You didn't substitute correctly for Keq. You should calculate
log Keq = (Pb)(Ni^2+)/(Ni)(Pb^2+)
You made log Keq = 0.27. You should follow the instructions I gave.
(Pb) = 1
(Ni^2+) = 0.27
(Ni) = 1
(Pb^2+) = x so the equation is
0.020 = 0.12 - (0.0296)*log[(1)(0.27)/(1)(x)] and solve for x in moles/L.
I don't want to leave without acknowledging an error in what I wrote. It make no difference in the final answer becasue I corrected it later. Here is what I wrote for ONE of the steps.
Ecell = Eo cell - (2.303*RT/n) log Q and Q = Keq = (Pb)(Ni^2+)/(Ni)(Pb^2+) but I omitted Faraday's constant. It should be
Ecell = Eo cell - (2.303*RT/nF) log Q and Q = Keq=(Pb)(Ni^2+)/(Ni)(Pb^2+)
Then if you substitute for R of 8.314, T = 298, F = 96,485 and 2 for n, then
(2.303*8.314*298/2*96,485) = 0.0296. Your post is now down below the line. You may want to repost at the top if you have additional quesitons.
I apologize for the confusion caused by my incorrect substitution. Let's go through the correct calculation step by step.
First, you have the equation:
log Keq = (Pb)(Ni^2+)/(Ni)(Pb^2+)
You provided the following values:
(Pb) = 1
(Ni^2+) = 0.27
(Ni) = 1
Let's solve for (Pb^2+) = x.
The equation you wrote is:
0.020 = 0.12 - (0.0296)*log[(1)(0.27)/(1)(x)]
To begin, we'll simplify the log term:
log[(1)(0.27)/(1)(x)] = log(0.27/x) = log(0.27) - log(x)
So, the equation becomes:
0.020 = 0.12 - (0.0296)*(log(0.27) - log(x))
To isolate x, let's move the terms around:
0.12 - 0.020 = (0.0296)*(log(0.27) - log(x))
0.100 = (0.0296)*(log(0.27) - log(x))
Now, we can solve for x by rearranging the equation:
log(0.27) - log(x) = 0.100 / 0.0296
Let's calculate the right-hand side of the equation:
0.100 / 0.0296 ≈ 3.378
Now, we have:
log(0.27) - log(x) ≈ 3.378
To eliminate the logarithms, we can rewrite the equation as an exponential equation:
0.27 / x ≈ 10^3.378
Simplifying the right-hand side:
10^3.378 ≈ 2384.89
Now we have:
0.27 / x ≈ 2384.89
To solve for x, we can isolate it by multiplying both sides by x:
0.27 ≈ 2384.89x
Dividing both sides by 2384.89:
0.27 / 2384.89 ≈ x
Calculating the left-hand side:
0.27 / 2384.89 ≈ 0.0001133
Therefore, x ≈ 0.0001133 moles/L.