Question

Equal masses of oxygen, hydrogen and methane are taken in a container in identical conditions. Find the ratio of the volumes of the gases.

Answer 1

1) Convert the mass into moles (use the formula n=m/Mr)
Since the masses are equal, you can take the mass as x. So, the number of moles would be:
n(O2) = x/32
n(H2) = x/2
n(CH4) = x/16

2) Divide the moles by the smallest value
Since under identical conditions, the same number of moles occupy the same volume, you can directly divide by the smallest value. Now, which one is the smallest value? Simple. The one with the largest denominator has the smallest value. For example, 1/25 is smaller than 1/10.

So, x/32 is the smallest.
(x/32)/(x/32) = 1.

Similarly, you can do it for the others. This now gives us the ratio of:
1:16:2
O2:H2:CH4

Answer 2

Hey !!

Oxygen             Hydrogen              Methane

  (O₂)                    (H₂)                         (CH₄)

Number of moles

$\frac{1}{34} = 0.031 , \frac{1}{2} = 0.5 ; \frac{1}{16} = 0.0625$

Simple Ratio     1       6       2

Equal number of moles of gases occupy equal volumes under similar conditions of temperature and pressure, therefore the ratio of the volumes of gases will be

                         1 : 16 : 2

Good luck !!