.

Solution:

STP is often defined as standard temperature (273.15 K) or (0°C) and pressure (1 atm).

We can use the ideal gas law equation:

                               PV = nRT

where P = pressure,

V = volume,

n = number of moles = $\frac{Mass(m)}{Molar mass(M)}$

R = universal gas constant = 0.082057 L·atm/K·mol.

T = temperature in Kelvins.

We can substitute m/M for n in the ideal gas equation.

PV = $\frac{mRT}{M}$

Rearrange to isolate M.

M * PV = mRT

M = $\frac{mRT}{PV}$

By substituting the given values in the expression we get,

M = $\frac{20g*0.082057 L.atm/K.mol * 273.15 K}{1 atm * 22.4 L}$

M = 20.01 g/mol

M = 20 g/mol

Hence, the molar mass of a gas at STP is 20 g/mol.

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