Use the freezing point depression relation

$\Delta T_f = i K_f m$

where:

• $\Delta T_f = 0.0405^\circ \mathrm{C}$
• $K_f = 1.86\, \mathrm{K\,kg\,mol^{-1}}$
• $m$ = molality
• $i$ = Van't Hoff factor

Interpret the given concentration

The solution contains $0.5\,\mathrm{mL}$ formic acid per $1\,\mathrm{L}$ solution.

Using density of formic acid:

$\text{mass of HCOOH} = 0.5\,\mathrm{mL} \times 1.05\,\mathrm{g\,mL^{-1}} = 0.525\,\mathrm{g}$

Calculate moles of formic acid

Molar mass of formic acid, $\mathrm{HCOOH}$:

$M = 46\,\mathrm{g\,mol^{-1}}$

Hence,

$n = \frac{0.525}{46} \approx 0.01141\,\mathrm{mol}$

Approximate mass of solvent

Since the solution is very dilute, $1\,\mathrm{L}$ solution is approximately $1\,\mathrm{kg}$ water.

So molality is approximately:

$m \approx \frac{0.01141}{1} = 0.01141\,\mathrm{mol\,kg^{-1}}$

Calculate Van't Hoff factor

$i = \frac{\Delta T_f}{K_f m}$

$i = \frac{0.0405}{1.86 \times 0.01141}$

$1.86 \times 0.01141 \approx 0.02122$

$i \approx \frac{0.0405}{0.02122} \approx 1.91$

Match with the given options

$i \approx 1.9$

Therefore, the correct option is C.

Comparison with stored answer

Stored correct answer: C

Derived answer: C

So the derived answer agrees with the stored answer.