Pb(s)|PbSO4(s)|SO2−4(aq,0.60 M)||H+(aq,0.70 M)|H2(g,192.5 kPa)|Pt. If E◦for the cell is 0.36 V at 25◦C, write
the Nernst equation for the cell at this temperature.
out of the five following choices, which one is correct
1.E= 0.36 + 0.01285 ln 192.5(0.70)2(0.60)
2.E= 0.36−0.02569 ln 192.5(0.70)2(0.60)
3.E= 0.36−0.01285 ln1.90(0.70)2(0.60)
4.E= 0.36 + 0.01285 ln 1.9(0.70)2(0.60)
5.E= 0.36−0.01285 ln 1.90(0.70)(0.60)
I don't agree with any of the answers. Look closely at the answers page from which you typed these. At least one answer should have a /0.60 in it. The 1.90 comes from 192.4/101.325 = 1.90
atm. Therefore, 3,4,or 5 should have the 0.60 in the denominator.
To write the Nernst equation for the cell at a given temperature, we need to use the formula:
E = Eo - (0.0592/n) * log(Q)
Where:
- E is the cell potential at the given temperature.
- Eo is the standard cell potential at 25°C.
- n is the number of moles of electrons transferred in the balanced equation.
- Q is the reaction quotient, which can be determined using the concentrations of the species involved in the cell reaction.
In the given cell, the balanced equation is:
Pb(s) + SO4^2-(aq) -> PbSO4(s) + 2e-
2H+(aq) + 2e- -> H2(g)
Comparing the two half-reactions, we can see that n = 2 since 2 moles of electrons are transferred in each half-reaction.
Now let's calculate the reaction quotient, Q. The reaction quotient is determined by the concentrations of the species involved in the cell reaction:
Q = [H+]^2 / [PbSO4][SO4^2-]
From the given concentrations:
[H+] = 0.70 M
[PbSO4] = 1 M (since it is a solid, its concentration is assumed to be 1)
[SO4^2-] = 0.60 M
Now, substitute the values into the Nernst equation:
E = 0.36 V - (0.0592/2) * log(0.70^2 / (1 * 0.60))
Simplifying the calculation:
E = 0.36 V - 0.0296 * log(0.49 / 0.60)
E = 0.36 V - 0.0296 * log(0.8167)
Using a calculator, calculate the log value:
log(0.8167) ≈ -0.0903
Now substitute the value:
E ≈ 0.36 V - 0.0296 * (-0.0903)
E ≈ 0.36 V + 0.00267168
E ≈ 0.36267168 V
Therefore, the correct Nernst equation for the given cell at this temperature is:
E = 0.36 V + 0.00267168
Option 1, E = 0.36 + 0.01285 ln 192.5(0.70)2(0.60), is the correct choice.