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Molar math

This article was originally written by [Lynda ABC] at chemistryiseasy.com. That website no longer exists.


We use the unit of a “mole” to talk about extremely large numbers of extremely tiny countable objects, such as molecules, atoms or electrons.

One dozen = 12 of something

One gross  = 144 of something

One kilo     = 1,000 of something

One mole   = 602,200,000,000,000,000,000,000 of something

(Well, not exactly. It is really 602,214,179,300,000,000,000,000, but we round off.
We usually don’t need to know all the digits, in order to use it. If you care to look into it, there’s a reason why it is this seemingly weird number.  We can look at that later if you like.)

Moles are used to count molecules, atoms or electrons.

(Technically it can also be used even for something like apples, if you really had a huge amount of them.)

The numerical value of the mole is usually written in scientific notation.


Can be written as 6.022 x 10^23.

“^23” means “to the 23rd power

So basically, a “mole” is just a very, VERY large number.

Four Simple Steps to Mastering Molar Math

1. Find the starting units and ending units in a problem.

2. Set up “conversion ratios” – these cancel out the unwanted starting units, and leave you with the desired ending units.

3. Find any of the 4 mole ratios listed below.

(1) A mole is “6.022 x 10^23 of anything.”

(2) A mole of gas at STP (Standard Temperature and Pressure) occupies a volume of 22.4 Liters.

(3) Be able to find the molar mass of any substance.

(4) Be able to find the “mole ratio” between two reactants, between two products, or between a reactant and a product from any balanced chemical equation.

4. Know how to set up a series of ratios to cancel the units you DON’T want and end up with the units you DO want. T


(1) Find Starting and Ending Units in a Problem

A unit is one of whatever it is you are counting or measuring.

For example, if you have 10 gallons of gasoline, “gallons” is the unit you are counting. If you drive 40 miles, “miles” is the unit of distance you are measuring.

Without units, our numbers don’t mean anything. If I said, “I have 30,” what would your question be? Wouldn’t it be “30 of what?”

All problems in molar math are really just “unit conversion” problems.

Example:  I want to convert units of “feet” to units of “inches.”

So we set up a conversion structure as shown below, leaving space for a “conversion factor” in between.

mole conversions

You may find other language variations in problems, but you should always be able to find the ending units and starting units and set up a structure as we have done above.


(2) Be Able to Set Up Conversion Ratios to cancel the unwanted starting units and leave you with the desired ending units.

What is a Conversion Ratio?

A “conversion ratio” is a ratio which converts one unit into another.

conversion 2


Turning Conversion Ratios Upside Down in Order to Cancel Units

The next thing to know about using “conversion ratios” in chemistry is that you can turn ANY ratio “upside down” in order to get the answer you are seeking.

For example, the ratio “12 inches/1 foot,” may be turned “upside down” as shown below.

Arrow pointing up with the words ‘right side up’ over the factor 12 inches/1 foot and an arrow pointing down with the words ‘upside down’ over 1 foot/12 inches.

The second form of the ratio is used when we want to convert from inches to feet, instead of from feet to inches. We set up the structure to START with inches and END with feet, as shown below.

conversion 3


Use ONLY Horizontal Fraction Bars

You also have to know is that it is FAR better to write all ratios in science with horizontal fraction bars, rather than diagonal bars.

This keeps everything easy to see when you have a string of ratios in a problem.

conversion 4


(3) Be able to find any of the 4 ratios related to the mole listed below.

types mole conversions


Ratio # 1: The Number of Particles in a Mole

While anything “countable” may be considered a particle, in chemistry, particles usually means molecules, ions or electrons.

The value of this ratio is given BY DEFINITION based on experiments in the real world.

This relationship may be written in one of two ways:

mole ratios

And remember, it doesn’t matter WHAT the particles are. The number of particles in a mole is ALWAYS the same.

Now let’s use this ratio in solving two example problems. In the first few examples, I go into excruciating detail, but after you get a feel for this kind of problem solving, it goes very quickly and is really very EASY.

(My assumption is that you already understand scientific notation and significant figures.)


Problem 1: Find the Number of Particles from Moles

You have 3.0 moles of substance. How many particles of substance do you have?

Analysis: You are given moles and are asked to find particles. So you start with units of moles and end up with units of particles in your answer.

Before you even begin to worry about the numbers, be sure to place the starting and ending units where they need to go.

mole to part1

Notice that we placed the units where they go first, without even worrying about the numbers.

We also left a blank space to write in the conversion ratio, once we determine what that is.

Next, we need to choose the correct version of the ratio between moles and particles to make the conversion work.

Again, not worrying about numbers, concentrate on just finding the UNITS which will cancel out moles and leave us with particles.

Below we see the two possible ways that units in the Conversion Ratio may be placed. Which one do you think is correct?

mole to part 2 poss

If you chose possibility “A,” you are correct. That placement allows us to cancel the unit “moles” and keep the unit “particles.”

mole to part 4

Now that our units are placed correctly, we can insert the numbers.

According to the problem, we start with 3.0 moles of substance. The number of particles in a mole is constant, so our conversion factor is constant.

(I have also placed grey numeral “1’s” into the problem to help us remember that even when there are no numbers or units written, the number “1” is always there.)

mole to part 5

Our final steps are to check the unit cancellation, do the calculation, determine significant figures and put the answer in final form.

mole to part 6

Here is a PDF handout of more molar math examples Molar Math


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