If Ksp for the dissolution of silver carbonate is 8.1x10-12, calculate the concentration of silver ions present in a saturated solution of silver carbonate
To calculate the concentration of silver ions (Ag+) in a saturated solution of silver carbonate (Ag2CO3), we can use the solubility product constant (Ksp) and the stoichiometry of the dissolution reaction.
The balanced equation for the dissolution of silver carbonate is:
Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^2-(aq)
From this equation, we can see that one mole of silver carbonate yields two moles of silver ions.
Let's assume x mol/L is the concentration of Ag2CO3 that dissolves. Since two moles of Ag+ ions are produced for every one mole of Ag2CO3 that dissolves, the concentration of Ag+ in the saturated solution will be 2x mol/L.
Now, we can use the solubility product constant (Ksp) to find the value of x.
The expression for Ksp is:
Ksp = [Ag+]^2 [CO3^2-]
Since Ag2CO3 only dissociates to form Ag+ and CO3^2-, and assuming the initial concentration of CO3^2- is negligible, we can equate Ksp to the concentration of Ag+ ions squared:
Ksp = [Ag+]^2
Rearranging this equation, we have:
[Ag+] = √Ksp
Plugging in the given value of Ksp = 8.1x10^-12, we can find the concentration of Ag+ ions:
[Ag+] = √(8.1x10^-12)
≈ 9.0x10^-6 mol/L
Therefore, the concentration of silver ions (Ag+) present in a saturated solution of silver carbonate is approximately 9.0x10^-6 mol/L.
To calculate the concentration of silver ions in a saturated solution of silver carbonate, we first need to set up the dissociation reaction of silver carbonate:
Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^2-(aq)
According to the reaction, one mole of Ag2CO3 dissociates to give 2 moles of Ag+ ions. The Ksp expression for the dissociation of silver carbonate is given as:
Ksp = [Ag+]^2 [CO3^2-]
Given that the Ksp value for silver carbonate is 8.1 x 10^-12, we can set up an equation with the concentration of Ag+ ions as x:
8.1 x 10^-12 = (x)^2 [CO3^2-]
Since Ag2CO3 dissociates to give 2 Ag+ ions, we can assume that if x is the concentration of Ag+ ions, then 2x is the concentration of CO3^2- ions. Therefore, we substitute 2x for [CO3^2-] in the equation:
8.1 x 10^-12 = (x)^2 (2x)^2
8.1 x 10^-12 = 4x^3
To solve for x, we rearrange the equation:
4x^3 = 8.1 x 10^-12
x^3 = (8.1 x 10^-12) / 4
x^3 = 2.025 x 10^-12
x = cuberoot(2.025 x 10^-12)
Using a calculator to find the cube root, the concentration of silver ions in a saturated solution of silver carbonate is approximately 1.25 x 10^-4 M (molar).
..........Ag2CO3 ==> 2Ag^+ + CO3^2-
I.........solid.......0.......0
C......x dissolves....2x......x
E..........solid......2x......x
Ksp = (Ag^+)^2(CO3^2-)
Substitute the E line into Ksp expression and solve for x = (Ag2CO3). Ag is twice that.