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.

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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.

Tf=i·Kf·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.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the The Colligative Properties concept. You can view video lessons to learn The Colligative Properties. Or if you need more The Colligative Properties practice, you can also practice The Colligative Properties practice problems.

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Based on our data, we think this problem is relevant for Professor Johnson's class at Southwestern Oklahoma State University.