at 23C the reaction CaCrO4 -> Ca2+ + CrO42- has an equilibrium constant of 7.1 x 10-4. what are the equilibrium concentrations of Ca2+ and CrO42- in a saturated solution?
To determine the equilibrium concentrations of Ca2+ and CrO42- in a saturated solution, we first need to write the balanced chemical equation and expression for the equilibrium constant.
The balanced chemical equation for the reaction is:
CaCrO4 ⇌ Ca2+ + CrO42-
The expression for the equilibrium constant (Kc) is:
Kc = [Ca2+][CrO42-] / [CaCrO4]
We have the value of the equilibrium constant (Kc) as 7.1 x 10-4. Since the reaction is at equilibrium in a saturated solution, the concentration of CaCrO4 will be constant and we can assume it is 1 (arbitrary unit).
So, the equation becomes:
7.1 x 10-4 = [Ca2+][CrO42-] / 1
Now, we can solve for the equilibrium concentrations of Ca2+ and CrO42-.
Let's assume the equilibrium concentration of Ca2+ is x and the equilibrium concentration of CrO42- is y.
Substituting the values into the equation:
7.1 x 10-4 = x * y / 1
Simplifying the equation, we have:
7.1 x 10-4 = x * y
Since the concentrations of Ca2+ and CrO42- are equal, we can substitute y with x:
7.1 x 10-4 = x * x
Simplifying further:
7.1 x 10-4 = x^2
Now, we can solve this equation to find the value of x, which represents the equilibrium concentration of Ca2+ in the saturated solution.
To determine the equilibrium concentrations of Ca2+ and CrO42- in a saturated solution, we need to use the equilibrium constant expression and solve for the unknown concentrations. The equilibrium constant expression for the given reaction can be written as:
K = [Ca2+][CrO42-]
Where [Ca2+] and [CrO42-] denote the concentrations of Ca2+ and CrO42- ions, respectively, at equilibrium.
Given that the equilibrium constant (K) is 7.1 x 10-4, we can set up the equation:
7.1 x 10-4 = [Ca2+][CrO42-]
Since we are dealing with a saturated solution, we can assume that the compound CaCrO4 fully dissociates, meaning that the initial concentration of CaCrO4 is equal to the initial concentrations of Ca2+ and CrO42-. Let's denote this initial concentration as 'x':
[Ca2+]0 = [CrO42-]0 = x
Therefore, we can rewrite the equilibrium constant expression as:
7.1 x 10-4 = (x)(x)
Now, we can solve this equation for 'x' using algebraic methods. Rearranging the equation, we have:
7.1 x 10-4 = x^2
Taking the square root of both sides, we get:
√(7.1 x 10-4) = x
Calculating the square root of 7.1 x 10-4, we find:
√(7.1 x 10-4) ≈ 2.66 x 10-2
Therefore, the equilibrium concentrations of Ca2+ and CrO42- in a saturated solution are approximately 2.66 x 10-2 M.