The depression in the freezing point observed for a formic acid solution of concentration 0.5 mL L–1 is 0.0405°C. Density of formic acid is 1.05 g mL–1. The Van’t Hoff factor of the formic acid solution is nearly (Given for water kf = 1.86 k kg mol–1)
ΔTf of formic acid = 0.0405°C
Concentration = 0.5 mL/L
and density = 1.05 g/mL
∴ Mass of formic acid in solution = 1.05 × 0.5 g
= 0.525 g
∴ According to Van’t Hoff equation,
ΔT_f=ik_f.m
0.0405=\(\frac{i×1.86×0.525}{46×1}\)
(Assuming mass of 1 L water = kg)
i=\(\frac{0.0405×46}{1.86×0.525}\)=1.9
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
The solutions can be classified into three types:
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types: