Solving a Solubility Problem: Ba(NO3)2 Crystallisation

[elliotyang]

Homework Statement

Given solubility of Ba(NO₃)₂ is
34g/100 H₂0 at 100^oC
5g/100g of H20 AT 0^oC
if one starts with 100g of (BaNO₃)₂ and make a saturated solution in water at 100^oC, and then cooled to 0^oC, how much Ba(NO₃)₂ is crystallised out of solution?
The resultant crystals carry along with them on surface 4g of H₂0 per 100g of the crystals.

Homework Equations

input=output

The Attempt at a Solution

Initial the concentrated solution would be 100g/300g H₂0 if i do not calculate wrongly.
then how should i proceed?

 

[Borek]

You have 100g/300g initially. Once you cool down the solution - amount of water won't change, amount of dissolved salt will. How much salt will be dissolved in 300g of water at 0ºC?

 

[Blueshift5]

One possible approach to solving this problem would be to first calculate the amount of Ba(NO3)2 that would be dissolved in 100g of water at 100oC, using the given solubility of 34g/100g. This would result in a saturated solution of 34g Ba(NO3)2 in 100g of water.

Next, we can use the principle of input=output to determine the amount of Ba(NO3)2 that will crystallize out of solution as it cools to 0oC. Since the solubility at 0oC is 5g/100g, we can expect that 5g of Ba(NO3)2 will remain dissolved in the cooled solution, leaving 29g to crystallize out.

Since the resultant crystals carry along 4g of water per 100g of crystals, we can calculate the total mass of the crystals by dividing the amount of Ba(NO3)2 that crystallized out (29g) by the percentage of Ba(NO3)2 in the crystals (100g/300g = 1/3). This gives us a total mass of 87g of crystals.

To determine the amount of Ba(NO3)2 in these crystals, we can use the percentage of Ba(NO3)2 in the crystals (1/3) and the total mass of the crystals (87g) to find that the crystals contain 29g of Ba(NO3)2.

Therefore, out of the initial 100g of Ba(NO3)2, 29g will crystallize out of solution as it cools to 0oC, leaving a solution with 5g of Ba(NO3)2 in 100g of water. The remaining 29g of Ba(NO3)2 will be in the form of crystals, along with 4g of water per 100g of crystals.