Question

The solubilities of three salts in water are shown in the graph. A plot has solubility in grams per liter on the y axis and temperature in degrees Celsius on the x axis. There are three solubility curves, P b (N O 3) 2, K C l, and K 2 C r 2 O 7. Relevant data is summarized. P b (N O 3) 2: 750 grams per liter at 40 degrees Celsius. K C l: 400 grams per liter at 40 degrees Celsius. K 2 C r 2 O 7: 200 grams per liter at 40 degrees Celsius. For each salt, determine how much will remain undissolved if 500 g is mixed into a liter of pure water at 40 ∘C. One significant figure is sufficient in each answer. Pb(NO3)2 : g KCl : g K2Cr2O7 : g

Answer 1

Answer : The solubilities of three salts in water are shown in the graph. A plot has solubility in grams per liter on the y axis and temperature in degrees Celsius on the x axis. There are three solubility curves, Pb(NO₃)₂, KCl, and K₂Cr₂O₇. Relevant data is summarized. Pb(NO₃)₂ : 750 grams per liter at 40 degrees Celsius. KCl: 400 grams per liter at 40 degrees Celsius. K₂Cr₂O₇ : 200 grams per liter at 40 degrees Celsius.

For each salt i.e. given above, we have determined how much amount will remain undissolved if 500 g is mixed into a liter of pure water at 40 ⁰C. One significant figure is sufficient in each answer. Pb(NO₃)₂ : g KCl : g and K₂Cr₂O₇ : g

For that now let us see the solubilites of the above given salt i.e. Pb(NO₃)₂, KCl, and K₂Cr₂O₇ which is given as above

That is, the solubility of the Pb(NO₃)₂ is 750 grams per liter at 40 degrees Celsius.

Similarly, the solubility of KCl is 400 grams per liter at 40 degrees Celsius

And the solubility of K₂Cr₂O₇ is 200 grams per liter at 40 degrees Celsius

So, if 500 g is mixed into a liter of pure water at 40 ⁰C then amount of the above given salt that would remain undissolved is shown as follows :

(1) The amount of Pb(NO₃)₂ that would remain undissolved is 0 gram. Since the solubility of the Pb(NO₃)₂ at 40 degrees Celsius is 750 grams per liter which is more than the 500 gram. So, if 500 g of Pb(NO₃)₂ is mixed into a liter of pure water at 40 ⁰C then amount of the Pb(NO₃)₂ salt that would remain undissolved is 0 gram since the solubility of Pb(NO₃)₂ is more than the amount of salt dissolved in water at 40 degrees Celsius. So, salt will completely dissolve in water at 40 degrees Celsius. And thus, amount of Pb(NO₃)₂   that would remain undissolved is 0 gram.

(2) The amount of KCl that would remain undissolved is 100 gram. Since the solubility of the KClat 40 degrees Celsius is 400 grams per liter which is less than the 500 gram. So, if 500 g of KCl is mixed into a liter of pure water at 40 ⁰C then amount of the KCl salt that would remain undissolved is 100 gram since the solubility of KCl is les than the amount of salt dissolved in water at 40 degrees Celsius. So, only 400 gram of KCl would dissolve in pure water at 40 degrees Celsius and the amount of salt left would be equal to which is shown as follows :

(Amount of total KCl available - Amount of KCl dissolved at 40 degrees Celsius) i.e.

(500 gram - 400 gram = 100 gram)

since Amount of total KCl available = 500 gram and Amount of KCl dissolved at 40 degrees Celsius = 400 gram (as seen from its solubility at 40 degrees Celsius)

Thus, if 500 g of KCl is mixed into a liter of pure water at 40 ⁰C then amount of the KCl that would remain undissolved is 100 gram.

(3) The amount of K₂Cr₂O₇ that would remain undissolved is 300 gram. Since the solubility of the K₂Cr₂O₇ at 40 degrees Celsius is 200 grams per liter which is less than the 500 gram. So, if 500 g of K₂Cr₂O₇ is mixed into a liter of pure water at 40 ⁰C then amount of the K₂Cr₂O₇ salt that would remain undissolved is 300 gram since the solubility of K₂Cr₂O₇ is les than the amount of salt dissolved in water at 40 degrees Celsius. So, only 200 gram of K₂Cr₂O₇ would dissolve in pure water at 40 degrees Celsius and the amount of salt left would be equal to which is shown as follows :

(Amount of total K₂Cr₂O₇ available - Amount of K₂Cr₂O₇ dissolved at 40 degrees Celsius) i.e.

(500 gram - 200 gram = 300 gram)

since Amount of total K₂Cr₂O₇ available = 500 gram and Amount of K₂Cr₂O₇ dissolved at 40 degrees Celsius = 200 gram (as seen from its solubility at 40 degrees Celsius)

Thus, if 500 g of K₂Cr₂O₇ is mixed into a liter of pure water at 40 ⁰C then amount of the K₂Cr₂O₇ that would remain undissolved is 300 gram.

Thus, finally Pb(NO₃)₂ : g KCl : g and K₂Cr₂O₇ : g would be equal to which is shown as follows :

Pb(NO₃)₂ : 0 g KCl : 100 g and K₂Cr₂O₇ : 300 g

Thus, if we express the above given result in kilograms we have

Pb(NO₃)₂ : 0 kg KCl : 0.1 kg and K₂Cr₂O₇ : 0.3 kg