Question

If a substance ‘A’ dissolves in a solution of a mixture of ‘B’ and ‘C’ with their respective number of moles as \(n_a\), \(n_b\), and \(n_c\), the mole fraction of C in the solution is:

• A. $\frac{n_C}{n_A + n_B + n_C} \\$
• B. $\frac{n_C}{n_A \times n_B \times n_C}$
• C. $\frac{n_C}{n_A - n_B - n_C} \\$
• D. $\frac{n_B}{n_A + n_B} \\$

Answer 1

The Correct Option is A

Solution: 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.

Calculating Mole Fraction of C: Given that the moles of substances are \(n_a\), \(n_b\), and \(n_c\), the total number of moles in the solution is:

\(n_a + n_b + n_c\).

The mole fraction of substance \(C\) can be calculated as follows:

\(\text{Mole fraction of } C = \frac{n_c}{n_a + n_b + n_c}\).

Conclusion: Therefore, the mole fraction of \(C\) in the solution is given by option (1): \(\frac{n_c}{n_a + n_b + n_c}\).

Answer 2

To determine the mole fraction of a component in a solution, we need to use the formula for mole fraction. The mole fraction is a way of expressing the concentration of a component in a mixture and 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.

Given:

• Number of moles of substance 'A': \(n_a\)
• Number of moles of substance 'B': \(n_b\)
• Number of moles of substance 'C': \(n_c\)

The formula for the mole fraction, \(X_c\), of substance 'C' is given by:

\(X_c = \frac{n_c}{n_a + n_b + n_c}\)

This formula gives us the ratio of the moles of 'C' to the total moles present in the solution (i.e., the sum of moles of 'A', 'B', and 'C'). Hence, the mole fraction is essentially a measure of how much of 'C' is present in proportion to the total amount of substances in the solution.

Now, let's evaluate the given options:

1. \(\frac{n_C}{n_A + n_B + n_C}\) - This matches the correct formula for the mole fraction of 'C'.
2. \(\frac{n_C}{n_A \times n_B \times n_C}\) - This does not represent a mole fraction, as it incorrectly involves multiplication of the moles, which is not how mole fraction is defined.
3. \(\frac{n_C}{n_A - n_B - n_C}\) - This is not applicable because it includes a subtraction, which is not relevant in the context of mole fractions.
4. \(\frac{n_B}{n_A + n_B}\) - This represents the mole fraction of 'B' in a different scenario and is not applicable for finding the mole fraction of 'C'.

Therefore, the correct answer is the first option: \(\frac{n_C}{n_A + n_B + n_C}\).

It's essential to understand that mole fractions are a fundamental way to express the composition of mixtures, particularly useful when analyzing chemical reactions in solutions, as they remain constant with temperature and pressure changes.