Question

The pressure of a 1:4 mixture of dihydrogen and dioxygen enclosed in a vessel is one atmosphere. What would be the partial pressure of dioxygen?
(A) $0.8\times {{10}^{4}}atm$
(B) $0.008N{{m}^{-2}}$
(C) $8\times {{10}^{4}}N{{m}^{-2}}$
(D) 0.25atm

Answer 1

Hint: Use Dalton’s Law of Partial Pressure in terms of mole fraction to find out the partial pressure of oxygen from the mixture of dihydrogen and dioxygen. It tells that the partial pressure of a specific gas in a mixture of gases is the product of the mole fraction of the specific gas and the total pressure in the system.

Complete step by step answer:
- Remember that partial pressure of a gas in a mixture of gas is the pressure a gas exerts when it occupies the same volume as that of the mixture of the gas at the same temperature.
- Let’s see Dalton's law of partial pressure first and then we can easily find partial pressure of oxygen from its mixture.
- According to the Dalton’s Law of Partial Pressure in terms of mole fraction, mathematically we can say,
     \[{{p}_{i}}={{\chi }_{i}}{{p}_{total}}\] ........(1)

Where, ${{p}_{i}}$ is partial pressure of a gas
     ${{\chi }_{i}}$ is mole fraction of a gas and
     ${{p}_{total}}$ stands for total pressure of the system

Now, we are given that, ${{p}_{total}}$ = 1 atm
- Here, we are given the ratio of Dihydrogen and Dioxygen gas in the mixture which is 1:4. So, we can assume that if one mole of Hydrogen gas is present in the system, then there will be four moles of dioxygen gas present in the system.
Now, we know that $\text{Mole fraction=}\dfrac{\text{Moles of component}}{\text{Total moles of solution}}$

So, to find mole fraction of dioxygen gas here in the mixture, we can write that
     \[\text{Mole fraction of Dioxygen=}\dfrac{\text{Moles of Dioxygen}}{\text{Moles of Dioxygen + Moles of Dihydrogen}}\]
So, we can write that \[\text{Mole fraction of Dioxygen=}\dfrac{4}{\text{4 + 1}}\]
     \[\text{Mole fraction of Dioxygen =}\dfrac{4}{5}\]

Now, we can use Dalton’s law of partial pressure here and can find partial pressure of oxygen gas here. So , its formula is
     \[{{p}_{i}}={{\chi }_{i}}{{p}_{total}}\]
We know the values of ${{\chi }_{1}}$ which is a mole fraction of dioxygen gas and ${{p}_{total}}$ . So, as we put those values into the equation of Dalton’s formula we will get
     \[{{p}_{i}}=\dfrac{4}{5}\times 1\]
     \[{{p}_{i}}=0.8atm\]

Now, we know that 1atm = $1\times {{10}^{5}}N{{m}^{-2}}$
So, \[{{p}_{i}}=0.8\times N{{m}^{-2}}=8\times {{10}^{-4}}N{{m}^{-2}}\]
Thus, we can conclude that the partial pressure of Dioxygen is \[8\times {{10}^{4}}\text{ N}{{\text{m}}^{-2}}\].
So, the correct answer is “Option C”.

Note: Make sure that you know the relation between the units of pressure because they will come often in these types of problems. Remember that mole fraction of a gas is the ratio of the moles of a specific gas to the total moles of the mixture of the gas so do not consider total moles of the mixture as the moles of component that is present in more abundance.