The voltage generated by the zinc concentration cell described by,
Zn(s)|Zn2 (aq, 0.100 M)||Zn2 (aq, ? M)|Zn(s)
is 24.0 mV at 25 °C. Calculate the concentration of the Zn2 (aq) ion at the cathode.
How would I go about this problem? I am extremely confused :/
Thank you so much in advance!!!
See your post below.
To solve this problem, you need to use the Nernst equation, which relates the concentration of species in an electrochemical cell to the cell voltage.
The Nernst equation is given by:
Ecell = E°cell - (0.0592/n) * log(Q)
where:
- Ecell is the cell voltage
- E°cell is the standard cell voltage
- n is the number of electrons involved in the redox reaction
- Q is the reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants (raised to their stoichiometric coefficients) at any point in the reaction.
In this case, since the cell is at 25 °C, the standard cell voltage E°cell can be calculated using the following equation:
E°cell = E°cathode - E°anode
E°cathode and E°anode are the standard reduction potentials of the cathode and anode, respectively.
For the zinc concentration cell, the reactions at the cathode and anode are as follows:
Cathode: Zn2+ (aq, ? M) + 2e- -> Zn (s)
Anode: Zn (s) -> Zn2+ (aq, 0.100 M) + 2e-
By looking up the standard reduction potentials in a table, you can find that E°cathode = 0 and E°anode = -0.762 V.
Now, substitute the given values into the Nernst equation. In this case, the cell voltage Ecell is 24.0 mV (or 0.024 V), and n = 2 because two electrons are involved in the redox reaction.
0.024 = 0 - (0.0592/2) * log(Q)
Solving for Q, you can rearrange the equation and plug in the numbers:
log(Q) = (0 - 0.024) / (0.0592/2)
log(Q) = -0.024 / 0.0296
log(Q) = -0.8108
To find Q, you need to take the antilog of both sides of the equation. However, since the value of Q can be equal to any number between 0 and infinity, the result of the antilog will not give you a single value for the concentration of Zn2+ (aq) at the cathode.
Therefore, the given information is insufficient to calculate the concentration of Zn2+ (aq) at the cathode in this scenario.