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Question: In a litre flask at a certain temperature, there are 2 gm of \({H_2}\) and 8 gm of \({O_2}\). The mo...

In a litre flask at a certain temperature, there are 2 gm of H2{H_2} and 8 gm of O2{O_2}. The mole fraction of O2{O_2} in the given mixture is:
A.0.20.2
B.0.40.4
C.0.30.3
D.0.10.1

Explanation

Solution

We can calculate the mole fraction of a substance in a solution by calculating the moles of each solute dividing by total number of moles of the solution. We can calculate the moles of the solute by converting the grams of the solute to moles of the solute using molar mass. The total moles of solution are calculated by adding the moles of each solute/solvent.
Formula used: We can calculate the mole fraction using the formula,
the mole fraction using the formula,
χA=Moles of A (in mol)Moles of A(in mol)+Moles of B(in mol)+Moles of C(in mol){\chi _A} = \dfrac{{{\text{Moles of A }}\left( {{\text{in mol}}} \right)}}{{{\text{Moles of A}}\left( {{\text{in mol}}} \right) + {\text{Moles of B}}\left( {{\text{in mol}}} \right) + {\text{Moles of C}}\left( {{\text{in mol}}} \right)}}
χA=Moles of A (in mol)Total mass{\chi _A} = \dfrac{{{\text{Moles of A }}\left( {{\text{in mol}}} \right)}}{{{\text{Total mass}}}}

Complete step by step answer: We can define Mole fraction as the ratio of moles of one substance in a mixture to the total number of moles of all substances. For a solution of two substances A and B, we can calculate the mole fraction using the formula,
χA=Moles of A (in mol)Moles of A(in mol)+Moles of B(in mol){\chi _A} = \dfrac{{{\text{Moles of A }}\left( {{\text{in mol}}} \right)}}{{{\text{Moles of A}}\left( {{\text{in mol}}} \right) + {\text{Moles of B}}\left( {{\text{in mol}}} \right)}}
χA=Moles of A (in mol)Total mass{\chi _A} = \dfrac{{{\text{Moles of A }}\left( {{\text{in mol}}} \right)}}{{{\text{Total mass}}}}
Now, coming back to the question, we have to calculate the mole fraction of oxygen. We can calculate the mole fraction of oxygen using the moles of oxygen and moles of hydrogen.
Given data contains,
Mass of hydrogen is 2gm2gm.
Mass of oxygen is 8gm8gm.
Let us now calculate the moles of oxygen and hydrogen using their molecular masses.
The molecular mass of oxygen is 32g/mol32g/mol.
The molecular mass of hydrogen is 1g/mol1g/mol.
The moles of oxygen is calculated as,
Moles of oxygen =GramsMolecular mass = \dfrac{{{\text{Grams}}}}{{{\text{Molecular mass}}}}
Moles of oxygen=8g32g/mol\dfrac{{8g}}{{32g/mol}}
Moles of oxygen=0.25mol0.25mol
The moles of oxygen is 0.25mol0.25mol
The moles of hydrogen is calculated as,
Moles of hydrogen =GramsMolecular mass = \dfrac{{{\text{Grams}}}}{{{\text{Molecular mass}}}}
Moles of hydrogen=2g1g/mol\dfrac{{2g}}{{1g/mol}}
Moles of hydrogen=1mol1mol
The moles of hydrogen is 1mol1mol.
From the moles of hydrogen and oxygen, we can calculate the mole fraction of oxygen as, χ(oxygen)=Moles of oxygen (in mol)Total mass{\chi _{\left( {oxygen} \right)}} = \dfrac{{{\text{Moles of oxygen }}\left( {{\text{in mol}}} \right)}}{{{\text{Total mass}}}}
χoxygen=0.25mol0.25mol+1mol{\chi _{oxygen}} = \dfrac{{0.25mol}}{{0.25mol + 1mol}}
χoxygen=0.2mol{\chi _{oxygen}} = 0.2mol
The mole fraction of oxygen is 0.2mol0.2mol.
Therefore, Option (A) is correct.

Note: We can calculate mole fraction from mass percent, molarity, molality. Some of the properties of mole fraction are,
It does not depend on temperature.
A mixture of mole fractions could be prepared by weighting the masses of the substances.
We can also calculate the mole fraction from Raoult’s law. The formula we use to calculate the mole fraction from Raoult’s law is,
Psolv=χsolvPosolv{P_{solv}} = {\chi _{solv}}{P^o}_{solv}
The vapor pressure of the solvent (Psolv)\left( {{P_{solv}}} \right) above a dilute solution is equal to the mole fraction of the solvent (χsolv)({\chi _{solv}}) times the vapor pressure of the pure solvent (Psolvo)\left( {{P_{solv}}^o} \right).