This page deals with simple calculations from equations involving electrolysis. You will need to be familiar with the routine calculations from equations covered previously in this section.
The Faraday constant is the single most important bit of information in electrolysis calculations. Make sure you really understand the next bit.
The That means that you can work out how much electricity has passed in a given time by multiplying the current in amps by the time in seconds.
If you are given a time in minutes or hours or days, then you For example, if a current of 2 amps flows for an hour, then: Number of coulombs = 2 x 60 x 60 = 7200 (60 minutes in each hour; 60 seconds in each minute.) That's easy!
Electricity is a flow of electrons. For calculation purposes, we need to know how to relate the number of moles of electrons which flow to the measured quantity of electricity. Suppose you have a simple electrode equation for the formation of copper on the cathode during the electrolysis of copper((I) sulfate solution.
You can read that as
It turns out that 1 mole of electrons flowing around a circuit is equivalent to 96500 coulombs. This is known as the Faraday constant, F.
So 96500 coulombs is called Whenever you have an equation in which you have 1 mole of electrons, that is represented in an electrical circuit by 1 faraday of electricity - in other words, by 96500 coulombs.
Calculate the mass of silver deposited at the cathode during the electrolysis of silver nitrate solution if you use a current of 0.10 amps for 10 minutes. (F = 96500 C mol The first thing to do is to work out how many coulombs of electricity flowed during the electrolysis.
Now look at the equation for the reaction at the cathode:
Just as with any other calculation from an equation, write down the essential bits in words:
Now put the numbers in. 1 mol of electrons is 1 faraday.
So, if 96500 coulombs give 108 g of silver, all you have to do is to work out what mass of silver would be produced by 60 coulombs.
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Note: If you aren't happy about the last step go via 1 coulomb: If 96500 coulombs give 108 g, then 1 coulomb would give 108 divided by 96500 g. 60 coulombs would produce 60 times this amount. | |

This example shows you how to do the calculation if the product you are interested in is a gas. Calculate the volume of hydrogen produced (measured at room temperature and pressure - rtp) during the electrolysis of dilute sulfuric acid if you use a current of 1.0 amp for 15 minutes. F = 96500 C mol Start by working out how many coulombs of electricity flowed during the electrolysis.
Now look at the equation for the reaction at the cathode:
Write down the essential bits in words:
Now put the numbers in. Two moles of electrons is 2 faradays.
So, if 2 x 96500 coulombs give 24 dm
Don't quote your answer beyond 2 decimal places. The current and the molar volume are only quoted to that degree of accuracy. | |

Note: If you can't follow the last bit of the calculation:
If 2 x 96500 coulombs give 24 dm In other words, you are working out 24/(2 x 96500) and then multiplying by 900. It is a different order from the way it is shown in the simple proportion sum shown above, but the answer is still exactly the same. In addition, if you feel happier working out the value of 2 x 96500 before you do anything else, that's what you should do. As long as you get the answer right, nobody is interested in the exact way you handle the sums. | |

This example shows you what to do if the question is reversed. How long would it take to deposit 0.635 g of copper at the cathode during the electrolysis of copper(II) sulfate solution if you use a current of 0.200 amp. F = 96500 C mol This time you can't start by working out the number of coulombs, because you don't know the time. As with any other calculation, just start from what you know most about. In this case, that's the copper, so start with the electrode equation.
You need to work out how many coulombs give 0.635 g of copper.
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Note: And again, if you still don't like simple proportion sums:
If 2 x 96500 coulombs give 63.5g of copper, then you would get 1g of copper if you divided the 2 x 96500 coulombs by 63.5. 0.635 g would be produced by multiplying this by 0.635. | |

Now what? You know how many coulombs you need, and you know what the current was in amps. You have got all the information you need to work out the time.
Don't waste time trying to convert that into minutes or hours (unless the exam question specifically asks you to).
Another gas example: Calculate the volume of oxygen produced (measured at room temperature and pressure - rtp) during the electrolysis of sodium sulfate solution if you use a current of 0.50 amp for 30 minutes. F = 96500 C mol Start by working out how many coulombs of electricity flowed during the electrolysis.
Now we need to look at the equation for the reaction at the anode. Unfortunately, there are two ways of looking at this, and you may come across either of them. The first one releases oxygen from water molecules:
The alternative way releases oxygen from hydroxide ions from the ionisation of the water:
Write down the essential bits in words. Both ways of looking at it say the same thing:
Now put the numbers in. Four moles of electrons is 4 faradays.
So, if 4 x 96500 coulombs give 24 dm
Or work out what volume you would get from 1 coulomb and then multiple by 900. Don't quote your answer beyond 2 decimal places. The current and the molar volume are only quoted to that degree of accuracy. **Where would you like to go now?**-
**To the calculations menu . . .**
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