at 30 degree celsius , the solubility of ag2co3 (Ksp= 8 * 10^-12) would be maximum in 1 litre of ?
a) pure water
b) 0.05 M NH3
To determine the solubility of Ag2CO3 at 30 degrees Celsius in each solution, we need to compare the solubility product constant (Ksp) of Ag2CO3 with the ion product (IP) in each solution.
The balanced equation for the dissolution of Ag2CO3 is:
Ag2CO3 (s) ⇌ 2Ag+ (aq) + CO3^2- (aq)
The solubility product constant (Ksp) expression for Ag2CO3 is:
Ksp = [Ag+]^2 [CO3^2-]
For pure water, the concentration of Ag+ and CO3^2- ions is unknown. Let's assume the solubility of Ag2CO3 in pure water is "x" moles per liter.
Therefore, the Ksp expression becomes:
Ksp = (2x)^2 (x) = 4x^3
Similarly, for 0.05 M NH3, we need to consider the reaction of Ag2CO3 with NH3:
Ag2CO3 (s) + 6NH3 (aq) ⇌ 2[Ag(NH3)2]+ (aq) + CO3^2- (aq)
The solubility expression for Ag2CO3 in this case becomes the solubility product constant (Ksp) for the complex [Ag(NH3)2]+ multiplied by the concentration of CO3^2- ion:
K' sp = [Ag(NH3)2+]^2 [CO3^2-]
Since 0.05 M NH3 is present, we can assume that the concentration of [Ag(NH3)2]+ is also 0.05 M.
For both cases, the ion product (IP) is equal to the product of the ionic concentrations.
For pure water:
IP = [Ag+]^2 [CO3^2-] = x^3
For 0.05 M NH3:
IP' = [Ag(NH3)2+]^2 [CO3^2-] = (0.05)^2 x
To find the solubility (x) that corresponds to the maximum solubility at 30 degrees Celsius, we need to compare the IP values with the Ksp and K'sp values.
For pure water:
IP = Ksp ⇒ x^3 = 8 * 10^-12 ⇒ x ≈ 2.52 * 10^-4 M
For 0.05 M NH3:
IP' = K'sp ⇒ (0.05)^2 x = 8 * 10^-12 ⇒ x ≈ 2.26 * 10^-8 M
Comparing the solubilities, we can see that the solubility of Ag2CO3 is maximum in 1 liter of pure water (choice a) at 30 degrees Celsius.
To determine which solution will result in the maximum solubility of Ag2CO3 at 30 degrees Celsius, we need to compare the solubility product constant (Ksp) values under different conditions.
The Ksp expression for Ag2CO3 can be written as:
Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^2-(aq)
The Ksp value for Ag2CO3 is given as 8 * 10^-12, which means that when Ag2CO3 dissolves, the concentration of Ag+ and CO3^2- ions in the solution will be equal to the square root of the Ksp value.
Now, let's evaluate the solubility of Ag2CO3 in each given solution and determine which one will result in the maximum solubility:
a) Pure water:
In pure water, there are no other ions present except H+ and OH-. Since Ag2CO3 dissociates into Ag+ and CO3^2- ions, the solubility will be limited based on the availability of these ions. Therefore, the pure water will result in the maximum solubility of Ag2CO3.
b) 0.05 M NH3:
Ammonia (NH3) is a weak base and can react with Ag+ ions to form a complex ion. This reaction reduces the concentration of Ag+ ions in the solution, reducing the solubility of Ag2CO3. Therefore, the presence of NH3 will decrease the solubility of Ag2CO3 compared to pure water.
In conclusion, the solubility of Ag2CO3 will be maximum in 1 liter of pure water at 30 degrees Celsius.