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Question: The density of methane at \(0.20atm\) pressure and \(27^\circ C\) is A: \(0.13g{L^{ - 1}}\) B: ...

The density of methane at 0.20atm0.20atm pressure and 27∘C27^\circ C is
A: 0.13gL−10.13g{L^{ - 1}}
B: 0.26gL−10.26g{L^{ - 1}}
C: 45.67gL−145.67g{L^{ - 1}}
D: 26.0gL−126.0g{L^{ - 1}}

Explanation

Solution

The molecular formula of methane is CH4C{H_4} . We have to consider it to be an ideal gas . To solve this question we will use the ideal gas equation PV=nRTPV = nRT . The density of a given thing can be found out by ρ=MV\rho = \dfrac{M}{V} .

Complete step by step answer:
As we know that ideal gas follows the ideal gas equation. The molecular mass of methane will be M=12+(4×1)=16M = 12 + (4 \times 1) = 16 as the molecular formula of methane is CH4C{H_4} . The ideal gas equation is PV=nRTPV = nRT . In the question the value of pressure and temperature is given. We know the value of molecular mass of methane so
⇒PV=nRT ⇒PV=mMRT ⇒ρ=mV=PMRT  \Rightarrow PV = nRT \\\ \Rightarrow PV = \dfrac{m}{M}RT \\\ \Rightarrow \rho = \dfrac{m}{V} = \dfrac{{PM}}{{RT}} \\\
Here we have considered that the given mass of the methane is mm . So we will now put the known value in the given equation to find the value of the density. We have converted the temperature given to KelvinKelvin scale.
ρ=PMRT=0.20×160.0821×300=0.13gL−1\rho = \dfrac{{PM}}{{RT}} = \dfrac{{0.20 \times 16}}{{0.0821 \times 300}} = 0.13g{L^{ - 1}}
So according to the above explanation and calculation the correct answer of the question is option
A: 0.13gL−10.13g{L^{ - 1}}

Hence option A is correct.

Additional information:
Ideal gases are gases which satisfy the ideal gas equation. The concept of ideal gas is hypothetical.
The molecules of ideal gas follow Newton’s laws of motion. The ideal gas consists of a large number of identical molecules. The collisions between the molecules are considered to be elastic collisions.
The volume of the actual atom of an ideal gas is considered to be zero. The molecules of the ideal gas feel no attraction or repulsion in between them. The molecular speed of the ideal gas is proportional to the Kelvin temperature.

Note:
Whenever we have to find the relation in between temperature , volume , number of molecules , pressure and density always use the ideal gas equation PV=nRTPV = nRT and also remember the density formula ρ=PMRT\rho = \dfrac{{PM}}{{RT}} .