Question

Use of the data booklet relevant to this question.
The gas laws can be summarized in the ideal gas equation below.
 \[PV = nRT\]
The volume of a sample of methane is measured at a temperature of ${60^ \circ }C$ and a pressure of 103kPa. The volume measured is $5.37 \times {10^{ - 3}}{m^3}$
Assume the gas behaved as an ideal gas.
What is the mass of the sample of methane, given two significant figures?
A. 0.00018g
B. 0.0032g
C. 0.18g
D. 3.2g

Answer 1

Hint: Gases are made up of molecules which are in constant random motion in straight lines. The molecules behave as rigid spheres. Pressure is due to collisions between the molecules and the walls of the container. The temperature of gas is proportional to the average kinetic energy of the molecules.

Complete step by step answer:
The volume of methane is measured at a particular temperature and a pressure. We have the given value is shown below;
P=103kPa=1 atm
 $V = 5.37 \times {10^{ - 3}}{m^3} = 5.37L$
 $T = {60^ \circ }C = 273 + 60 = 333K$
m=(?)
here we use ideal gas law,
 \[PV = nRT\]
We put the given value in the equation,
 $
   \Rightarrow 1 \times 5.37 = n \times 0.0821 \times 333 \\
   \Rightarrow n \approx 0.2mol \\
 $
Molecular mass of methane is 16 g.
So molecular mass of a sample of methane is
 $ = n \times M$
 $ = 0.2 \times 16$
 $ =3.2g $

Therefore, option (D) is the correct answer.

Note: An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but otherwise do not interact with each other. Such a gas, all the internal energy is in the form of kinetic energy.