Calculate the thiocyanate concentration at equilibrium if the irone (III) ion concentration is 0.23 M and the complex ion concentration is 0.625 M t equilibrium. Keq= 138M^-1
I will assume the Keq given is for the reaction
Fe^3+ + SCN^- ==> [FeSCN]^2+
K = [FeSCN]^2+/[Fe^3+][SCN^-]
Substitute the numbers in the problem and calculate the only unknown there.
To calculate the thiocyanate (SCN-) concentration at equilibrium, we can use the equilibrium expression for the reaction:
Fe3+ + SCN- ⇌ Fe(SCN)2+
The equilibrium constant (Keq) for this reaction is given as 138 M^-1.
Let's assume that the initial concentration of SCN- is x (M).
Using stoichiometry, we can see that the initial concentration of Fe(SCN)2+ is also x (M).
The concentration of Fe3+ is given as 0.23 M.
At equilibrium, the concentration of Fe3+ will be reduced by x M, and the concentration of SCN- will be increased by x M (according to the stoichiometry of the balanced equation).
Thus, the concentration of Fe3+ at equilibrium will be (0.23 - x) M, and the concentration of Fe(SCN)2+ at equilibrium will be (0.625 + x) M.
Now, we can substitute these values into the equilibrium expression:
Keq = [Fe(SCN)2+] / ( [Fe3+] * [SCN-] )
138 = (0.625 + x) / ( (0.23 - x) * x )
Multiplying both sides of the equation by (0.23 - x) * x, we get:
138 * (0.23 - x) * x = 0.625 + x
Simplifying the equation:
31.74x - 138x^2 = 0.625 + x
Rearranging the terms:
138x^2 - 31.74x + 0.625 - x = 0
138x^2 - 32.74x + 0.625 = 0
Now, solving this quadratic equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
a = 138, b = -32.74, c = 0.625
Substituting these values into the quadratic formula:
x = (-(-32.74) ± sqrt((-32.74)^2 - 4 * 138 * 0.625)) / (2 * 138)
x = (32.74 ± sqrt(1070.2676 - 345.6)) / 276
x = (32.74 ± sqrt(724.6676)) / 276
x = (32.74 ± 26.920) / 276
There are two possible solutions for x:
1. x = (32.74 + 26.920) / 276 = 0.238 M
2. x = (32.74 - 26.920) / 276 = 0.023 M
Therefore, there are two possible equilibrium concentrations for SCN-:
1. 0.238 M
2. 0.023 M
To calculate the thiocyanate concentration at equilibrium, we need to use the equilibrium constant expression and solve for the unknown. The equilibrium constant expression for the reaction is:
Keq = [Fe(SCN)²⁺] / [Fe³⁺][SCN⁻]
Given:
[Fe³⁺] = 0.23 M
[Fe(SCN)²⁺] = 0.625 M
Keq = 138 M⁻¹
Let's substitute these values into the equilibrium constant expression:
138 = (0.625) / (0.23)[SCN⁻]
To solve for [SCN⁻], rearrange the equation to isolate [SCN⁻]:
[SCN⁻] = (0.625) / (0.23 * 138)
Now, calculate the value of [SCN⁻]:
[SCN⁻] = 0.025 M
Therefore, the thiocyanate concentration at equilibrium is 0.025 M.