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Quantitative Electrolysis

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You might have seen an Olympic athlete bite their gold medal and leave their bite marks imprinted on it. How cool is that gold, a metal, is softer than our teeth? Now if you do that with your gold medal from any local sporting event, unsurprisingly you will see no marks and worst-case scenario you will lose your teeth. What a scam it is just gold-plated! But hey how do you gold plate something anyway?

Well, the answer is through Electrochemistry specifically a process called quantitative electrolysis. Quantitative electrolysis is uniquely capable of utilizing the relationship between current, mass and time, a principle described by Faraday and exploited all over the modern industry. From aluminium production to gold-plated medals and even charging your car's battery all rely on quantitative electrolysis in one form or another.

Care to explore?

• We will see the quantitative electrolysis definition and basics.
• Then, we will explore two Faraday's Laws of Electrolysis.
• Next, the three most important formulae for quantitative electrolysis.
• We will also see the way time and current can be calculated to know the deposition mass during an electrolysis reaction.
• Than, the formulae with examples showcasing how you can use each.
• We will finish by answering the next question: How can you calculate Avogadro's constant through electrolysis experimentally?

Definition of Quantitative Electrolysis

What exactly is quantitative electrolysis? You probably have a grasp of the concept of electrolysis in electrochemistry. If not, you can check out our articles on Electrochemistry and Electrochemical Cells. We delve into the basics and details of electrochemistry and the different types of cells, an electrolytic cell being one of them.

So, what does an electrolytic cell do?

Electrolytic cells can make non-spontaneous reactions occur by supplying energy into the system, in the form of current.

The other type of cell which we encounter in electrochemistry is a galvanic cell, in other words-a non-rechargeable battery. In galvanic cells, spontaneous redox reactions occur producing electrical energy.

To understand the difference between the galvanic and electrolytic cell, let us imagine a situation where a rock falls from the top of the hill. Isn't it spontaneous? You don't need to invest in additional energy. Now imagine the opposite. You want to push the rock from down the hill to the top. You should do the work, because the rock is not going to crawl itself to the top spontaneously. It is a non-spontaneous process where you will need energy to do the work.

The first scenario, the spontaneous process is what happens in a galvanic cell while the second scenario, the non-spontaneous process happens in an electrolytic cell. Supplying voltage to the battery converts it into an electrolytic cell by driving the electron flow in the opposite direction.

Non-spontaneous reaction is a chemical reaction which doesn't happen on its own.

After we got the basics covered regarding electrolytic cells, we can move on to discussing quantitative electrolysis. So, we know that electrolytic cells can make certain reactions proceed which usually don't occur in nature. This is all dependent on the potential applied. With potential difference comes electron flow or less formally current, but you have to wonder; how much current are we putting through the cell exactly and if the amount matters or not? Or how long does it take to put through some specified amount of current? In the following, we are going to look into this in more detail!

Quantitative electrolysis is a process where the amount of charge during the electrolysis process is specifically controlled. This allows control over the amount of a substance undergoing the reaction.

Here we will discuss Faraday's Laws and how they relate to electrochemistry. Faraday's Laws are broken into two laws which govern quantitative electrolysis; hence the discussion will concern the two laws.

The First Law of Electrolysis as proposed by Faraday is the simplest concept you can have regarding electrolysis. It states that the amount of chemical reaction that occurs at the electrodes is proportional to the flow of electrons (electricity passed through the electrolyte).

This means that the flow of electrons in the external circuit determines the reaction that proceeds within the electrolytic cell. This usually concerns the amount of deposited material on the electrode being proportional to the current, as it is most noticeable or easiest to measure in the context of an electrolytic cell. This means that the reaction that proceeds, which often is determined by the chemical deposition of the electrolyte through the discharge of electrons is proportional to the flow of electrons which occurs alongside the reaction.

In other words, the amount of electricity being passed into the system has a directly proportional output-mass of the chemical deposition of the electrolytic reaction, which is quantifiable/measurable.

The Second Law of Electrolysis as proposed by Faraday concerns the chemical nature of the reactants and electrolytes. It states that the same amount of electricity through different electrolytes will produce a different mass of chemical deposition.

What does that exactly mean?

Take, for example, two different solutions which have different metal ions in them. If you apply the same amount of current through both, do you expect the same results? Not really, and that is because the two solutions differ in chemical and physical properties based on the metal ions.

Faraday's Second Law of Electrolysis delves into this phenomenon. It's what Faraday refers to as "Chemical Equivalent" or "Equivalent Weight". Basically, what this phenomenon tells us is that different ions will require a different amount of electricity to be deposited due to the difference in the electrons that need to be discharged. This will be equivalent to the chemical composition of the atom, which often is summarised by the valency.

Here, the mass of chemical deposition that occurs will be different based on the amount of electrons needed to be discharged, even if the amount of electricity passed through the system remains the same for two different electrolytes.

In the next section, you will clearly see how we can quantify this relationship based on the electrons and how we can determine the amount of deposited mass based on these factors.

Quantitative Electrolysis Formulae

In this section, we will take the two Laws of Electrolysis as proposed by Faraday and apply them. We will see how the laws fit neatly into equations which we can use to quantitatively deduce different aspects of electrolysis.

There are three main formulae which you need to know to grasp the concept of quantitative electrolysis. We will go over each one in detail.

The Faraday and how it relates to the Mole

Here is the first formula you need to know:

$F = Le$

Where:

• e = charge on the electron.

This simple formula describes the relationship between the Faraday's constant and Avogadro's constant. We know that Avogadro's constant is 6.02 x 1023 atoms mol-1. By performing calculations, we can deduce that 1 mole of electrons will carry 96320 Coulombs. This is The Faraday (F), often written as 9.65 x 104 C mol-1.(C = Coulombs).

$$Faraday's~ constant(F) = 9.65 \times 10^4~C~mol^{-1}$$

Here we will go over another formula encapsulating how the Faraday relates to electrochemistry. You learned above what the Faraday is,and let us understand its relationship with charge.

Take a look at the equation below:

$n = \frac{Q}{F}$

Where:

• n = number of moles (mol).
• Q = Charge (in Coulombs).
• F = Faraday's Constant = 9.65 X 104 C mol-1 (Coulombs per mol).

This formula states the relationship between the charge and the F .

Since F is a constant, you need to know the current to calculate the number of moles that are liberated during an electrolysis reaction.

Knowing the amount of electrons discharged will give you the information of the mass of the chemical deposited. We know that the number of electrons is related to the mass by the Mole concept. You can use further calculations involving the Avogadro's constant and the electrolyte's physical properties, such as the relative atomic mass, to calculate the mass of a substance deposited during the electrolysis.

Charge, Current, and Time

Here we will go over another equation which explains the relationship between the charge, current and time.

$Q = It$

Where:

• Q = Charge in Coulombs.
• I = Current in amperes or Coulombs/sec.
• t = time in seconds.

Through this formula, you can quantitatively determine the charge running through your electrolytic system.

Why is this important? Calculating charge is very important, as if that is known, we can plug it into the equation above (relating to the number of moles of electrons discharged during the electrolysis reaction) to understand the mass of chemical deposition.

Take a look at the next few sections where we discuss how these formulae can be used in different contexts, and also we will see how we can determine the Avogadro's constant.

Quantitative Electrolysis Diagram

Here you will see a flowchart where you can visualise how different aspects of quantitative electrochemistry can come together. Observe how all the different terms are interchangeable, and if you know one of them, you can find out the rest.

Diagram of Quantitative Electrolysis. Source: Klimczyk, StudySmarter Original

Examples of Quantitative Electrolysis

Here we will examine how quantitative electrolysis can be applied to different chemical contexts. We will go over a few examples for you to understand how to perform calculations using the Laws of Faraday and the formulae of quantitative electrolysis.

Determining Charge

Charge can be calculated from the current and time allowed for the electrolysis reaction to proceed. Take a look at the example below.

Question:

Calculate the charge transferred into the system when a current of 5 A is used for 3 minutes.

Solution:

We know that the formula is $$Q = It$$

Time is needed in seconds, so converting it into seconds from minutes,

$$60s \times 3 = 180s$$

Plugging in the values, we get...

$Q = 5A \times 180s = 900C$

You can use the same formula in reverse to calculate how long electrolysis needs to be run for, or how much current you need for a specific time frame.

Determining Mass Deposited

Here we will go over how you can determine the amount of a substance/mass deposited if the charge is known.

Question:

The following equation represents the electrolysis of bromine, which comes from the electrolysis of molten lead (II) bromine.

$2Br^- \rightarrow Br_2 + 2e^-$

If the charge transferred is 24,120C, what is the mass of bromine produced?

Solution:

We can use the following equation: $$n = \frac{Q}{F}$$

Plugging in the values we get:

$n= \frac{24120 \cancel {C}}{96500 \cancel{C} mol^{-1}} = 0.25 mol$

$n = 0.25 mol$ (of electrons discharged)

Dividing this by 2 will determine the number of moles of bromine produced:

$\frac{0.25 \text{mol of electrons}}{2} = 0.125 \text{mol of bromine produced}$

Further performing stoichiometric calculations, by multiplying the number of moles of bromine produced by the relative atomic mass of bromine will determine the mass of bromine produced:

$0.125 \times 160 = 20g$

Thus, 20 grams of bromine are produced with a charge of 24,120 C (Coulombs).

It is important to note that you can calculate the charge which was transferred if you know the amount of mass gained during the electrolysis reaction. This will come in very handy for the last part of this topic.

So, how can you determine Avogadro's constant with electrolysis? As we know that all of these aspects are interconnected, meaning you can determine the moles and hence Avogadro's constant through calculations through the formulae of quantitative electrolysis.

So, how do we go about calculating Avogadro's constant from electrolysis experimentally? We know that the two aspects are interconnected through the following formula:

$F = Le$

This means that L (which is Avogadro's constant) can be calculated through the following equation:

$L = \frac{F}{e}$

We know that 'e' is the charge of one electron, so we need to calculate the F experimentally. This can be done in many different ways, one of which is to set up any electrolysis experiment and run it for some time. You can then calculate the charge, as well as weight your electrodes to find out how much mass has been deposited.

Once you know the mass and charge for the experiment, you can calculate how much charge is required to deposit 1 mole of the substance. From there, you can divide this by the charge on one electron and determine your Avogadro's number.

Quantitative Electrolysis - Key takeaways

• Quantitative electrolysis deals with calculations regarding the current, time, electrons discharged, and mass deposited during an electrolysis.
• Quantitative electrolysis is a process where the amount of charge during the electrolysis process is specifically controlled. This allows control over the amount of a substance undergoing the reaction.
• Quantitative electrolysis relies on of the two Laws of Electrolysis as proposed by Faraday.
• The three formulae you need to remember are:
• $$F = Le$$
• $$Q = It$$
• $$n = \frac{Q}{F}$$
• F = 9.65 X 104 C mol-1 (Coulombs per mol)
• You can experimentally calculate the Avogadro's number through electrolysis.

An important formula for electrolysis is regarding charge, which is Q = It. Here charge (in C) is calculated by multiplying the current (in A) by the time (in s).

One aim of electrolysis can be to determine Avogadro's constant experimentally.

Electrolysis can be performed on molten salts, or on salts in an aqueous solution.

Quantitative electrolysis is governed by the two Faraday's Laws of Electrolysis.

An electrolysis experiment allows for a non-spontaneous reaction to take place by putting in electrical energy into the system.

Quantitative Electrolysis Quiz - Teste dein Wissen

Question

Is electrolysis performed on spontaneous reactions?

No

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Question

On what type of reactions is electrolysis performed on?

Non-spontaneous reactions

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Question

What is the source of energy in electrolysis?

Flow of electrons (electricity)

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Question

What laws are used for quantitative electrolysis?

The two Faraday's Laws of Electrolysis

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Question

State the formula to calculate charge from current and time

Q = It

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Question

State the formula to calculate charge from number of moles discharged.

Q = eF

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Question

F = Le

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Question

What units is charge calculated in?

Couloms (C)

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Question

What units is current measured in?

Amperes (A) or C/s

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Question

What units is time in to calculate charge?

seconds (s)

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Question

What do you need to measure to determine Avogadro's constant experimentally?

The mass change on the electrodes. Charge is not measured, rather calculated by the time and current.

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Question

What is the value of the Faraday?

96 500 C mol-1

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Question

Can you find out the moles of electrons discharged by the discharged mass?

Yes

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Question

Can charge be calculated by knowing just the amount of time you ran electrolysis for?

No

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Question

Can you determine the time you need to run your electrolysis based on the amount of electroplating you want to do?

Yes

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