Question

A solution containing $80gofNaN{O}_3$in $75gof{H}_{2}O$at ${50}^{\circ }C$is cooled to ${20}^{\circ }C$

a. How many grams of $NaN{O}_3$remain in solution at ${20}^{\circ }C$?

b. How many grams of solid $NaN{O}_3$crystallized after cooling?

Short answer

(part a) $66gof{\mathrm{NaNO}}_3$remaining in the solution ${20}^{\circ }C$when a solution containing $80gofNaN{O}_3$in $75gof{H}_{2}O.$

(part b) $14gof{\mathrm{NaNO}}_3$remained in the solution crystalized after cooling.

Step-by-step solution

Introduction (part a).

A solution in science is a blend of different substances in varying proportions that can be varied continuously up to the limit of solubilization.

Given Information (part a, b).

A solution have $80gofNaN{O}_3$in $75gof{H}_{2}O$

Temperature is ${50}^{\circ }C$and to ${20}^{\circ }C$

Explanation (part a).

Find the quantity of $NaN{O}_3$in solution at ${20}^{\circ }C.$

Then,

$88\mathrm{g}\text{of}{\mathrm{NaNO}}_3=100\mathrm{g}\text{of}{\mathrm{H}}_2\mathrm{O}$

Therefore, the factor of conversion are,

localid="1652685655746" $\frac{88\mathrm{g}{\mathrm{NaNO}}_3}{100g{H}_2\mathrm{O}}\text{and}\frac{100g{H}_2\mathrm{O}}{88\mathrm{g}{\mathrm{NaNO}}_3}$

Find out the grams of $NaN{O}_3$out of localid="1652685822899" $80gofNaN{O}_3$in $75gof{H}_{2}O$

$$\begin{gathered} \text{Amount of}{\mathrm{NaNO}}_3=75\mathrm{g}{\mathrm{H}}_2\mathrm{O}\times \frac{80\mathrm{g}{\mathrm{NaNO}}_3}{100\mathrm{g}{\mathrm{H}}_2\mathrm{O}} \\ =66gof{\mathrm{NaNO}}_3 \end{gathered}$$

Explanation (part b).

Find the quantity of $NaN{O}_3$can be crystalized after cooling process at ${20}^{\circ }C$

Therefore,

$88\mathrm{g}\text{of}{\mathrm{NaNO}}_3=100\mathrm{g}\text{of}{\mathrm{H}}_2\mathrm{O}$

Hence, the factor of conversion are,

$\frac{88\mathrm{g}{\mathrm{NaNO}}_3}{100g{H}_2\mathrm{O}}\text{and}\frac{100g{H}_2\mathrm{O}}{88\mathrm{g}{\mathrm{NaNO}}_3}$

Now find the grams of $NaN{O}_3$in which $80gofNaN{O}_3$in $75gof{H}_{2}O$at${20}^{\circ }C$

$$\begin{gathered} \text{Amount of}{\mathrm{NaNO}}_3=75\mathrm{g}{\mathrm{H}}_2\mathrm{O}\times \frac{80\mathrm{g}{\mathrm{NaNO}}_3}{100\mathrm{g}{\mathrm{H}}_2\mathrm{O}} \\ =66gof{\mathrm{NaNO}}_3 \end{gathered}$$

The grams of crystalized $NaN{O}_3$is find by subtracting fully dissolved $NaN{O}_3$at ${20}^{\circ }C$with fully dissolved$NaN{O}_3$at ${50}^{\circ }C,$

$$\begin{gathered} \text{crystallizable}{\mathrm{NaNO}}_3\text{at}{20}^{\circ }\mathrm{C}=80.0\mathrm{g}-66\mathrm{g} \\ =14\mathrm{g} \end{gathered}$$$75gof{H}_{2}O$