Question

Which of the following terms are unitless?

Answer 1

Analysing the options:

In option (A)

Molality is equal to the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. So, the unit of Molality is $molk{g}^{-1}$ hence it is not a unitless quantity.

In option (B)

Molarity is equal to the number of moles of solute per litre of solution. So, the unit of Molarity is $mol{L}^{-1}$, hence it is not a unitless quantity.

In option (C)

Mole fraction is the ratio of number of moles of a component divided by total number of moles. So, both units (i.e. mol) in numerator and denominator cancels out. Hence, it is a unitless quantity.

In option (D)

Mass percent of a solution can be defined as mass of solute divided by the mass of solution and multiplied by 100. So, both units (i.e. g) in numerator and denominator cancels out.
Hence it is a unitless quantity

Mass percent $=\frac{Massofsolute}{Massofsolution}\times 100$

Hence from the above analysis, it is concluded that both options (C) and (D) are the unitless quantity.