Question

The sum of mole fractions of solute and solvent of a solution is equal to-
A.Number of moles of solute
B.Number of moles of solvent
C.Number of moles of solution
D.Unity

Answer 1

Use the formula of mole fraction which is given as-
Mole fraction=$\dfrac{{{\text{Moles of solute or solution}}}}{{{\text{Total moles of solution}}}}$
Then assume the moles of solute to be n and moles of solvent to be N. The total moles of solution will be the sum of moles of solute and solvent (n+ N).Then use the above mentioned formula to find the mole fraction of solute and mole fraction of solvent and add then to get the Sum of mole fraction of solute and solvent.

Complete step by step answer:
We have to find the sum of mole fractions of solute and solvent of a solution
We know that mole fraction is given as-
Mole fraction=$\dfrac{{{\text{Moles of solute or solution}}}}{{{\text{Total moles of solution}}}}$
Now let us assume that solution contains n number of moles of solute and N number of moles of solvent, then we can write the total moles of solution=n +N
Now on using the formula of mole fraction and putting the given values to find the mole fraction of solute, we get-
Mole fraction of solute=$\dfrac{n}{{n + N}}$ --- (i)
Where n is the number of moles of solute and N is the moles of solvent.
Now on using the formula of mole fraction and putting the given values to find the value of mole fraction of solvent, we get-
Mole fraction of solvent=$\dfrac{N}{{n + N}}$ --- (ii)
Where n is the number of moles of solute and N is the moles of solvent
Now we can write the sum of mole fraction of solute and solvent as-
Sum of mole fraction of solute and solvent = Mole fraction of solute +mole fraction of solvent
On putting the values from eq. (i) and (ii) we get,
Sum of mole fraction of solute and solvent=$\dfrac{n}{{n + N}} + \dfrac{N}{{n + N}}$
On taking LCM we get,
Sum of mole fraction of solute and solvent=$\dfrac{{n + N}}{{n + N}} = 1$
Hence Sum of mole fraction of solute and solvent is unity.

So the correct answer is D.

Note:
Mole fraction is actually a way to represent concentration of solute and solvent in a solution. Students may get confused between mole fraction and mass fraction. Both are different ways to represent composition of a solution or mixture.
Mole fraction only represents a fraction of molecules.
Mass fraction represents percentage of solute or solvent by weight. It is also called weight fraction.