In electrochemistry, we are often interested in the number of electrons that have flowed through our cell. This is then related to the mass of the reactants consumed or products formed. However, we generally don't measure charge in the lab. Instead, we measure current.
\[\rm{current = {charge \over time}}\]
Current is the amount of electrical charge that flows during a period of time. Typically we measure this in units of Amperes or Amps. Where 1 Amp (A) = 1 Coulomb (C) per second (s)
\[\rm{Ampere = A = {Coulomb \over second}={C \over s} }\]
We can rearrange this relationship to find the time it takes to get a certain charge with a particular current or the total charge from a current flowing for a given time. Or we could use the charge and time to calculate the current. You should be able to manipulate this in any way given two of the variables to find the third.
In keeping track of how much chemistry is taking place in an electrochemical cell, we have a great advantage since we can direct and measure the exact amount of electric current that flows through the cell (thanks to the wonders of electrical measurement).
So we need a means by which we can convert charge to numbers of electrons.
For this we use Faraday's Constant, \(F\). Faraday's Constant is given the symbol \(F\) and is defined as the charge in coulumbs (C) of 1 mole of electrons. Faraday's constant is approximately 96485 C mol-1. You can calculate \(F\) by multiplying the charge on one electron (1.602 x 10-19) by Avogadro's number (6.022 x 1023).
So imagine we have the following electrochemical cell
Zn | Zn2+ || Ag+ | Ag
How much charge will flow through the cell if 5 g of zinc react? For this we need the balanced electrochemical equation. For the potentials, all we needed was to identify the half-reactions. For stoichiometry we need a balanced equation. For this cell, the balanced equation is
\[\rm{Zn(s) + 2Ag^{+} \rightarrow Zn^{2+} + 2Ag(s)}\]
In addition, we need to realize that the number of electrons that are flowing per zinc is 2 (it is the number of electrons that cancelled out in the overall balanced reaction). We can figure this out using oxidation numbers. Zn is going from 0 to a +2 oxidation state. This is most obvious if you write out the two balanced half-reactions
\[\rm{ox: Zn(s) \rightarrow Zn^{2+} + 2e^-}\]
\[\rm{red: [{Ag^+ + e^- \rightarrow Ag(s)}] \times 2}\]
For this reaction, we would say the number of electrons, \(n\), is two. For every mole of zinc that reacts, it produces two moles of electrons. For every mole of electrons we have \(F\) coulombs of charge.
Faraday's ConstantFor a voltaic cell, the chemistry is spontaneous. Therefore once the cell is connected the chemistry drives electrical current through the external circuit.
The amount of chemistry can be quantified by measuring the current over time. Typically, the current might change over long periods of time, but for short periods, it would likely be constant. Therefore we can relate the current and time to the total charge that has passed between the anode and the cathode. Knowing the charge, we can figure out how many moles of electrons there were. Knowing how many electrons will tell us about how many moles of reactants have been consumed and how many moles of product are formed.
In a typical alkaline battery the half-reactions are
\[\rm{Zn(s) + 2OH^-(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^-}\]
\[\rm{2MnO_2(s) + H_2O(l) + 2e^- \rightarrow Mn_2O_3(s) + 2OH^-(aq)}\]
Note: the batteries are called alkaline because they have a basic pH not because they use alkali metals. Also, the liquid water and hydroxide are not really a "liquid solution" as they are typically in a more solid suspension.
Assuming you had such a battery and used it to power your wireless mouse. This device might draw 1 mA of current (I think personally that is a bit high, but maybe you are really active with your computer mouse). You can run a typical AA battery at this current level for 2000 hours. If you ran your battery at a constant 1 mA for 2000 hours, how many grams of Zn would be consumed?
Well first, we need to convert current to charge. Current is charge per time. So charge is current multiplied by time. 2000 hours = 7.2 × 106 seconds. 1 mA = 10-3 A. So the total charge is (10-3 C s-1)(7.2 × 106 s) = 7200 C.
How many electrons is this? We need to use Faraday's constant.
Moles of electrons = 7200 C / 96,485 C mol-1 = 0.0746 moles of electrons.
Looking at our oxidation half reaction, we see that for every mole of zinc there are two moles of electrons. So the moles of Zn = moles of electrons/ 2 = 0.0746/2 = 0.0373 moles of Zn. The grams of Zn is then just this number of moles times the atomic mass of Zn. Grams of Zn = 0.0373 mol × 65.4 g mol-1 = 2.44 g
There is no difference in working stoichiometry problems for electrolytic cells vs voltaic cells. It is simply a conversion between current, time, and charge and using Faraday's constant to convert between charge and numbers of moles.
Below is a video of a worked example.
Stoichiometry for Electrolytic Cells© 2013 mccord/vandenbout/labrake