Solution:
[I⁻] = 0.0352M
Explanation:
Referring to the equilibrium:
I₃⁻(aq) ⇄ I₂(aq) + I⁻(aq)
Kc is defined by the equation:
Kc = 0.25 = [I₂] [I⁻] / [I₃⁻]
Equilibrium is established when the proportion [I₂] [I⁻] / [I₃⁻] matches 0.25
Initially, we have 0.0401M for both [I₂] and [I⁻]. When the reaction stabilizes, xM of both [I₂] and [I⁻] gets consumed, leading to xM of [I₃⁻]. We represent this as:
[I₃⁻] = X
[I₂] = 0.0401M - X
[I⁻] = 0.0401M - X
X is referred to as the reaction coordinate.
Substituting into Kc gives:
0.25 = [I₂] [I⁻] / [I₃⁻]
0.25 = [0.0401M - X] [0.0401M - X] / [X]
0.25X = 0.00160801 - 0.0802X + X²
Thus, we have 0 = 0.00160801 - 0.3302X + X².
Solving for X yields:
X = 0.0049M → Valid solution
X = 0.3252M → Invalid solution due to negative concentrations.
The equilibrium concentrations calculate to:
[I₃⁻] = X
[I₂] = 0.0401M - X
[I⁻] = 0.0401M - X
[I₃⁻] = 0.0049M
[I₂] = 0.0352M
[I⁻] = 0.0352M
