# Coulomb Force

Do you know what happens when you rub a balloon against your clothes and then hold it up against a wall? It sticks to the wall! Perhaps as a kid (or maybe even now), you did it as a party trick and amazed everyone with this "magic trick"! Sorry to burst your balloon, but these fun tricks are possible because of the electrostatic attraction between charged particles. When you rub a balloon on your clothes, it gets negatively charged, so when held near a positively charged wall, it's attracted to it! Coulomb's law best describes this relationship between attractive and repulsive forces of charged particles

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Coulomb's law explains the interactions between negatively and positively charged particles such that similar charges repel and opposite charges attract. In chemistry, it commonly applies to the electrostatic charge in ionic bonds.

This overview will explore Coulomb's Law and its applications for ionic bonds!

• We will look more specifically at the definition of Coulomb force and examples.
• Then, we will investigate the different variables in the Coulomb force equation.
• After, we will examine the magnitude of Coulomb force in the context of ionic bond interaction strength.
• We will look at the applications of coulomb force for ionic bonds.
• Finally, we will briefly address the Coulomb force of repulsion.

## Coulomb Force Definition and Examples

Thinking back to our balloon example, what caused the balloon to stick to the wall? It was an electrostatic force, also known as Coulomb Force.

Coulomb Forces are the attractive or repulsive forces between ions due to their charge.

Fig. 1: Ions attracting and repulsing according to Coulomb's law.

Remember, the attraction between negatively charged particles on the balloon and the positively charged wall caused it to "stick"! But repulsive forces were actually at play here too! The wall was initially neutral, but when the negatively charged balloon is brought near, it repels the negatively charged electrons from the area. This leaves the wall more positively charged than the balloon; thus, it sticks! From this one example, we can see the fundamental principles of Coulomb's force: Opposites attract and like repels!

It mimics the age-old love myth that opposites attract, and it turns out this concept is true in relationships when applied to the relationship between charged particles! Hopefully, this will be easy to remember!

Coulomb's Law was actually published by a physicist and is widely recognized as a crucial development for studying electromagnetism and electrical fields. However, as we will soon see, the concepts of Coulomb's Law easily apply to our understanding of ionic bonds!

Now, let's think for a second about how and why this physics concept matters to us chemists. What keeps the subatomic particles of an atom together? How are ionic chemical bonds formed? These are different questions with the same answer: the electrostatic attraction between oppositely charged particles!

• Atoms are made up of positively charged protons that are orbited by negatively charged electrons.
• Ionic bonds are made up of positively charged cations and negatively charged ions. These opposite charges are attracted to one another!

We will spend most of our time exploring what the Coulomb Law tells us about the energy involved in ionic bonds. To do that, we first must know Coulomb's Law mathematically and what it means!

## Coulomb Force Equation

The equation commonly associated with Coulomb Force is $F={k}\frac{q_1 q_2}{r^{2}}$ but since we are interested in the energy associated with ionic bonds we can use the following equation

$E={k}\frac{q_1 q_2}{r}$

We get from the initial equation of force to energy by taking the integral. You don't necessarily have to know how to apply this equation mathematically. You need to be able to conceptually use it to make comparisons and defend answers about ionic bonds and solids!

Let's break apart these different variables.

E = energy required to break apart ions (force of attractive and repulsive forces)

Q1 and Q2 = the charge of the cation and anion

r = refers to the distance between the nuclei of the two ions (bond length)

k = Coulomb's constant and not relevant to the chemistry side of things

This equation is the mathematical expression that backs up Coulomb's Law. Now that we know some foundational aspects of Coulomb's force, we can redefine Coulomb's Law according to this equation. First, what does this equation tell us about ionic bonds and charged particles in general?

1. It shows a proportional relationship between the magnitude of charges and the strength of the ionic bond
2. It shows an inversely proportional relationship between the distance between the ions and the strength of the ionic bond

Coulomb's law explains that two oppositely charged ions will attract another with a force proportional to the magnitude of their charges and inversely proportional to the distance between them.

## The Magnitude of Coulomb Force

So what are we calculating when we figure out the magnitude of a force or, in this case, the magnitude of energy in an ionic bond? We are looking at the strength of the interactions between cations and anions.

Based on what we've already covered this means the strength of the ionic bond depends on two factors:

1. charge of ions: as the charges increase, the ions are more strongly attracted to one another which increases the ionic strength

2. size of ions: as the size increases, the internuclear distance between ions increases which decreases ionic strength

To test your grasp on all this knowledge, let's try and apply it when comparing the strength of two ionic bonds!

Which ionic bond is stronger, NaCl or KCl? Why?

• First, let’s look at the charges on each ion: Na = +1, Cl = -1 and K = +1, Cl = -1
• Since the charges are the same, it must be the distance between the ions that is affecting the strength.
• Let's look at the ionic radii of Na vs. K: K is further down the period, so we know it is bigger, and Na is smaller.
• According to Coulomb's Law, ionic bond strength increases as ion size decreases. So NaCl has stronger lattice energy and is a stronger ionic bond.

If you want to review Periodic Trends, check out Periodic Trends to be more confident in determining the charges and radius of different ions!

We can also use Coulomb's law to estimate the lattice energy of ionic compounds.

Lattice energy is the energy needed to break an ionic compound and separate the oppositely charged ions. It is called lattice energy because ionic compounds exist in a crystal lattice structure, and it is the energy required to separate these lattices of ions into separate ions.

Check out Structure of Ionic Solids for more information on crystal lattices and how lattice energy is related to various properties of ionic solids!

Let's continue looking at different applications of Coulomb's Law in chemistry!

## Applications of Coulomb Force

We already know one of the most important applications of Coulomb's forces is the interaction strength of ionic bonds and lattice energy, but Coulomb forces are everywhere, so there are a couple more applications worth mentioning!

1. Lattice Energy and Solubility

• Lattice Energy directly impacts the solubility of an ionic solid. The stronger the ionic bond, the less soluble it is. According to Coulomb's Law, if it requires more energy to break apart ions, the ions have a high charge and are close together. If it's harder for the ions to be separated, doesn't it make sense that it's less likely that ions will attach to water molecules?

2. Ionization Energy

• Coulomb's Forces also apply to the ionization energy of ions.

Ionization energy refers to the energy required to move an electron from an atom, thus turning it into an ion.

The same principles of distance and charge apply to elements, except between the negatively charged electrons and a positively charged nucleus. The greater the distance between the nucleus and valence electrons, and the weaker the charge of the nucleus, means it takes less energy to remove the electron.

## Coulomb Force of Replusion

Thinking back to Coulomb's Law, it includes attractive forces between opposite charges and repulsive forces between like charges. Arguably, attractive forces between oppositely charged particles are very significant and prevalent throughout chemistry. This is why we've focused most of our time on them. However, repulsive forces exist in situations like electron-electron expulsion and even within the nucleus between positively charged protons.

We won't go too deep into the mechanics of a nucleus, but once you understand Coulomb's law, you may turn your mind to the atom. What subatomic particles are in a nucleus? Positively charged protons and neutral neutrons. How is this possible if like charges repel like charges… shouldn't the atom not be able to hold together? It is another force that holds protons and neutrons together called nuclear force. Protons do experience electrical repulsion, but the nuclear force overpowers them. Science never ceases to amaze!

You should now be familiar with Coulomb's law and how we can use it to understand ionic bonds and strength. For more examples of how to apply the concept of coulomb force to ionic bonds, work through the flashcards!

## Coulomb Force - Key takeaways

• Coulomb's law explains the electrostatic attraction between negatively charged and positively charged ions in an ionic bond.
• Lattice energy refers to the energy needed to separate ions from their lattice structure. It measures the strength of ionic bonds.
• As the charges of the ions increase and the radii of the ions decrease, the lattice energy increases
• When comparing the strength of an ionic bond, solubility, or ionization energy, compare the charges and ionic radii of the ions.

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What is coulomb force?

Coulomb force is the attractive or repulsive force between particles due to their charge.  In chemistry, it is used to determine the strength of attraction between oppositely charged cations and ions in an ionic bond.

How to calculate coulomb force?

To calculate coulomb force you use the equation. K is coulomb's constant, q1 and q2 are the charges of the ions, and r is the internuclear distance of the ions. In chemistry, it is more important to know how to conceptually happy this formula rather than mathematically calculate it.

What is the unit of Coulomb force?

The unit of Coulomb force is traditionally Newtons. In chemistry, the units of coulomb force is redefined in Joules as the energy needed to break apart an ionic bond.

How is coulomb law used in chemistry?

In chemistry, coulomb's law can be used to compare the relative strength of ionic bonds using their charge and distance. It can also be used to determine the lattice energy of ionic compounds and the ionization energy of elements.

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