Energy of Chemical Bonds - Basics

 General Chemistry Index

Where are we going with this? This page will give the ability to use laboratory observations and data to compare and contrast ionic, covalent, network, metallic, polar, and non-polar substances with respect to constituent particles, strength of bonds, melting and boiling points, and conductivity; provide examples of each type.

Energy of Chemical Bonds - Basics

Lead Author: Dr. Anne Gull

Chemical energy is a type of energy that is stored in the bonds of compounds. When compounds are formed, some energy is required to "shove" the atoms together. When those bonds are broken, that energy is released.

In typical chemical reaction, some bonds break (and give off energy) and other bonds form (taking in energy. If the total energy given off exceeds the energy need, the excess energy is given off as heat and/or light. When a reaction gives off energy, it is exothermic. Energy exits the reaction. When a reaction takes in energy, it is endothermic. Energy enters the reaction.

Every combination of atoms has a specific bond energy. Knowing the bond energy allows the calculation of energy given off.

For example, the bond between carbon and hydrogen stores 413,000 joules for every mole. That means that one mole of those bonds will give off that much energy.

Chemical energy is stored in bonds, so it’s a type of potential energy that can be released when a chemical reaction occurs. Each type of bond has a unique amount of energy. Some of the values are shown in the chart below. These energy amounts are measured for 1 mole.

The figure below shows the energy stored in several common bonds:

C-H	413000 J
C-C	347000 J
C-O	358000 J
C=O*	799000 J
O-H	467000 J
O-O	146000 J

* for CO2
For other C=O bonds, see this.

In order to figure out how much potential energy is inside a chemical substance, you need to look at the structure to see the bonds (the lines between elements represent the bonds). 

The dash or single line (-) is a single bond. The double line (=) is a different kind of bond, a double bond. There is also triple bonds (≡) three lines.

The energies for the different bonds are different. It is important to recognize the difference and make sure you are using the correct bond energy from the table.

More Bond Energies 

For more information and the energies of other types of bonds, see this link:

Click Here

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Bond_Energies


NOTE: The energies on the linked page are given in kilojoules, so multiply by 1000 to get joules per mole.

Example #1 Methane

https://www.daviddarling.info/encyclopedia/M/methane.html

In the molecule above, there are 4 C-H bonds, so the potential energy stored in this molecule is 4 times the value of each C-H (413000). So there is 4(413000) = 1652000 J of potential energy in one mole of this type of molecule.There are 3 C-H bonds, 1 C-O bond and 1 O-H bond so the potential energy stored in each bond would be added up.

Example #2 Methanol

https://www.daviddarling.info/encyclopedia/M/methanol.html

There are 3 C-H bonds, 1 C-O bond and 1 O-H bond so the potential energy stored in each bond would be added up.

3 C-H 3(413000) J

1 C-O 1(358000) J

1 O-H 1(467000) J

Total 2,064,000 J

Light and Optics: Introduction

Light

Light is one form of electromagnetic (EM) energy. Light is defined within a narrow range of electromagnetic frequencies which stimulate the receptors of the eye.  Included in light is the frequencies just beyond what humans can see. Infrared light has a slightly too low of a a frequency for humans to see. Ultraviolet light has a slightly too high frequency for humans to see.

All forms of electromagnetic energy are affected by interacting with matter. When light interacts with matter, it either reflects off of it,  refracts around it, or passes through.

One of the properties of light (and other EM types) is that it will propagate at different rates through different mediums. Though the difference is generally slight, it makes a difference.

Optics

Light, because it can be easily observed, provides many opportunities to EM radiation.

Notice how the pencil seems to bend. This occurs because
light travels at different rates through air and water (and glass).

The difference between the speed of light in a vacuum and the speed of light in air is very, very minimal (on a scale of X 10⁸⁾. However, the difference in speed between light in air and light in water water results in light bending at the waters surface.

The differences in speed also explain how lenses can reshape light. Glass can bend the light in one of two ways.

Focusing is the process of taking light that is moving in a straight line and concentrates it into a smaller area. The rays of light (particle model) are bent such that they converge (align into a tighter, smaller area).

Light can also be "un focused." Light that is traveling in a straight line can be dispersed into a wider area. The rays of light (particle model) are bent such that they diverge (spread out over a wider area).

Both lenses and mirrors can converge (focus) and diverge light. First… There are these three words you need to understand.

From Google

Concave: A shape that has a recessed center relative to the outer edges. The center caves in.

Flat: The center and the edges are in the same plane. (A window)

Convex: A shape that has a protruding center relative to the outer edges. NOT like a cave (see above).

So, which types of lens and mirror do what?

• Focus occurs with convex lenses and concave mirrors.
• Dispersion occurs with concave lenses and convex mirrors.

STOP - NOTICE!Throughout the vast domain of information on optics, lenses, and light, there exists a variety of sets of variables that identify different measures. The "distance to the object from the lens," for example can be found as… 

d… do… D… Do… u… o… 

This variation is very frequent. This discussion reflects that with examples and images used from other sources.

Focal Length

Every lens has a focal length. That is the distance from the lens to the point where parallel light will be focused:

An example of a convex mirror which spreads the light
making objects appear smaller than they actually are.

Convex lenses have a positive focal length. The image appears some distance behind the lens. The lens is between the object and the image.

Concave lenses have a negative focal length. No image appears, but the focal point is in front of the lens, between the object and the lens.

Concave mirrors have a positive focal length. The image appears some distance behind the lens. The lens is between the object and the image.

Convex mirrors have a negative focal length. No image appears, but the focal point is in front of the lens, between the object and the lens.

A flat mirror and a flat piece of glass (window) work into this schema, falling between convex and concave. Imagine a lens that is convex. As the radius of the curve increases, it gets closer and closer to a flat piece of glass (a window). Likewise, a mirror can flatten out as well.

The object appears inside the mirror an equal distance, but behind the mirror. More on this to come!

Depending on the substance from which a lens is made as well as the geometry of the lens, there is a relationship between the distance from the object to the lens, o, the focal length of the lens f, and the distance from the lens to the projected image i.

Object ------ o ------ Lens ----- i -------Image

That relationship is:

1/o + 1/i = 1/f

Solving for f… (consult with a math teacher if you have questions!)

(i/i)(1/o) + (o/o)(1/i) = 1/f

(i/io) + (o/io) = 1/f

(i + o)/(i)(o)  = 1/f


f = (i)(o)/(i + o)


So, knowing i and o, we can easily find f:

EXAMPLE:

An object is 2 cm from a lens and the image appears 5 cm from the lens. Find the focal length.

f = (i)(o)/(i + o)
f = (2 • 4)/(2 + 4)
f = 8 / 6
f = 1.333 cm

An interesting property to examine is the relationship of image size to object size in consideration of where the object is located and where the image appears.

Image from http://www.retremblay.net/PhyLifePart01/Individual_labs_files/lab10.pdf

The formula

Hi/Ho = Di/Do ( see eq. 1 above) 

is not difficult to work with. Cross multiplying will quickly reduce the problem to a simple solution, for instance:

EXAMPLE:

Find the height of the image, Hi, when the object has a height of 3 cm and where the object is 8 cm from the lens and the image is 4 cm from the lens.

Hi/Ho = Di/Do
Hi/3cm = 8cm/4cm 

cross multiply to get 

(4cm)(Hi) = 24cm² 

Hi = 6cm

Lastly, we can talk about magnification. How much bigger or smaller is the image compared to the object?.

This one is pretty easy!

M = hi/ho

So… divide…

EXAMPLE (without units, which would be a distance unit for hi and ho):

A lens has a magnification, M, of 1.25. I f the height of the object is 6, what is the height of the image?
M = hi/ho
1.25 = hi/6
(6)(1.25) = (hi/6)(6/1)
7.5 = hi

Conclusion

A very large portion of society has a daily encounter with optics: those who wear glasses or contacts and those take photos (camera or phone!)

While the need to calculate "things" rarely comes up, a fundamental understanding of lenses and light add to the daily life experience.

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¹ "propagates" is used to describe the motion of waves through a medium. Mechanical waves (such as sound) propagate by transferring energy through collision of molecules. Electromagnetic waves propagate differently and do not rely on matter as a medium. Once upon a time, scientists theorized that the universe was filled with something they called the aether that was responsible for the propagation of electromagnetic waves.

Electromagnetic Energy: Introduction

Energy can appear within creation in several forms, and one of those forms is electromagnetic energy. This is a huge topic of physics, and it will be introduced by taking a look at light.

Electromagnetic energy (EM) is a category of energy forms that propagates¹ through space at the speed of light, c, which is 3 X 10⁸ m/s or 186,000 mph. Electromagnetic energy is categorized by it's wavelength and frequency. Certain form of EM are defined by ranges of wavelength and frequency.

Because EM travels at the speed of light, wavelength, λ, and frequency, f, are reciprocals and conform to the wave equation:

v = fλ

Since v is always the speed of light for all EM forms, as f goes up, λ goes down.

Ranges of frequencies (and thus wavelengths) determine the type of EM in question. Certain ranges are called radio waves (AM and FM have different frequency ranges—take a look at your car radio tuner, perhaps). Other familiar ranges include radar, x-ray, and microwave ovens.

Electromagnetic energy behaves differently in different situation. In many cases, it behaves like a wave that will reflect (bounce off of) from surfaces or refract (bend around) edges or objects. However, in other cases, it behaves like a particle. Thus, EM energy is thought to have both properties that are explained by both wave and particle models. In reality, the complexities of EM energy are not fully explained by either model, but each model is useful for gaining understanding of different principles of EM energy.

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¹ "propagates" is used to describe the motion of waves through a medium. Mechanical waves (such as sound) propagate by transferring energy through collision of molecules. Electromagnetic waves propagate differently and do not rely on matter as a medium. Once upon a time, scientists theorized that the universe was filled with something they called the aether that was responsible for the propagation of electromagnetic waves.

Heat of Fusion and Heat of Vaporization

From kinetic theory, it is understood that as energy enters a substance, the molecules of the substance gain kinetic energy. Temperature is, in fact, defined as the average kinetic energy of the molecules of a substance.

As energy continues to flow into a substance, the kinetic energy of the molecules increase (that is to say the temperature goes up). This is true throughout the range of temperatures of the substance except at a few points: phase changes.

Heat of Fusion

When a substance reaches the melting point (heating up) or freezing point (cooling off), the temperature stops changing. When heating up, the added energy no longer increases the kinetic motion of the molecules but rather begins to break the bonds that hold a solid into a fixed shape and volume.

The amount of energy needed to break the bonds that holds a solid together is related to called the heat of fusion and is related to specific characteristics of the substance. Substances have different values for heat of fusion.

The amount of energy needed to break the bonds is also related to how much of the substance is present. Naturally, the more of something you have, the more energy it takes to melt it.

The total amount of heat needed to convert a substance from a solid to a liquid is determined by the value of the heat of fusion and how much of the substance is present, and can be found using the formula

Q = mΔHf

where Q is the heat (energy needed), m is the mass, and ΔHf is a number specific to each substance. ΔHf is often provided in calories per gram, joules per gram, or joules per mole.

The process of going from liquid to solid work similarly, but in reverse. Instead of taking heat to break the bonds, the substance has to give off heat in order for the bonds to form. The amount is the same, and the same equation can be used.


Heat of Vaporization

In a similar way to that a substance goes from a solid to a liquid, the process of going from a liquid to a gas requires energy to break the bonds of the liquid that give a liquid its definite volume. The energy stops increasing the temperature of the substance, but instead go into breaking the bonds.

This can easily be observed with a thermometer in a boiling liquid. No matter how long the pot sits on the heat source, the temperature of the water will only go so high—100° C—and after that, the energy from the heat source converts the water to a gas (steam).

How much heat is needed is, like melting, a function of the type of substance and the amount present. The more of a substance, the more energy needed to convert it all to a gas.

Thus, a formula emerges that is very like that for melting:

Q = mΔHv

where Q is the heat (energy needed), m is the mass, and ΔHv is a number specific to each substance. ΔHv is often provided in calories per gram, joules per gram, or joules per mole.


EXAMPLE

How much heat is needed to convert 8 grams of ice (solid) entirely to water (liquid) where ΔHf  for water is 333.55 J/g.

Q = mΔHv 

Q = (8 gr )(333.55 J/g) 

Q = (8 gr )(333.55 J/g)   

Q = 2,688.4 J

Values for ΔHv and  ΔHv can be found on many, many websites.

Nuclear Energy

In the 21st Century, the concept of nuclear energy is not strange to most people. Generally speaking, people know about nuclear bombs and nuclear power plants. Many people can explain that the sun (that stars) are giant nuclear plants that give off energy.

In the 1990s, the band, They Might Be Giants produced a song that stated:

The sun is mass of incandescent gas, a gigantic nuclear furnace
Where hydrogen is built into helium at a temperature of millions of degrees

-- They Might Be Giants - "Why Does the Sun Shine? (The Sun is a Mass of Incandescent Gas)"


So, how exactly does nuclear energy work? 

This goes back to the four basic forces that exist. Some people will recall they are:

gravitational
electromagnetic
strong (nuclear)
weak (nuclear)

Nuclear energy is associated with the last two. It takes a lot of energy to hold an atom together. That energy can be released when the atom is split.

Nuclear fission, the splitting of an atom's nucleus, releases a great deal of stored energy by… we'll get to that in a moment.

Another process related to the nucleus (hence the term nuclear) is when two or more nuclei are shoved together. This also results in the release of a great deal of energy!

Nuclear fusion, the joining of two or more atom's nuclei, releases energy by… stand by! Getting to that soon.

Both fission and fusion release energy. But how? And why so much?

Fission and fusion both involve altering the nuclei of atoms. Fission splits a nucleus and fission joins two or more. It is important to note that both fission and fusion result in atoms that have different atomic numbers (number of protons) than the original elements. For instance fusing hydrogen (atomic number 1) results in heliums (atomic number 2).

Something else happens when fission and fusion take place. Those of you who like to break the laws will really like this! (Note: breaking laws is agains the law and should not be done, ever. Unless you are fission or fusion.)

The law of conservation of matter is broken. The mass before and after nuclear reactions is different. The law of conservation of matter says that matter cannot be created or destroyed. Well…

There is also a law of conservation of energy that says that energy cannot be created or destroyed--that it only changes form. Well…

The processes of fission and fusion do not follow these laws. BUT!! The change in mass and the change in energy are related. In fact, they are exactly connected. Not only is the change in mass and energy connected, but they are connected by the most famous physics formula ever!

E = mc²

Yep!

This is what you've been waiting for ever since you first discovered Einstein's most famous formula!

So what does that mean?

It means that the conversion of matter to energy joins with the laws of conservation to result in a new, combined law:

The total of mater and energy is a constant never changing, but possibly interchanging.


Back to fusion and fission…

In nuclear reactions (both fission and fusion), energy is released (here are the conclusions) …by converting some amount of matter into energy. The amount of energy released is found using the equation

E = mc²

where E is the energy given off in joules, m is the mass in kilograms, and c is the speed of light (also the speed of an electromagnetic wave [energy]) which is a constant:

c = 299 792 458 m / s 

Now, nearly never is c written that way. The normal procedure is to write it in scientific notation as: 

c = 3 X 10⁸ m/s 

So, who doesn't like exponential notation? 

Working with the equation is not difficult. Find c²  then multiply by the mass. Done.


DIVERSION INTO MATH

So, a review of finding the square in exponential notation seems in order…

Let's find y where:

y = x²

and x = 200

y = x²
y = 200²
y = 40,000

Now, 200 = 2  X  10²

So…
y = x²
y = 200²
y = (200)²
y = (2  X  10²)²

Recall that to raise an exponent to the power of an exponent, you multiply exponents. thus…

y = (2  X  10²)²
y = 4  X  10⁴

It is fine to leave the equation above as is, but for the sake of proof, we can take it one more step:

y = 4  X  10⁴
y = 40,000


BACK TO NUCLEAR ENERGY

Working with the equation

E = mc²

is not difficult. Find c²  then multiply by the mass. Done.

Thus,  given any mass in kilograms, multiply by c² to find the amount of energy in joules that is given off. Finding c² and working out examples is left as an exercise for the reader.

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REFERENCES:

https://www.studentenergy.org/topics/nuclear

https://www.pbs.org/wgbh/nova/einstein/lrk-hand-emc2expl.html