I was doing this company exam and I didn't quite get this question about electrochemistry. It says a( student set up the following electrolytic cells. Each electrode is made of graphite. Each battery provides 1 V, and each battery was attached to its respective cell for the same duration. Assume each cell is functioning under standard conditions.) In the solutions for the exam it says: Each battery provides 1 V, therefore under standard conditions no reaction occurs in the case of the Zn(NO3)2 cell as a voltage of at least 1.99 V is required according to the electrochemical series. How do you know that min voltage of at least 1.99 is required from the electrochemical series?
thanks
Just like how you can work out the voltage produced by a spontenous reaction occuring in a galvanic cell, you can work out the voltage needed to force the reaction to occur the opposite way.
using the example of a Zn2+(aq)/Zn(s) half cell and a Cu2+(aq)/Cu(s) half cell:
The relevant electochemical reactions are:
and
The discharging/spontaneous reaction will be
This will occur to produce a positive voltage of 0.34+0.76 =1.1V
Note that the E0 value for the Zn2+/Zn half cell shown above as -0.76 is made positive since the reaction occurs in the opposite direction to what is listed on the electrochemical series.
For this set up, the recharge/nonspontaneous reaction is the reverse of the discharge reaction:
And this will require a voltage to force the reaction to occur. The magnitude of the voltage input can be calculated as equal to the magnitude of the voltage output of the discharge reaction. This would mean that for this recharge reaction, 1.1V is required as an input. You could also think about this interms of calculating the hypothetical voltage produced by this recharging cell using V=-(0.34)+(-0.76)=-1.1V produced (meaning 1.1 V is consumed by the cell)
Applying this to your question, the relevant half cell reactions are:
and
^note that I am assuming the first reaction is relevant since I can't see the set up referred to in the question
The recharge reaction relevant here would thus be:
Just as we did above, we can calculate the neccasary input voltage for this to occur using the relevant E0 values. Thus V=-(1.23)+(-0.76) = -1.99V (indicating that -1.99 volts are produced --> meaning 1.99 volts must be inputted to force the reaction to occur).
Since the battery only supplied 1V, we can then say that no reaction will occur since the voltage input is not sufficient to force the recharge reaction.