Question

Define Mole Fraction. Calculate the mole fraction of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] in a solution containing 98% \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] by mass.

Answer 1

Hint: Mole fraction can be defined as the ratio of number of moles of one component to the total number of moles of all the components. This includes the solvent and solute present in the solution. It is denoted by the letter X.

Complete step by step answer:
Let us suppose that a solution contains the components A and B and suppose that $W_A$ g of A and $W_B$ g of B are present in it, then,
Number of moles of A, \[{{\text{n}}_{\text{A}}}\]=\[\dfrac{{{{\text{W}}_{\text{A}}}}}{{{{\text{M}}_{\text{A}}}}}\] and
Number of moles of B, \[{{\text{n}}_{\text{B}}}\]=\[\dfrac{{{{\text{W}}_{\text{B}}}}}{{{{\text{M}}_{\text{B}}}}}\]
Where \[{{\text{M}}_{\text{A}}}\]and \[{{\text{M}}_{\text{B}}}\] are the molecular masses of A and B.
Therefore, mole fraction can be said as
\[{{\text{X}}_{\text{A}}}{\text{ = }}\dfrac{{{{\text{n}}_{\text{A}}}}}{{{{\text{n}}_{\text{A}}}{\text{ + }}{{\text{n}}_{\text{B}}}}}\] and
\[{{\text{X}}_{\text{B}}}{\text{ = }}\dfrac{{{{\text{n}}_{\text{B}}}}}{{{{\text{n}}_{\text{A}}}{\text{ + }}{{\text{n}}_{\text{B}}}}}\]
In this question we have 98 percent \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] by mass in the solution, means mass of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] in the solution will be 98 g and the mass of water will be 2g.
Now we have to find out the number of moles of each component so as to find out the mole fraction
Number of moles of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\]=\[\dfrac{{{\text{Given}}\;{\text{mass}}\;{\text{of}}\;{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}}{{{\text{Molecular}}\;{\text{mass}}\;{\text{of}}\;{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}}\]
  Given mass=98g and molecular mass=98g
  Now by substituting the values we get the number of moles of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] =\[\dfrac{{{\text{98g}}}}{{{\text{98g}}}}\]=1 mole.
Similarly, the number of moles of \[{{\text{H}}_{\text{2}}}{\text{O}}\]= \[\dfrac{{{\text{Given}}\;{\text{mass}}\;{\text{of }}{{\text{H}}_{\text{2}}}{\text{O}}}}{{{\text{Molecular}}\;{\text{mass of }}{{\text{H}}_{\text{2}}}{\text{O}}}}\]
Given mass =2g and molecular mass =18g
By substituting the values, we get the number of moles of \[{{\text{H}}_{\text{2}}}{\text{O}}\]=\[\dfrac{{{\text{2g}}}}{{{\text{18g}}}}\]=0.1g
Now we have to calculate the mole fraction of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\], \[{{\text{X}}_{{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}}{\text{ = }}\dfrac{{{{\text{n}}_{{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}}}}{{{{\text{n}}_{{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}{\text{ + }}}}{{\text{n}}_{{{\text{H}}_{\text{2}}}{\text{O}}}}}}\]
\[{{\text{X}}_{{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}}{\text{ = }}\dfrac{{\text{1}}}{{{\text{1 + 0}}{\text{.1}}}}{\text{ = 0}}{\text{.9}}\]
The mole fraction of the solvent can be found by subtracting the mole fraction of the solute from one as the sum of mole fractions of components in a solution will always be one.
Therefore, the mole fraction of \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] containing 98 percent \[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\] by mass is 0.9

Additional information: Mole fraction is independent of the temperature. The number of moles of a particular compound does not increase or decrease with difference in temperature.

Note:
The concentration of a solution refers to the amount of solute present in the given quantity of solution or solvent. There are many ways of finding out the concentration of a solution. Some of them are the mass percentage, volume percentage, normality, molarity etc.