For a dilute solution, mole fraction of solute is given as (n= no. of moles of solute) and (N= number of moles of solvent)

Answer: The correct answer is (C) n/N. Because in a very dilute solution, the number of moles of the solvent (N) is significantly larger than the number of moles of the solute (n). Therefore, the total number of moles in the solution (n+N) is approximately equal to N. The mole fraction of the solute is defined as the ratio of the number of moles of the solute to the total number of moles in the solution. Thus, for a dilute solution, the mole fraction of the solute is approximately n/N.

Complete Answer:

The mole fraction of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution.   

Let:

• n = number of moles of solute
• N = number of moles of solvent

The total number of moles in the solution is n+N.

Therefore, the mole fraction of the solute (x_solute​) is given by:

X_solute​  = (number of moles of solute​) / (total number of moles)

= (n)/(n+N)

Now, let’s consider a dilute solution. A dilute solution is one in which the amount of solute is very small compared to the amount of solvent. Mathematically, this means that n<<N (the number of moles of solute is much less than the number of moles of solvent).

In such a case, when we look at the denominator (n+N), since n is negligibly small compared to N, we can approximate the denominator as:

n+N ≈ N

Therefore, for a dilute solution, the mole fraction of the solute can be approximated as:

X_solute​ ≈ n/N

This simplified expression is Option (C), which is used commonly in dilute solutions.

Now let’s examine why the other options are incorrect:

• (A) N/n: This represents the ratio of the number of moles of solvent to the number of moles of solute. This is the inverse of a quantity related to concentration, but it is not the mole fraction of the solute. In a dilute solution, N is much larger than n, so this ratio would be a very large number, not a fraction between 0 and 1, which is characteristic of mole fractions.
  
• (B) (N)/(n+N): This represents the mole fraction of the solvent, not the solute. The mole fraction of the solvent is the number of moles of the solvent divided by the total number of moles in the solution. In a dilute solution, this value would be very close to 1.
  
• (D) Both B and C: As explained above, option B represents the mole fraction of the solvent, and option C represents the approximate mole fraction of the solute in a dilute solution. Therefore, both cannot be the correct answer for the mole fraction of the solute.

In summary, for a dilute solution where the number of moles of solute (n) is significantly less than the number of moles of solvent (N), the mole fraction of the solute is approximately given by n/N.

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