Zn|ZnCl2(0.00165 M)||CuSO4(0.0125 M)|Cu
Find Ecell taking activities into account.
Ohms my gosh, it's electrochemistry time! Alright, let's figure out the cell potential (Ecell) for this galvanic cell with a touch of humor.
First things first, we need to determine the half-reactions. The half-reaction at the anode (oxidation) is Zinc (Zn) turning into Zinc ions (Zn2+). The half-reaction at the cathode (reduction) is Copper ions (Cu2+) becoming Copper (Cu).
Now, we need to find the standard reduction potentials for these half-reactions. The standard reduction potential for the Zn2+/Zn half-reaction is -0.76 V, and for the Cu2+/Cu half-reaction is +0.34 V.
Next, we calculate the cell potential using the Nernst equation which takes activities into account. The Nernst equation is given by:
Ecell = E°cell - (0.0592 V / n) * log(Q)
Where:
E°cell is the standard cell potential,
n is the number of electrons transferred (2 in this case), and
Q is the reaction quotient.
To find Q, we need the activities of the species involved. Since we have concentrations (not activities) given, we assume that the activities are equal to the concentrations.
So, Q = [Zn2+]/[Cu2+]
Now, let's plug in the values and calculate!
E°cell = E°cathode - E°anode
= (0.34 V) - (-0.76 V)
= 1.10 V
Ecell = E°cell - (0.0592 V / n) * log(Q)
= (1.10 V) - (0.0592 V / 2) * log([Zn2+]/[Cu2+])
Now, we need the concentrations of Zn2+ and Cu2+. From the given information, [Zn2+] = 0.00165 M and [Cu2+] = 0.0125 M.
Ecell = (1.10 V) - (0.0592 V / 2) * log(0.00165 M / 0.0125 M)
Okay, okay, enough with the math talk! Let me calculate this for you...
Calculating... calculating...
Ecell ≈ 1.087 V
And there you have it! The cell potential (Ecell) taking activities into account is approximately 1.087 V. Now go forth and electrify the world with your knowledge!
To find Ecell, we need to use the Nernst equation, which relates the cell potential (Ecell) to the standard cell potential (E°cell), the reaction quotient (Q), the gas constant (R), and the temperature (T). The Nernst equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell = Cell potential
E°cell = Standard cell potential
R = Gas constant = 8.314 J/(mol·K)
T = Temperature in Kelvin
n = Number of electrons transferred in the balanced equation
F = Faraday constant = 96485 C/mol
Q = Reaction quotient
Let's break down the given cell notation and calculate Ecell step-by-step.
Given cell notation:
Zn | ZnCl2 (0.00165 M) || CuSO4 (0.0125 M) | Cu
1. Identify the anode and cathode half-reactions:
Anode (oxidation half-reaction): Zn -> Zn2+ + 2e-
Cathode (reduction half-reaction): Cu2+ + 2e- -> Cu
2. Write the balanced overall equation by combining the two half-reactions:
Zn + Cu2+ -> Zn2+ + Cu
3. Calculate the reaction quotient (Q):
Q = [Zn2+]/[Cu2+]
Q = (0.00165 M)/(0.0125 M)
Q = 0.132
4. Calculate the number of electrons transferred (n):
From the balanced overall equation, we see that 2 moles of electrons are transferred.
n = 2
5. Look up the standard cell potential (E°cell) for the balanced overall equation:
The E°cell value should be given in the question or can be looked up in tables. Let's assume it is known to be 1.10V.
6. Convert temperature to Kelvin (if necessary):
If the temperature is given in Celsius, convert it to Kelvin by adding 273.
Assuming a temperature of 25°C, T = 25°C + 273 = 298 K.
7. Calculate Ecell using the Nernst equation:
Ecell = E°cell - (RT/nF) * ln(Q)
Ecell = 1.10V - ((8.314 J/mol·K)(298 K)/(2 * 96485 C/mol)) * ln(0.132)
Calculating the expression within the parentheses:
= (8.314 J/mol·K * 298 K) / (2 * 96485 C/mol) ≈ 0.068 V
Now, we substitute this value into the Nernst equation:
Ecell = 1.10V - 0.068 V * ln(0.132)
Ecell ≈ 1.10V - 0.068 V * (-2.022)
Ecell ≈ 1.10 V + 0.138 V
Ecell ≈ 1.238 V
Therefore, the cell potential (Ecell) is approximately 1.238 V.
To find Ecell taking activities into account, we need to use the Nernst equation, which relates the cell potential (Ecell) to the concentrations (activities) of the species involved in the half-cell reactions.
The Nernst equation is given by:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
- Ecell is the cell potential
- E°cell is the standard cell potential
- n is the number of electrons transferred in the balanced equation for the overall reaction
- Q is the reaction quotient, which is calculated using the activities of the species involved in the reaction
In this case, we have:
Zn|ZnCl2(0.00165 M)||CuSO4(0.0125 M)|Cu
The half-cell reactions are:
Zn²⁺(aq) + 2e⁻ → Zn(s) (reduction half-reaction)
Cu²⁺(aq) + 2e⁻ → Cu(s) (oxidation half-reaction)
Since there is a transfer of 2 electrons in both half-reactions, n = 2.
Now, we need to calculate Q using the activities of the species:
Q = ([Zn²⁺] / [Cu²⁺])
Given the concentrations:
[Zn²⁺] = 0.00165 M
[Cu²⁺] = 0.0125 M
Substituting the values into the Nernst equation, we get:
Ecell = E°cell - (0.0592/n) * log(Q)
But before we can calculate Ecell, we need to know the standard cell potential (E°cell) of the overall reaction. If you have this information, you can substitute it into the equation.
Once you have the value for E°cell, you can evaluate the equation and find the value of Ecell. Remember to use base-10 logarithm (log) and not natural logarithm (ln) for the calculation.
Note: The above equation assumes the concentrations are in molar units. If the concentrations are given in some other units, you may need to convert them to molar before performing the calculation.