Hello guys, can you please answer this question with explanation and formula because I'm absolutely lost :(
What is the Cu2+ concentration at 25°C in the cell Zn(s)½Zn2+(1.0 M)½½Cu2+(aq)½Cu(s)? The cell emf is 1.03 V. The standard cell emf is 1.10 V.
a. 2.4 M
b. 0.004 M
c. 1.0 M
d. 0.07 M
e. 0.1 M
Thanks in advance
To determine the concentration of Cu2+ in the given electrochemical cell, we can use the Nernst equation. The Nernst equation relates the cell potential (Ecell) to the concentrations of reactants and products in the cell.
The Nernst equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell = cell potential (1.03 V in this case)
E°cell = standard cell potential (1.10 V in this case)
R = gas constant (8.314 J/mol*K)
T = temperature (in Kelvin, 25°C = 298 K)
n = number of moles of electrons transferred in the balanced redox equation
F = Faraday's constant (96485 C/mol)
Q = reaction quotient (ratio of product concentrations to reactant concentrations)
In this case, we have a half-cell reaction:
Zn(s) → Zn2+(aq) + 2e-
Cu2+(aq) + 2e- → Cu(s)
The balanced redox equation for the overall cell reaction is obtained by adding the two half-cell reactions together:
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)
In the Nernst equation, Q represents the ratio of product concentrations (Zn2+ and Cu) to reactant concentrations (Zn and Cu2+). Since the concentrations of solid species (Zn and Cu) are always constant and equal to 1, we only need to consider the concentration of Cu2+ in the solution.
Now, let's calculate the value of Q:
Q = [Zn2+] / [Cu2+]
Since the concentration of Zn2+ is given as 1.0 M, we need to determine the concentration of Cu2+ to find Q.
Using the Nernst equation, we can rearrange it to solve for ln(Q):
ln(Q) = (E°cell - Ecell) / (RT/nF)
We know the values of E°cell, Ecell, R, T, and F. Now, substitute these values into the equation and solve for ln(Q):
ln(Q) = (1.10 V - 1.03 V) / ((8.314 J/mol*K) * 298 K / (2 * 96485 C/mol))
Calculating this expression will give us the value of ln(Q), where Q represents the ratio of product concentrations (Zn2+ and Cu) to reactant concentrations (Zn and Cu2+).
After calculating ln(Q), we can then calculate the value of Q by taking the exponent of ln(Q):
Q = e^(ln(Q))
Finally, we can calculate the concentration of Cu2+ using the calculated value of Q and the known concentration of Zn2+:
Q = [Zn2+] / [Cu2+]
[Cu2+] = [Zn2+] / Q
Substitute the value of [Zn2+] (1.0 M) and Q into the equation to calculate [Cu2+].
Based on the provided answer choices, determine which option matches the calculated concentration of Cu2+.
I hope this explanation clarifies the process of determining the Cu2+ concentration in the given electrochemical cell.
To find the concentration of Cu2+ at 25°C in the given cell, we can use the Nernst equation:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
Ecell = Cell emf
E°cell = Standard cell emf
n = Number of moles of electrons transferred in the balanced equation
Q = Reaction quotient
Let's break down the given cell reaction:
Zn(s) + ½Zn2+(1.0 M) ⇌ ½Cu2+(aq) + Cu(s)
The cell reaction involves the transfer of two electrons:
Zn(s) ⇌ Zn2+(aq) + 2e-
Cu2+(aq) + 2e- ⇌ Cu(s)
Since two electrons are transferred, n = 2.
Now let's substitute the given values into the Nernst equation:
1.03 V = 1.10 V - (0.0592/2) * log(Q)
Simplifying:
0.07 V = (0.0296) * log(Q)
Dividing both sides by 0.0296:
log(Q) = 0.07 V / 0.0296
log(Q) = 2.364
To find Q, we need to take the antilog of both sides:
Q = 10^2.364
Q ≈ 233.57
Now that we have the value of Q, we can find the concentration of Cu2+ using the reaction quotient Q:
Q = [Cu2+][H2]/[Zn2+]
Since the concentration of Zn2+ is given as 1.0 M, we can rearrange the equation:
[Cu2+] = Q * [Zn2+]/[H2]
Substituting the values:
[Cu2+] = 233.57 * 1.0 M / 1.0 M
[Cu2+] ≈ 233.57 M
Therefore, the concentration of Cu2+ in the cell at 25°C is approximately 233.57 M.
None of the given answer choices matches this value, so it seems there might be an error in the question or the provided answer choices. It is recommended to double-check the values and select the nearest answer choice if applicable.