Question

Potassium nitrate has a solubility of $32gofKN{O}_{3}in100.gof{H}_{2}Oat20°C$. Determine if each of the following forms an unsaturated or saturated solution at $20°C:(9.3)$

a. adding localid="1653998424495" $32gofKN{O}_{3}to200.gof{H}_{2}O$

b. adding localid="1653998430681" $19gofKN{O}_{3}to50.gof{H}_{2}O$

c. addinglocalid="1653998451738" $68gofKN{O}_{3}to150.gof{H}_{2}O$

Short answer

(Part a) $KN{O}_3$was entirely dissolved in water, resulting in an unsaturated solution

(Part b) The leftover localid="1653998461330" $3g$of solid remained undissolved, resulted in a saturated solution.

(Part c) the rest localid="1653998465888" $20g$of solid is left undissolved, leading in a saturated solution.

Step-by-step solution

Introduction (Part a).

(a) At a specific temperature, a saturated mixture containing the maximum quantity of liquid sample. There is very little solute in an imbalanced solution than could be absorbed.

Given data (a).

We must first establish the maximum quantity of $KN{O}_3$that can dissolve in localid="1653998493497" $200gof{H}_{2}Oat2°C$in order to ascertain whether an unsaturated or saturated solution occurs when localid="1653998499549" $2gofKN{O}_3$is given to localid="1653998504462" $200gof{H}_{2}Oat2°C.$

Potassium nitrate has such a reactivity of localid="1653998560045" role="math" $32gofKN{O}_{3}in100gof{H}_{2}O$at a ratio of $20°C$. The relevant data can be gathered can be obtained using the soluble data:

$\frac{32gKN{O}_3}{100g{H}_{2}O}and\frac{100g{H}_{2}O}{32gKN{O}_3}$

Explanation (a).

The greatest quantity of $KN{O}_3$that may be absorbed in localid="1653998527806" $200gof{H}_{2}O$can now be computed as follows:

localid="1653998540264" $200.\cancel{g{H}_{2}O}\times \frac{32gKN{O}_3}{100\cancel{g{H}_{2}O}}=64gKN{O}_3$

The highest quantity of $KN{O}_3$that may dissolve in localid="1653998549092" $200gof{H}_{2}Oat20°Cis64g.$. When localid="1653998576223" $2gofKN{O}_3$is mixed with localid="1653998570419" $200g$of water, it totally dissolves and creates an unsaturated solution.

Given data (b).

(b) Specify the total quantity of $KN{O}_3$that can breakdown in $50gof{H}_{2}O$to identify if an unsaturated or saturated solution occurs when $19gofKN{O}_3$is given to $50gof{H}_{2}Oat20°C$.

Potassium nitrate does have a concentration of localid="1653998591666" $32gofKN{O}_{3}in100g$of water at $20°C$. The appropriate data obtained can be derived using the solubility data:

$\frac{32gKN{O}_3}{100g{H}_{2}O}and\frac{100g{H}_{2}O}{32gKN{O}_3}$

Explanation (b).

The largest quantity of $KN{O}_3$that may melt in localid="1653998603689" $50gof{H}_{2}O$can now be computed as follows:

localid="1653998614487" $50.\cancel{g{H}_{2}O}\times \frac{32gKN{O}_3}{100\cancel{g{H}_{2}O}}=16gKN{O}_3$

The quantity of $KN{O}_3$that may absorb in localid="1653998623052" $50gof{H}_{2}Oat20°Cis16g.$Only localid="1653998630296" $19gofKN{O}_3$can mix fully in water if localid="1653998634749" $16gofKN{O}_3$is introduced tolocalid="1653998639634" $50g$of water, remaining localid="1653998644610" $3g$of material undissolved to produce a saturated solution.

Given data (c).

(c) Specify the maximum quantity of $KN{O}_3$that can breakdown in localid="1653998658703" $150gof{H}_{2}O$to establish how an unsaturated or saturated solution develops when localid="1652703476811" $68gofKN{O}_3$is added to localid="1653998676500" $150gof{H}_{2}Oat20°C$.

Potassium nitrate really does have a concentration of localid="1653998684808" $32gofKN{O}_{3}in100g$ of water at $20°C$. The corresponding changes took place can be estimated using the solubility data:$\frac{32gKN{O}_3}{100g{H}_{2}O}and\frac{100g{H}_{2}O}{32gKN{O}_3}$

Explanation (c).

The optimum quantity of$KN{O}_3$that may melt in localid="1653998708262" role="math" $150gof{H}_{2}O$can now be computed by dividing:

localid="1653998726210" $150.\cancel{g{H}_{2}O}\times \frac{32gKN{O}_3}{100\cancel{g{H}_{2}O}}=48gKN{O}_3$

The volume of $KN{O}_3$that may disintegrate in localid="1653998737914" $150gof{H}_{2}Oat20°Cis48g.$Only localid="1653998759481" $68gofKN{O}_3$can dissolve totally in water if localid="1653998744447" $48gofKN{O}_3$is put tolocalid="1653998752126" $150g$of water, allowing localid="1653998767149" $20g$of substance undissolved to create a saturated solution.