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Solubility of a salt of strong acid and strong base in pure water

Let us consider a salt of this type as AgCl. Let the solubility of the salt be s mol/L. Such salt do not hydrolyze.
 
Description: 22199.png
Description: 22207.png
 
Knowing the solubility product, solubility s of AgCl can be calculated.

Solubility of a salt of strong acid and strong base in presence of a common ion (incapable of forming complex)

Let us calculate the solubility of AgCl in 0.1 M AgNO3 solution.
 
AgCl(s) Ag+ (aq) + Cl(aq)
AgNO3 Ag+ + NO3
 
Let the solubility of AgCl in the presence of 0.1 M AgNO3 be s ‘ mol/L. Then
 
Description: 22215.png
Description: 22222.png
Description: 22230.png
Description: 22240.png
 
s‘ can be ignored with respect to 0.1 M. Therefore,
(0.1 + s ‘) = 0.1
∴ Description: 22251.png
 
s‘ can be calculated provided we know KSP of AgCl. It can be noticed that s‘ would be less than s.

Solubility of a salt of strong acid and strong base in a solvent capable of forming complex

Let us consider the solubility of AgCl in c M NH3 (as solvent). Let the solubility of AgCl in ammonia be s" mol/L, and x mol/L is the amount of salt-forming complex.
 
Description: 22266.png
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Description: 22281.png
 
where Kf is the equilibrium constant for the formation of complex ion/species and is called the formation constant.
 
Kf values of complex formation are very high, so almost entire amount of Ag+ would be converted into complex. This means that the value of x approaches s". Thus (s" x) would be very small. Let this small value be y. Also the value of x is small, so 2x can be ignored with respect to c. Therefore,
 
(c – 2x) c
∴ KSP = y × s"; Description: 22289.png
 
Knowing the values of KSP, Kf, and c, we can calculate the value of s" and x. It can notice that s" would be greater than s. Thus, complex formation increases the solubility of a salt.

Solubility of a salt of weak acid and strong base in pure water

Let the salt of this type be CH3COOAg and its solubility be s mol/L. Such salts undergo hydrolysis. Out of CH3COO and Ag+ ions, CH3COO ion will get hydrolyzed.
 
Let the amount of CH3COO ion getting hydrolyzed be x mol/L.
 
Description: 22297.png
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KSP = (sx) × (s)
Description: 22312.png
 
Solving these two equations, we get the values for s and x.

Solubility of a salt of weak acid and strong base in acidic buffer

Let the solubility of CH3COOAg be s' mol/L in acidic buffer. Now, in the presence of free H+ (from acidic buffer), the anion of weak acid will form weak acid at equilibrium, but [H+] in a buffer will remain constant.
 
Description: 22319.png
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∴ KSP = (s' – x') × (s')
Description: 22338.png
 
Knowing the values of KSP, Ka, and the concentration of H+ ions in the buffer, we can calculate s'  and x'. The value of s' would be greater than s. This implies that the solubility of a salt of weak acid and strong base is more in acidic buffer than in pure water.

Simultaneous solubility of two or more sparingly soluble salts

Simultaneous solubility means the solubility of a sparingly soluble salt in the presence of another sparingly soluble salt having a common ion. Let us assume the simultaneous solubilities of AgCl and AgBr in a solution are x and y mol/L, respectively.
 
Description: 22353.png; KSP = [Ag+]total × [Cl]
 
Description: 22363.png; KSP = [Ag+]total × [Br]
 
KSP of AgCl = (x + y) × x
 
KSP of AgBr = (x + y) × y
 
From the above two expressions, we can calculate the simultaneous solubilities of AgCl and AgBr.




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