the Keq of Mg(OH)2 is 2(10^-11). calculate the concentration of Mg ions in a saturated solution of this compound
Usually this is called Ksp.
..........Mg(OH)2 ==> Mg^2+ + 2OH^-
I.........solid.......0.........0
C.........solid.......x.........2x
E.........solid.......x.........2x
Plug the E line into the Ksp expression and solve for x = (Mg^2+)
To calculate the concentration of Mg ions in a saturated solution of Mg(OH)2, we need to make use of the equilibrium constant (Keq) and the balanced chemical equation for the dissociation of Mg(OH)2.
The balanced chemical equation for the dissociation of Mg(OH)2 in water is:
Mg(OH)2 ⇌ Mg2+ + 2OH-
From the equation, we can see that for every 1 mol of Mg(OH)2 that dissociates, 1 mol of Mg2+ and 2 mol of OH- are formed.
Now, let's assign some variables:
Let "x" represent the concentration of Mg2+ ions in mol/L.
Since Mg(OH)2 dissociates to form 1 mol of Mg2+ ion for every 1 mol of Mg(OH)2, the concentration of Mg2+ ions will also be "x" mol/L.
The concentration of OH- ions will be 2x mol/L because for every 1 mol of Mg(OH)2, 2 mol of OH- ions are formed.
The equilibrium constant (Keq) expression for this equation is:
Keq = [Mg2+][OH-]^2
Given that Keq is 2 × 10^-11 and OH- concentration is 2x, we can substitute these values into the Keq expression:
2 × 10^-11 = x (2x)^2
2 × 10^-11 = 4x^3
Rearranging the equation:
x^3 = (2 × 10^-11) / 4
x^3 = 5 × 10^-12
Now, we can solve for x by taking the cubic root of both sides:
x = (5 × 10^-12)^(1/3)
x ≈ 7.94 × 10^-4 mol/L
Therefore, the concentration of Mg2+ ions in a saturated solution of Mg(OH)2 is approximately 7.94 × 10^-4 mol/L.