Question

The density in gram per litre of a mixture containing an equal number of moles of methane and ethane at STP is
A.$1.03$
B.$1.10$
C.$0.94$
D.$1.20$

Answer 1

Hint:Density of a substance is defined as the mass per unit volume of the substance. The molar volume of any gas at standard temperature and pressure is equal to $22.4$ litres.

Complete step by step answer:
As it is known that the formula of density of a substance is equal to,
${ }\rho\text{ = }\dfrac{\text{m}}{\text{V}}$
Where “m” is the mass of the substance and “V” is the volume of the substance.
The molar volume, which is the volume occupied by one mole of any gas at standard conditions of temperature and pressure, is equal to $22.4$ litres. This molar volume is equal for all gas, as long as they are at STP and this value is equal to the gram molecular weight or the gram atomic weight of the gas, as the gram molecular weight or the gram atomic weight of as gas also contains one mole of a gas.
The gram molecular weight of methane$\text{C}{{\text{H}}_{\text{4}}}$= $\left[ 12+\left( 1\times 4 \right) \right]=16$$\text{g/ mol}$
The gram molecular weight of ethane${{\text{C}}_{\text{2}}}{{\text{H}}_{\text{6}}}$= $\left[ \left( 12\times 2 \right)+\left( 1\times 6 \right) \right]=30$$\text{g/ mol}$
The total mass of the gases = $16+30=46$$\text{g/ mol}$
The total molar volume of the gas = $22.4\times 2=44.8$Litres.
Therefore the density of the gas mixture at STP = $\dfrac{46}{44.8}=1.026$$\text{g mo}{{\text{l}}^{\text{-1}}}\text{ Litr}{{\text{e}}^{\text{-1}}}$

So, the correct answer is option A.

Note:
One mole a substance is defined as the amount of matter present in $6.023\times {{10}^{23}}$ particles of that substance, where the particles can refer to molecules, atoms, ions, and subatomic particles. The gram molecular weight of a substance is equal to the molecular weight of the substance expressed in grams and is also the mass of $6.023\times {{10}^{23}}$ molecules of the substance.