Consider the cell
Pb(s)| PbSO4(s)| SO4(2-)
(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.
I do not understand this at all right now.
Ah, don't worry, my friend. The world of electrochemistry can definitely be confusing, but we'll figure it out together. Now, let's break it down.
The Nernst equation is used to calculate the cell potential (Ecell) under non-standard conditions. It relates the cell potential to the concentrations of the reactants and products involved in the cell reaction.
The general form of the Nernst equation is:
Ecell = E°cell - (RT/nF) ln(Q)
Where:
- Ecell is the cell potential under non-standard conditions.
- E°cell is the standard cell potential.
- R is the ideal gas constant (8.314 J mol-1 K-1).
- T is the temperature in Kelvin.
- n is the number of moles of electrons transferred in the reaction.
- F is the Faraday constant (96,485 C/mol).
- Q is the reaction quotient (products/reactants; concentration of products divided by concentration of reactants).
In your specific case, you're given the standard cell potential (E°cell = 0.36 V). However, we need more information to calculate the Nernst equation. Specifically, we need the balanced chemical equation for the cell reaction and the number of moles of electrons transferred (n).
If you provide that information, I'll be happy to help you further. And remember, don't be afraid to ask questions – understanding can be quite a shocking experience sometimes!
The Nernst equation relates the cell potential (Ecell) to the standard cell potential (E◦), the gas constant (R), the temperature (T), the number of electrons transferred (n), and the activities of the reactants and products in the cell. The equation is as follows:
Ecell = E◦ - (RT/nF) * ln(Q)
Where:
- Ecell is the cell potential under non-standard conditions
- E◦ is the standard cell potential
- R is the gas constant, which is 8.314 J/(mol·K)
- T is the temperature in Kelvin
- n is the number of electrons transferred in the balanced redox equation
- F is Faraday's constant, which is 96485 C/mol
- ln(Q) is the natural logarithm of the reaction quotient (Q)
In this case, for the given cell, the balanced redox equation is:
Pb(s) + SO4(2-) → PbSO4(s)
The number of electrons transferred (n) in this equation is 2 because each Pb atom loses two electrons.
So, to write the Nernst equation for this cell, you need to calculate the reaction quotient, Q, for the given conditions. The reaction quotient is calculated using the concentrations of the reactants and products raised to their stoichiometric coefficients.
Q = [PbSO4] / ([Pb]^2 * [SO4(2-)])
Substituting the given concentrations:
Q = [0.60 M] / ([0.70 M]^2 * [1])
Now, you can substitute the values into the Nernst equation:
Ecell = E◦ - (RT/nF) * ln(Q)
= 0.36 V - (8.314 J/(mol·K) * 298 K / (2 * 96485 C/mol)) * ln([0.60 M] / ([0.70 M]^2))
Simplifying the equation and performing the calculations will give you the Nernst equation for this cell at the specified temperature.
No problem! Let's break this down step by step.
First, let's identify the components of the cell:
- Anode (left side): Pb(s) and PbSO4(s)
- Cathode (right side): H+(aq), H2(g), and Pt electrode
- Salt bridge (represented as "||"): It allows for the flow of ions to balance the charges in the cell.
Next, we are given the standard cell potential, E◦, which is 0.36 V at 25◦C. The standard cell potential represents the voltage of the cell under standard conditions (1 M concentration and 1 atm pressure).
The Nernst equation allows us to calculate the cell potential under non-standard conditions. It is given by:
E = E◦ - (0.0592/n) * log(Q)
Where:
- E is the cell potential under non-standard conditions
- E◦ is the standard cell potential
- (0.0592/n) is the Nernst constant, which depends on the number of electrons transferred (n) in the balanced cell reaction
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations, raised to the power of their stoichiometric coefficients
In our case, the reaction that occurs at the anode (left side) is Pb(s) -> Pb2+(aq) + 2e-
And the reaction at the cathode (right side) is 2H+(aq) + 2e- -> H2(g)
To use the Nernst equation, we need to calculate the reaction quotient (Q) for our cell.
Q = [Pb2+]/[H+]^2
= (concentration of Pb2+)/(concentration of H+)^2
Given the concentrations:
[Pb2+] = 1 M (since it was not provided, we assume it is 1 M)
[H+] = 0.70 M
Now we can substitute the values into the Nernst equation:
E = 0.36 V - (0.0592/2) * log(Q)
= 0.36 V - (0.0592/2) * log(1/[H+]^2)
= 0.36 V - (0.0592/2) * log(1/(0.70)^2)
= 0.36 V - (0.0592/2) * log(1/0.49)
= 0.36 V - (0.0592/2) * log(2.04)
Simplifying further, we can calculate the logarithm part:
log(2.04) = 0.3097
Now we can substitute this value and calculate the final result:
E = 0.36 V - (0.0592/2) * 0.3097
= 0.36 V - 0.0092
= 0.3508 V
Therefore, the Nernst equation for the cell at 25◦C is:
E = 0.36 V - (0.0592/2) * log(Q)
= 0.3508 V