What mass of sample A would be needed to produce a saturated solution of A in 150g of water at 313k?

So, you know that potassium nitrate, #"KNO"3#, has a solubility of #"155 g"# per #"100 g"# of water at #75^@"C"# and of #"38.0 g"# at #25^@"C"#.

What that means is that at #75^@"C"#, you can dissolve as much as #"155 g"# of solid potassium nitrate in water without the solution becoming saturated.

Once you hit that #"155 g"# mark, the solution becomes saturated, which means that the solution can't dissolve any more solid.

Now, the same thing can be said for the solution at #25^@"C"#. At this temperature, dissolving less than #"38.0 g"# of potassium nitrate per #"100 g"# of water will result in an unsaturated solution.

At the #"38.0 g"# mark, the solution will become saturated.

Now, take a look at how the solubility graph for potassium nitrate looks like

So, you are starting with #"100 g"# of saturated solution at #75^@"C"#. Mind you, you have #"100 g"# of solution that contains as much dissolved potassium nitrate as possible.

This solution will contain

#100.0 color(red)(cancel(color(black)("g solution"))) * "155 g KNO"_3/((155 + 100)color(red)(cancel(color(black)("g solution")))) = "60.78 g KNO"_3#

Now, potassium nitrate's solubility is given per #"100 g"# of water. Calculate how much water you have in this initial solution

#m_"water" = "100.0 g" - "60.78 g" = "39.22 g"#

Next, determine how much potassium nitrate can be dissolved in #"39.22 g"# of water at #26^@"C"# in order to make a saturated solution, i.e. have the maximum amount of dissolved potassium nitrate possible

#39.22 color(red)(cancel(color(black)("g water"))) * "38.0 g KNO"_3/(100color(red)(cancel(color(black)("g water")))) = "14.9 g KNO"_3#

This means that when the initial solution is cooled from #75^@"C"# to #25^@"C"#, the amount of water that it contained will only hold #"14.9 g"# of dissolved potassium nitrate.

The rest will crystallize out of solution

#m_"crystallize" = "60.78 g" - "14.9 g" = color(green)("45.9 g")#

The answer is rounded to three sig figs.

Last updated at June 12, 2021 by

(a) At 313K, 

Mass of potassium nitrate needed to produce a saturated solution of potassium nitrate in 100g water = 62g

Mass of potassium nitrate needed to produce a saturated solution of potassium nitrate in 1g water = 62g/100g

Mass of potassium nitrate needed to produce a saturated solution of potassium nitrate in 1g water = 62gx50g/100g

          = 62g/2

           =31 g

(b) Solubility of solids in liquid decreases with decrease in temperature.

Room temperature is 298K while the saturated solution was formed at 253K. Hence, she will find crystals of potassium chloride when the solution cools down.

(c) Solubility is the maximum amount of solute which can be dissolved in 100 gm of Solvent at a particular temperature.

Hence the solubility of the following at 293K is

• Potassium Nitrate - 32
• Sodium Chloride - 36
• Potassium Chloride - 35
• Ammonium Chloride - 37

(d) From the above table we can see that the solubility of a salt is directly proportional to the temperature. 

As the temperature increases the solubility also increases. 

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A student, while the testing the solubility of potassium nitrate at 313 k, is found that the solubility is 62 in 100 g of water. What masses of potassium nitrate would be needed to produce a saturated solution of potassium nitrate in 50 g of water at313k?

Text Solution

Solution : (a) Mass of potassium chloride in 100 g of water in saturated solution = 46 g <br> Mass of potassium chloride in 50 g of water in saturated solution = `((46 g))/((100 g)) xx (50g) = 23 g` <br> (b) When the solution is cooled, the solubility of salt in water will decrease. This means that upon cooling, it will start separating from the solution in crystalline form.

Solubility of potassium nitrate at  313K = 62/100

100 g of water contains potassium nitrate = 62 g

50 g of water contains potassium nitrate  = 62/100 X 50 = 31g

Thus, 31 g potassium nitrate would be needed to produce a saturated solution of potassium nitrate in 50 g of water at 313 K.

Hope it helped to clear your delimma

Thank you

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