# Problem: When HNO2 is dissolved in water it partially dissociates according to the equation HNO2 ⇌ H+ + NO2–. A solution is prepared that contains 7.050 g of HNO2 in 1.000 kg of water. Its freezing point is found to be -0.2929 ˚C. Calculate the fraction of HNO2 that has dissociated.

###### FREE Expert Solution

We’re being asked to calculate the fraction of HNO2 that has dissociated. The solution is prepared that contains 7.050 g of HNO2 in 1.000 kg of water. Its freezing point is found to be -0.2929 ˚C.

HNO2 ⇌ H+ + NO2

When calculating the freezing point of a solution, we’re going to use the equation for Freezing Point Depression.

$\overline{){\mathbf{∆}}{{\mathbf{T}}}_{{\mathbf{f}}}{\mathbf{=}}{\mathbf{i}}{\mathbf{·}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{·}}{\mathbf{m}}}$

∆Tf = change in freezing point = Tf pure solvent –Tf solution
Kf = freezing point depression constant
i = van' t Hoff factor of the solute = no. of ions
m = molality

We're going to calculate the freezing point of the solution using the following steps:

Step 1: Calculate the moles of solute.
Step 2: Calculate the molality of the solution.
Step 3: Calculate the change in temperature (ΔTf).
Step 4: Calculate the van't Hoff factor (i).
Step 5: Calculate the fraction dissociated.

Step 1: Calculate the moles of solute (sucrose).

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###### Problem Details

When HNO2 is dissolved in water it partially dissociates according to the equation HNO2 ⇌ H+ + NO2. A solution is prepared that contains 7.050 g of HNO2 in 1.000 kg of water. Its freezing point is found to be -0.2929 ˚C. Calculate the fraction of HNO2 that has dissociated.