Question

Equal masses of ${{H}_{2}}$​, ${{O}_{2}}$​ and methane have been taken in a container of volume V at temperature 270C in identical conditions. The ratio of the volumes of gases ${{H}_{2}}$​: ${{O}_{2}}$​: methane would be:
A. 8:16:1
B. 16:8:1
C. 16:1:2
D. 8:1:2

Answer 1

Hint: Remember that the number of moles of a gas is given by:
$n=\dfrac{Mass\text{ }of\text{ }gas}{Molar\text{ }mass\text{ }of\text{ }gas}$
Also, it is extremely important to note that one mole of a gas at STP occupies 22.4 litres of volume. Bearing all of this information in mind, try to solve this question.

Step-by-Step Solution:
Before solving this question, let us first understand the fundamentals of gases. Upon doing so, we shall apply these fundamentals to this question.
Recall that the molar mass of a pure substance is the mass of 6.02 x 1023 (Avogadro's number) molecular units of that substance. Similarly, equal volumes of gases, measured at the same temperature and pressure, contain an equal number of molecules.
These volumes depend on the temperature and pressure. Therefore, to ensure convenient comparison, it is required for us to define a set of conditions which in this case are T = 273 K and P = 1 atm. These conditions are referred to as standard temperature and pressure, usually denoted as STP. Substituting these values into the ideal gas equation of state,
$PV=nRT$
We find a volume of 22.414 litres for 1 mole.
Let us now apply these concepts to help solve this question.
Assume that 100 g each of hydrogen, oxygen and methane are present.
The volume of gases is directly proportional to the number of moles of gases.
The molar mass of hydrogen, oxygen and methane are 2 g/mol, 32 g/mol and 16 g/mol respectively.
The number of moles of hydrogen, oxygen and methane are $\dfrac{100}{2}$, $\dfrac{100}{32}$ and $\dfrac{100}{16}$​ respectively. The ratio of the volumes of hydrogen, oxygen and methane will be $\dfrac{100}{2}$​:$\dfrac{100}{32}$​:$\dfrac{100}{16}$ ​= 16:1:2
Therefore, we can safely conclude that the answer to this question is c)

Note: Remember that volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.