# Electrolysis Calculator

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD and Rijk de Wet
Last updated: Apr 06, 2022

Electrochemistry is the perfect fusion of physics and chemistry: it's not an easy topic, but our calculator will do the job, helping you calculate the electrolysis equation. Here you will learn:

• What is electrolysis?
• How to calculate Faraday's law of electrolysis;
• Calculations for the electrolysis of water.

Are you charged up? Let's start!

## What is electrolysis?

Electrolysis is a chemical technique that uses electric currents to allow otherwise non-spontaneous chemical reactions.

🔎 An electrical current is defined by the flow of electrons. An electron $\text{e}^-$ is a fundamental particle with unitary charge, or charge exactly equal to $1.602176634\cdot 10^{-19}\ \text{C}$. Here, $\text{C}$ stands for coulomb, the unit of the electric charge.

To understand electrolysis, we need to introduce its ingredients:

• Two electrodes;
• An electric current flowing between them; and
• An electrolyte surrounding the electrodes.

The electrolyte is an electric conductor (often a solution with free ions) that carry the charge from one electrode to the other. The excess of electrons at one of the electrodes (and the shortage at the other) drive chemical reactions of either oxidation or reduction.

The chemical reactions cause the transformation of one chemical species into another. Let's analyze a standard copper-zinc cell (a battery).

The electrolyte can be a copper salt (not the normal salt) in an aqueous solution, for example $\text{CuSO}_4$ (copper sulphate). The two electrodes are two metal objects of copper and zinc. Without the need to apply an external electric current to the system, a current will flow (of course, only if the two electrodes are connected to complete the circuit). Inside the solution, two reactions happen:

$\small \begin{split} \text{Zn}_{\text{(s)}} &\rightarrow \text{Zn}^{2+}_{\text{(aq)}} + 2\text{e}^-\\ \text{Cu}^{2+}_{\text{(aq)}} + 2\text{e}^- &\rightarrow \text{Cu}_{\text{(s)}} \end{split}$

The subscripts $(\text{aq})$ and $(\text{s})$ tell us the form of the elements on each side of the reaction. $\text{aq}$ stands for aqueous, meaning that the element is in solution (for example the copper after the dissolution of the solfate salt). On the other hand, $\text s$ means solid: in our electrolytic cell, this describes elements on the electrodes.

Look at the first reaction: the solid zinc from the electrode breaks up in a zinc ion positively charged and two electrons. At the same time, the bottom equation describes the creation of solid copper from the ions dissolved in the electrolyte solution. This process needs two electrons (coming from the zinc electrode: remember that they are connected) and creates free negatively charged $\text{SO}_4^{2-}$ ions, which then travel to the zinc electrode, balancing the negative charged that flowed from zinc to copper.

How do you quantify the mass that an electrode gained or lost? Michael Faraday, famous physicist, to the rescue!

Michael Faraday is a well-known name in physics: he was one of the pioneers of electricity. If you want, read more at our Faraday's law calculator. He developed an interest in electrolysis, which led to the two laws of electrolysis bearing his name. We are learning about the first one here!

The first law of electrolysis concerns the accumulation (or removal) of mass on the electrodes. This quantity is directly proportional to the electric current flowing in the electrolyte. Faraday introduced a proportionality constant $Z$ (defined as mass per unit of current) called the electrochemical equivalent, which allows us to write Faraday's electrolysis equation:

$\small m = Z \cdot Q$

Where:

• $m$ is the mass; and
• $Q$ is the charge.

🙋 You can also write the charge $Q$ as the product of the current $I$ and the time $t$: the coulomb SI unit is defined as $\text{C}=\text{A} \cdot \text{s}$.

## How to calculate Faraday's law of electrolysis

Faraday's law of electrolysis calculations are straightforward: the only thing you need to know apart from the charge and the mass is the electro-chemical constant. You can easily find tables of its values online, like .

Let's use the same example as before: an electrolytic cell with copper and zinc electrodes, but this time in the other direction.

We supply the cell a current of $0.1\ \text{A}$ for one minute: what is the mass variation at the electrodes?

First let's check the values of the electro-chemical constant for both copper and zinc. By checking a table we find that:

\small \begin{align*} Z_{\text{Cu}}&=3.295\cdot 10^{-7}\ \text{kg}/\text{C}\\ Z_{\text{Zn}}&=1.58\cdot 10^{-7}\ \text{kg}/\text{C} \end{align*}

Now we have all the elements to calculate $m_{\text{Cu}}$ and $m_{\text{Zn}}$.

\small \begin{align*} m_{\text{Cu}} &= Z_\text{Cu} \cdot Q \\ & = \left( 3.295\cdot 10^{-7}\ \text{kg}/\text{C} \right) \\ &\quad\times \left(0.1\ \text{A} \cdot 60\ \text{s}\right) \\ & = 1.977\cdot 10^{-6}\ \text{kg} \\ & = 1.977\ \text{mg} \end{align*}

Similarly,

\small \begin{align*} m_{\text{Zn}} & = \left(1.58\cdot 10^{-7}\ \text{kg}/\text{C}\right) \\ &\quad\times \left(0.1\ \text{A}\cdot 60\ \text{s}\right)\\ & =0.948\cdot 10^{-6}\ \text{kg} \\ & = 0.948\ \text{mg} \end{align*}

In the equations above, we leveraged the fact that the charge $Q$ has units $\text{A}\cdot\text{s}$ and can be calculated by multiplying the current $0.1\ \text{A}$ with the time $60\ \text{s}$.

Now, remember which direction the reactions are going: the copper ions pass from the solution to the electrodes (thus, we add the mass). In contrast, the zinc ions migrate from the electrode to the solution (and we subtract the mass). It is possible to put this idea in mathematical terms by carefully considering the flow of charge in the system and using the appropriate sign.

## How to use our Faraday's law of electrolysis equation calculator

To use our Faraday's law of electrolysis calculator, simply insert the values you know in the relative fields. Select the element whose $Z$ you're using, or insert a customized one by choosing Custom at the bottom of the list.

⚠️ Be careful and always use the appropriate measurement units!

Let's try to calculate the water electrolysis! First, select the value of the electro-chemical constant for hydrogen $\text{H}_2$, which is one of the components of water, $\text{H}_2\text{O}$. Now let's assume that you connected your phone's battery to it. An average battery contains a charge of $4,\!000\ \text{mAh}$ (milliampere-hour). Insert this value in the Charge field after selecting the correct unit ($\text{mAh}$). How much hydrogen would we produce?

\small \begin{align*} m_{\text{H}_2} & =1.044\cdot 10^{-7} \cdot 4,\!000\ \text{mAh} \\ & \approx 1.5\ \text{g} \end{align*}

To find the value for the oxygen, change the element in the list of constants.

\small \begin{align*} m_{\text{O}_2} & =8.28\cdot 10^{-8} \cdot 4,\!000\ \text{mAh} \\ & \approx 1.2\ \text{g} \end{align*}

And this was only using the battery of a phone. Imagine how much gas you can produce using a Tesla!

🔎 The electrolysis of water is a technology that, in the future, may help develop new clean engines that use hydrogen as fuel.

## FAQ

### What is Faraday's law for electrolysis?

The first Faraday's law for electrolysis is an equation that links the mass of a chemical species added or removed at an electrode and the charge in an electrolytic cell.

The electrolysis equation describes the relation:

m = Z × Q

Where:

• m is the mass in kg (kilogram);
• Q is the charge in C (coulomb); and
• Z is the electrochemical constant of proportionality in kg/C (kilograms per coulomb).

### How do I calculate the mass lost at one electrode?

To calculate the mass lost at one electrode, you must know the value of the electrochemical constant Z and the charge — or electric current — flowing towards/from the electrode. Apply the first Faraday's law of electrolysis to calculate the mass, or go to omnicalculator.com to do it with even fewer troubles!

### What is the electrolysis constant Z?

Z is the electrochemical constant, a quantity defined for every chemical species used as an electrode. Its dimensions are mass over electric charge, with units usually chosen between grams and milligrams and coulomb.

### How do I calculate water electrolysis?

Water electrolysis is a process in which an electric current breaks the water molecule into the gaseous elements hydrogen and oxygen. To calculate the mass of gas produced, you can use Faraday's law of electrolysis, keeping in mind that the electrochemical constant is computed for the diatomic gases H₂ and O₂.

Davide Borchia
Electrochemical constant (Z)
Copper (Cu)
Charge (Q)
C
Current (I)
A
Time (t)
sec
Mass (m)
kg
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