Use the following table for problems 9.25 to 9.28: A solut...

Question

Use the following table for problems 9.25 to 9.28: <TABLE>A solution containing 80. g of NaNO₃ in 75 g of H₂O at 50 °C is cooled to 20 °C.b. How many grams of solid NaNO₃ crystallized after cooling?

Accepted Answer

Welcome back everyone. The solubility of potassium hydrogen sulfate at 25 Celsius and 60 Celsius is given in the table below. A solution was made by dissolving 105 g of potassium hydrogen sulfate and 150 g of water at 60 degrees Celsius. The solution is then cooled to 25 Celsius. And we need to determine the mass of solid potassium hydrogen sulfate that precipitated out after cooling. So below, we have our solubility table in grams per grams of water for our substance, potassium hydrogen sulfate at both 25 Celsius which has a solubility of 51 g and then at degrees Celsius with the solubility of 77 g of potassium hydrogen sulfate. So based on this given solubility at 60 degrees Celsius, we would outline that we have g of potassium hydrogen sulfate dissolved in 100 g of water. And this proportion we can set equal to our unknown solubility X in grams of potassium hydrogen sulfate and 150 g of solvent being water. So we want to solve for X and we are going to need to cross multiply So that in our next line, we find that we have X grams of potassium hydrogen sulfate times 100 g of water set equal to 11,550 g of potassium hydrogen sulfate hydrate. And now isolating for our unknown soluble of potassium hydrogen sulfate in grams. We're going to divide both sides by 100 g of water and sorry, our decimal point should be after our zero in 100 g. So that would cancel out 100 g of water on the left of our equation. And also dividing by 100 g of water. On the right, we can cancel out our term for water. And this would allow us to determine that our solubility of potassium hydrogen sulfate in grams would be equal to a value of about 115 point five g. Now, going back to our prompt, we're told that 105 g of potassium hydrogen sulfate is dissolved in 150 g of water at 60 Celsius. And because we determined its solubility is 115.5 because 105 g is less than its solubility or by its, I mean potassium hydrogen sulfate solubility as 115.5. Then therefore, all of the potassium hydrogen sulfate is dissolved at 60 degrees Celsius. Now we need to recognize that the prompt tells us that we're then cool our solution to 25 degrees Celsius And so we're going to need to calculate a new solubility based on this temperature change. And so now at 25 degrees Celsius from our diagram or from our table rather, we're given a solubility for potassium hydrogen sulfate of 50.6 grams, a potassium hydrogen sulfate dissolved in 100 g of water. And we can set this proportion equal to our unknown solubility in grams of potassium hydrogen sulfate per g of solvent being water. So following the same steps of four and cross multiplying to sulfur our solubility at 25 degrees Celsius of our cold solution. We'd have X grams of potassium hydrogen sulfate multiplied by 100 g of water set equal to 7590 g of potassium hydrogen sulfate hydrated in water and dividing to sulf for our unknown solubility in 150 g, we're going to divide both sides from the left on or buy 100 g of water. So that that term will cancel on the left and we're going to divide again by g of water on the right, which will cancel our term water on the right. And this would leave us with our solubility of potassium hydrogen sulfate in grams equal to a value of 75.9 g of potassium hydrogen sulfate in 150 g of so solution or water, we'll say at 25 degrees Celsius And so now we're just going to take our difference between our solubility that we just determined to determine our mass of potassium hydrogen sulfate that is precipitated. So we would take our original solubility at 60 Celsius being 105 g. So 105 g subtracted from our solubility at 25 Celsius, once the solution is cooled, which we determine to be 75.9 g. And from this difference, we'll find our amount of potassium hydrogen sulfate precipitated, equal to 29.1 g. So this would be 29.1 g would be our final answer of our mass of potassium hydrogen sulfate that is precipitated. I hope that this made sense and let us know if you have any questions.

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