I am having trouble getting the right answer for this question please help.
Calculate Kc for the FeSCN2+ formation equilibrium
[FeSCN2+] = 3.49x10^-5 M
[Fe3+] = 4.39x10^-4 M
[SCN-] = 1.93x10^-4
Kc = [FeSCN2+] / ([Fe3+]-[FeSCN2+]) * ([SCN-] - [FeSCN2+])
I keep getting 546.266 M, but the answer is not right. It should be 412.
I am using the ICE method (initial, Change, Equilibrium).
Amanda
Where did you come up with the Kc expression? It should be
Kc = [FeSCN]^2+/(Fe^3+{)(SCN^-).
Kc = [3.49E-5]/[4.39E-4][1.93E-5]\ 411.9 which rounds to 412. :-)
To calculate Kc using the ICE method, you need to set up an ICE table and then apply the equilibrium expression. Let's go through the steps together to figure out the correct answer:
Step 1: Write the balanced chemical equation for the FeSCN2+ formation equilibrium:
Fe3+ + SCN- ⇌ FeSCN2+
Step 2: Set up an ICE table:
Initial: [Fe3+] = 4.39x10^-4 M
Initial: [SCN-] = 1.93x10^-4 M
Initial: [FeSCN2+] = 3.49x10^-5 M
Change: -x
Change: -x
Change: +x
Equilibrium: [Fe3+] = (4.39x10^-4 - x) M
Equilibrium: [SCN-] = (1.93x10^-4 - x) M
Equilibrium: [FeSCN2+] = (3.49x10^-5 + x) M
Step 3: Substitute the equilibrium concentrations into the equilibrium expression:
Kc = [FeSCN2+] / ([Fe3+]-[FeSCN2+]) * ([SCN-] - [FeSCN2+])
Substitute in the equilibrium concentrations:
Kc = ((3.49x10^-5 + x))/((4.39x10^-4 - x)) * ((1.93x10^-4 - x) - (3.49x10^-5 + x))
Step 4: Simplify the expression:
Multiply the numerators and denominators of the two fractions:
Kc = ((3.49x10^-5 + x)((1.93x10^-4 - x) - (3.49x10^-5 + x))/((4.39x10^-4 - x)((1.93x10^-4 - x) - (3.49x10^-5 + x)))
Expand and simplify the expression further:
Kc = ((3.49x10^-5 + x)(1.93x10^-4 - x - 3.49x10^-5 - x))/((4.39x10^-4 - x)(1.93x10^-4 - x - 3.49x10^-5 - x))
Kc = ((3.49x10^-5 + x)(1.93x10^-4 - 2x - 3.49x10^-5))/((4.39x10^-4 - x)(1.93x10^-4 - 4.49x10^-5 - 2x))
Step 5: Solve for x by assuming x is small compared to the initial concentrations:
Since x is small compared to the initial concentrations, we can approximate (1.93x10^-4 - x - 3.49x10^-5 - x) as (1.93x10^-4 - 3.49x10^-5) and (1.93x10^-4 - 4.49x10^-5 - 2x) as (1.93x10^-4 - 4.49x10^-5).
Substitute these approximations into the expression:
Kc = ((3.49x10^-5 + x)(1.93x10^-4 - 2x - 3.49x10^-5))/((4.39x10^-4 - x)(1.93x10^-4 - 4.49x10^-5 - 2x))
Kc = ((3.49x10^-5 + x)(1.93x10^-4 - 2x - 3.49x10^-5))/((4.39x10^-4 - x)(1.93x10^-4 - 4.49x10^-5))
Step 6: Simplify the expression further:
Expand the numerator and denominator using FOIL method (First, Outer, Inner, Last):
Numerator: (3.49x10^-5)(1.93x10^-4) - (3.49x10^-5)(2x) - (3.49x10^-5)(3.49x10^-5) + (x)(1.93x10^-4) - (x)(2x) - (x)(3.49x10^-5)
Denominator: (4.39x10^-4)(1.93x10^-4) - (4.39x10^-4)(4.49x10^-5) - (4.39x10^-4)(2x)
Simplify further:
Numerator: (6.746x10^-9 - 6.98x10^-5 + 1.8757x10^-9x - 2x^2 - 1.2171x10^-5x)
Denominator: (8.493x10^-8 - 1.973x10^-5 - 8.78x10^-4x)
Step 7: Combine like terms:
Numerator: (6.746x10^-9 - 1.2171x10^-5x + 1.8757x10^-9x - 2x^2 - 6.98x10^-5)
Denominator: (8.493x10^-8 - 8.78x10^-4x - 1.973x10^-5)
Step 8: Set up the equation Kc = 412 and solve for x:
412 = (6.746x10^-9 - 1.2171x10^-5x + 1.8757x10^-9x - 2x^2 - 6.98x10^-5)/(8.493x10^-8 - 8.78x10^-4x - 1.973x10^-5)
Using numerical methods or calculators, you can solve this equation to find the value of x. Once you have x, substitute it back into the equilibrium expressions to find the equilibrium concentrations. Finally, substitute these concentrations into the Kc expression to calculate the value of Kc.
Please note that the value of Kc provided in your question was 412, not the value you obtained (546.266 M). Double-check your calculations as there might have been an error in one of the steps.