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.
Well, let's try to break it down in a fun and simple way, shall we?
Imagine you have a fancy cell, like a VIP room for electrons to party in. In this VIP cell, you have some ingredients, or in other words, chemicals, that are looking to have a good time and react with each other.
On one side of the cell, you have some lead (Pb) that wants to dance with some sulfur and oxygen (PbSO4). They are all hanging out in a solution, so let's say it's like a wild pool party.
On the other side of the cell, you have some hydrogen ions (H+). These hydrogen ions bring the party vibes, and they want to react with some other hydrogen molecules (H2) to make water (H2O). So basically, it's like a hot tub party over there.
Now, these two sides of the cell are connected by a magical barrier called the platinum (Pt) electrode. This platinum electrode is like the bouncer of the cell, controlling the flow of electrons to make sure the party doesn't get out of hand.
But here's where things get interesting. The partygoers on each side of the cell have different energy levels, and they want to balance things out. So, they start a negotiation.
The Nernst equation is like the magic equation that helps you calculate the energy exchange at this party. It takes into account the concentrations of the chemicals and the temperature, to give you the voltage of the cell.
So, if you want the Nernst equation for this cell at 25◦C, it would look something like this:
Ecell = E°cell - (0.0592/n) * log(Q)
Here, Ecell is the voltage of the cell, E°cell is the standard voltage at 25◦C (which is 0.36 V in this case), n is the number of electrons involved in the reaction, and Q is the reaction quotient (which involves the concentrations of the chemicals in the cell).
Now, this equation might seem a bit complex, but fear not! With a little practice and some mathematical pizzazz, you'll be able to calculate the voltage of the cell and rock this electrochemistry party!
Remember, always keep the humor flowing while learning about science. It makes things much more enjoyable!
The Nernst equation is used to calculate the cell potential (Ecell) at non-standard conditions. It is given by:
Ecell = E°cell - (RT/nF)ln(Q)
Where:
- Ecell is the cell potential at non-standard conditions
- E°cell is the standard cell potential
- R is the gas constant (8.314 J/(mol⋅K))
- T is the temperature in Kelvin (25◦C = 298 K)
- n is the number of moles of electrons transferred in the balanced equation for the cell reaction
- F is the Faraday constant (96,485 C/mol)
- ln(Q) is the natural logarithm of the reaction quotient (Q)
In this case, the cell reaction is:
Pb(s) + PbSO4(s) + 2H+(aq) -> 2PbSO4(s) + H2(g)
The number of moles of electrons transferred is 2, as shown in the balanced equation.
The reaction quotient (Q) is determined from the concentrations of the species involved in the cell reaction. Since the concentrations are given, Q can be calculated as follows:
Q = [SO4(2-)] / [H+]^2
Substituting the given concentrations, Q = (0.60 M) / (0.70 M)^2
Finally, substituting all the values into the Nernst equation will yield the cell potential at this temperature.
To understand and write the Nernst equation for the given cell at 25°C, we need to know the overall cell reaction and the expression for the Nernst equation. Let's break it down step by step:
1. Overall Cell Reaction:
The given cell notation indicates two half-cell reactions separated by double vertical lines. The anode half-cell (oxidation) is represented on the left, and the cathode half-cell (reduction) is represented on the right.
The half-cell reactions can be determined as follows:
At the anode (left half-cell): Pb(s) → PbSO4(s) + 2e^-
At the cathode (right half-cell): 2H+(aq) + 2e^- → H2(g)
The overall cell reaction will be the sum of these two half-cell reactions:
Pb(s) + 2H+(aq) → PbSO4(s) + H2(g)
2. Nernst Equation:
The Nernst equation relates the cell potential (E_cell) to the standard cell potential (E°), the gas constant (R), the temperature (T), the number of electrons transferred (n), and the concentrations of the ion species involved in the half-cell reactions.
The Nernst equation is given as follows:
E_cell = E° - (RT / nF) * ln(Q)
Where:
E_cell = Cell potential
E° = Standard cell potential
R = Gas constant (8.314 J/K*mol)
T = Temperature in Kelvin
n = Number of electrons transferred in the cell reaction
F = Faraday's constant (96485 C/mol)
Q = Reaction quotient (concentration of products divided by the concentration of reactants, each raised to the power of their respective stoichiometric coefficient)
For our given cell notation, the number of electrons transferred (n) in the overall cell reaction is 2.
3. Plug in the Values:
Now, we can plug in the values into the Nernst equation based on the given information:
E_cell = 0.36 V (given)
E° = 0.36 V (given, since it is the standard cell potential)
R = 8.314 J/K*mol
T = 25°C + 273.15 = 298.15 K (convert to Kelvin)
n = 2 (since 2 electrons are transferred)
F = 96485 C/mol
The only missing information is the reaction quotient (Q) for the overall cell reaction.
4. Finding the Reaction Quotient (Q):
To find Q, we need to express it in terms of the concentrations of reactants and products involved in the overall cell reaction.
For the given cell notation, the concentrations are as follows:
[H+] = 0.70 M (given)
[SO4(2-)] = 0.60 M (given)
[PbSO4(s)] = 1 (solid does not affect concentration)
Based on the stoichiometry of the overall cell reaction, we can write the expression for Q as follows:
Q = ([PbSO4(s)] * [H2(g)]) / ([Pb(s)] * [H+]^2)
Since [PbSO4(s)] = 1 (solid doesn't affect concentration):
Q = [H2(g)] / ([Pb(s)] * [H+]^2)
5. Final Step - Nernst Equation:
Now, we have all the required values to calculate the Nernst equation:
E_cell = E° - (RT / nF) * ln(Q)
E_cell = 0.36 V - (8.314 J/K*mol * 298.15 K / (2 * 96485 C/mol)) * ln([H2(g)] / ([Pb(s)] * [H+]^2))
Therefore, the Nernst equation for the given cell at 25°C is:
E_cell = 0.36 V - (0.02493 V) * ln([H2(g)] / ([Pb(s)] * [H+]^2))
Note: Ensure that the units for all the values are consistent (J, V, K, C, M).