Question

Which of the following terms is unitless?

• A. Molality
• B. Molarity
• C. Mole fraction
• D. Mass percent

Answer 1

Answer: (C), (D)

Mass percent

Explanation of correct options:

(C) Mole fraction and (D) Mass percent

Mole fraction :

• The property of a number with no units of measurement is a unitless value.
• Mole fraction is the ratio of the number of moles of a particular component to the total number of moles of the solution.
• $\mathrm{Mole}\mathrm{fraction}=\frac{\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{a}\mathrm{particular}\mathrm{component}}{\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{the}\mathrm{solution}}$

Mass percent :

• $\mathrm{Mass}\mathrm{percent}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{solute}}{\mathrm{Mass}\mathrm{of}\mathrm{solution}}\times 100$
• In such unitless values, the ratio or percentage of two numbers have the same units.

Explanation of incorrect options:

(A) Molality

• Molality can be defined as the number of moles of the solute present $1000\mathrm{g}$ in the solvent.
• Molality(m)= $\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{Solute}\left(\mathrm{n}\right)/\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{solvent}\mathrm{in}\mathrm{Kg}$
• Unit of Molality is $\mathrm{mol}{\mathrm{Kg}}^{-1}$.

(B) Molarity

• Molarity is a unit of the concentration measuring the number of moles of a solute per liter of solution.
• Molarity(M) = $\mathrm{Moles}\mathrm{of}\mathrm{solute}/\mathrm{Volume}\mathrm{of}\mathrm{solution}\left(\mathrm{in}\mathrm{Litre}\right)$
• Unit of Molarity is $\mathrm{mol}{\mathrm{L}}^{-1}$.

Hence, options (C) and (D) are correct., Mole fraction and Mass percent are unitless terms.