Question

For a dilute solution, mole fraction of solute is given as (n= no. of moles of solute) and (N= number of moles of solvent):
A. $\dfrac{n}{N}$
B. $\dfrac{N}{n}$
C. $\dfrac{N}{n+N}$
D. Both B and C

Answer 1

One way to express relative amounts of substances in a mixture is with the help of the mole fraction. Mole fraction (denoted by X) is the ratio of moles of one substance in a mixture to the total number of moles of all substances. It has no units.

Complete step-by-step answer: We have already understood that mole fraction represents the number of molecules of a particular component of a mixture divided by the total number of moles in the given mixture.
It is a way of expressing the concentration of solution.
Let us explain it with the help of an example.
Suppose a solute A is dissolved in a solvent B to make a solution. Then mole fraction of A means the ratio of the number of moles of A to the total moles present in solution (it means moles of A + moles of B). This can be expressed as represented below.
Mole fraction of A = $\dfrac{\text{moles of A}}{\text{moles of A + moles of B}}$
Similarly, Mole fraction of B = $\dfrac{\text{moles of B }}{\text{moles of A +moles of B}}$
In the question, it is given to us that moles of solute = n
And moles of solvent = N
Mole fraction of solute refers to the ratio of moles of solute to the total moles of solute and solvent
Therefore, mole fraction of solute = $\dfrac{\text{moles of solute}}{\text{moles of solute + moles of solvent}}$
mole fraction of solute = $\dfrac{\text{n}}{\text{n+N}}$
Now, we know that in a solution, the amount of solvent is much greater than the amount of solute. In such conditions, while considering the total moles the moles of solute can be neglected.
Therefore, if N >>> n
Then n + N = N
Hence the mole fraction of solute can be written as depicted below;
Mole fraction of solute = $\dfrac{n}{N}$

Hence, the correct option is A.

Note: Mole fraction is useful when two reactive components are mixed together, as the ratio of the two components is known if the mole fraction of each is known. Mole fraction can be generated from various concentrations including molarity, molality etc. It should be noted that moles of solute in a solution is only considered negligible when solute is in very less quantity than that of solvent, otherwise not.