Recall the definition of mole fraction

For any component in a solution, $x_i = \frac{\text{moles of component } i}{\text{total moles of all components}}$

Identify the components present

The solution contains three substances: $A$, $B$, and $C$.

Their moles are: $n_A,\; n_B,\; n_C$

Write total number of moles

$n_{\text{total}} = n_A + n_B + n_C$

Mole fraction of $C$

Therefore, the mole fraction of $C$ is $x_C = \frac{n_C}{n_A + n_B + n_C}$

Match with the options

• A: $\frac{n_C}{n_A \times n_B \times n_C}$ ❌ incorrect
• B: $\frac{n_B}{n_A+n_B}$ ❌ this is not mole fraction of $C$
• C: $\frac{n_C}{n_A+n_B+n_C}$ ✅ correct
• D: $\frac{n_C}{n_A-n_B-n_C}$ ❌ incorrect

Final answer

The correct option is: $\boxed{\text{C}}$