What is the total mass of KNO_3 that must be dissolved in 50 grams of H_2O at 60°C to make a saturated solution?

Mar 11, 2016

${\text{58 g KNO}}_{3}$

Explanation:

In order to solve this problem, you must take a look at the solubility graph for potassium nitrate, ${\text{KNO}}_{3}$, which looks like this

Now, the solubility graph shows you how much solute can be dissolved per $\text{100 g}$ of water in order to make an unsaturated, a saturated, or a supersaturated solution.

You're looking to make a saturated potassium nitrate solution using $\text{50 g}$ of water at ${60}^{\circ} \text{C}$. Your starting point will be to determine how much potassium nitrate can be dissolved in $\text{100 g}$ of water at that temperature in order to have a saturated solution.

As you can see, the curve itself represents saturation.

If you draw a vertical line that corresponds to ${60}^{\circ} \text{C}$ and extend it until it intersects the curve, then draw a horizontal line that connects to the vertical axis, you will find that potassium has a solubility of about $\text{115 g}$ per $\text{100 g}$ of water.

Use this as a conversion factor to help you find how much potassium nitrate can be dissolved in $\text{50 g}$ of water at the same temperature

50color(red)(cancel(color(black)("g water"))) * overbrace("115 g KNO"_3/(100color(red)(cancel(color(black)("g water")))))^(color(purple)("solubility at"color(white)(a) 60^@"C")) = "57.5 g KNO"_3

You should round this off to one sig fig, since that's how many sig figs you have for the mass of water, but I'll leave it rounded to two sig figs, just for good measure

${m}_{K N {O}_{3}} = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{58 g} \textcolor{w h i t e}{\frac{a}{a}} |}}}$