Depression in Freezing Point:
The depression in the freezing point of a solution is directly proportional to the molality (m) of the solute in the solution. The equation used to calculate the depression in freezing point is:

ΔTf = Kf * m

where ΔTf is the depression in freezing point, Kf is the cryoscopic constant of the solvent, and m is the molality of the solute.

Given Information:
- Depression in freezing point of 0.01 molal aqueous HCOOH solution = 0.02046 ℃
- Freezing point depression of 1 molal aqueous urea solution = -1.86 ℃

Calculating the cryoscopic constant (Kf) of water:
To calculate the cryoscopic constant (Kf) of water, we can use the given information of the freezing point depression of the 1 molal urea solution.

ΔTf = Kf * m

-1.86 ℃ = Kf * 1 molal

Kf = -1.86 ℃ / 1 molal = -1.86 ℃/m

Calculating the molality (m) of the HCOOH solution:
Using the equation for freezing point depression, we can calculate the molality (m) of the HCOOH solution.

ΔTf = Kf * m

0.02046 ℃ = -1.86 ℃/m * 0.01 molal

Solving for m:

m = -1.86 ℃/ (0.02046 ℃ * 0.01 molal) = -1.86 ℃/0.0002046 ℃/molal

m ≈ 90.74 molal

Calculating the pH of the HCOOH solution:
Formic acid (HCOOH) is a weak acid that partially dissociates in water. The dissociation of HCOOH can be represented by the following equation:

HCOOH ⇌ H+ + HCOO-

Since the molality (m) of the HCOOH solution is approximately equal to the molarity, we can assume that the concentration of HCOOH is 0.01 M.

The dissociation constant (Ka) of formic acid is 1.8 x 10^-4 mol/L. Using this information, we can write the equilibrium expression for the dissociation of HCOOH:

Ka = [H+][HCOO-] / [HCOOH]

Let x be the concentration of H+ ions. Since the concentration of HCOOH is 0.01 M, the concentration of HCOO- ions is also 0.01 M.

Substituting the values into the equilibrium expression:

1.8 x 10^-4 = x * 0.01 / 0.01

x = 1.8 x 10^-4

Taking the negative logarithm of the concentration of H+ ions gives us the pH:

pH = -log[H+]

pH = -log(1.8 x 10^-4)

pH ≈ 3

Therefore, the pH of the HCOOH solution is approximately 3.