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Molar math

Molar math



Introduction to the Mole

Before you can do molar math successfully, you must first know what a mole IS.

If you are NOT completely clear about what a mole IS, quickly browse the page at the following link. Then come back when you think you understand enough to go on. What is a Mole?

We use the unit of a “mole” in science to talk about extremely large numbers of extremely tiny countable objects, such as molecules, atoms or electrons, objects which are obviously way too small to see.

We use the unit “mole” just like we use the unit “dozen.”
One dozen means “12 of something.”
In chemistry, one“mole” means “602,200,000,000,000,000,000,000 of something.” (“Six-hundred-two-sextillion-two-hundred-quintillion of something.”)

The “something” can be anything which is “countable” by individual units.

“Countable” as opposed to something without a definite particle nature, such as light or energy.

A “mole” is usually used to count molecules, atoms or electrons, but technically it can also be used as a numerical unit even for something like apples, if you really wanted to take the time to count that long. (Actually you could not count that many apples in an entire lifetime, even with the help of many friends!)

The numerical value of the “mole” is frequently written using scientific notation as 6.022 x 10^23.

(“^23” means “to the 23rd power, or something multipled by 10 and then multipled by 10 again and again and again, until 23 times.)

Four Simple Steps to Mastering Molar Math

With a little patience, you can learn the 4 simple steps listed below.


1. Be able to find “starting units” and “ending units” in a problem.

2. Be able to set up “conversion ratios” to cancel the unwanted starting units and leave you with the desired ending units.

3. Be able to find any of the 4 mole ratios listed below.
(There are ONLY 4!)

(1) Know that a mole is “6.022 x 10^23 of anything.”
(2) Know that 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 that you DO want.
This is the secret to being able to solve ALL mole problems in chemistry.

That’s all there is to it!

(1) Be Able to Find Starting and Ending Units in a Problem

What is a unit and why is it important?
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.

Units are extremely important in science. 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?” Reporting WHAT we are measuring or counting is essential to understanding. So we must always use units.

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

Say I want to convert units of “feet” to units of “inches.” My starting units are “feet” and my ending units are “inches.” Using this information, I would set up a conversion structure as shown below, leaving space for a “conversion factor” in between.

Conversion factor set up with an arrow showing the starting units, feet, and the ending units, inches.  There is an empty horizontal fraction bar in between where the conversion factor will go, once we determine what that is.  feet x (?/?) = inches.

We will talk about “conversion factors” later. But first you need to be sure you can find starting and ending units from the wording of problems. Practice with the following examples. We will use nonsensical units so you can concentrate on the LANGUAGE which gives you clues to the starting and ending units.

(1) How many bars are in a plick?
Ask yourself, “what are you trying to find?” The answer is “bars.”
Which words give you the clue that these are your ending units? “How many.”
What are your starting units? “plick” Which words give you the clue? “are in.”
So you would set up the structure this way:

Conversion set up showing starting units, plick, and ending units, bars, with a blank horizontal fraction bar in the middle.  Plick x (?/?) = bars.

(2) Convert jupos to babs.
What are your ending units? “babs.” Which word gives you the clue? “to.”
What are your starting units? “jupos.” Which word gives you the clue? “Convert.”
Set up the structure like this:

Conversion set up with start units, jupos, ending units, babs, and a blank horizontal fraction bar in between.  jupos x (?/?) = babs.

(3) Given 15 beebos, how many gibbers do you have?
What are your ending units? “gibbers.”
What word clue tells you that? “how many.”
What are your starting units? “beebos.”
What word clue tells you that? “Given.”
Set up the structure like this:

Conversion set up showing start units, beebos, ending units, gibbers, and a blank fraction bar in between.  beebos x (?/?) = gibbers.

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.

Here is an example of a conversion ratio using feet and inches.
12 inches/1 foot

We can use this conversion ratio to convert feet to inches as follows:

feet x (12 inches/1 foot) = inches, but feet is cancelled with foot.  The middle ratio is labeled as the conversion ratio.

Notice that using the conversion ratio, “12 inches/1 foot,” the starting units of “feet” cancel, leaving the ending units,“inches.”

Placing ratios correctly to cancel units is the second basic skill needed to solve ALL mole problems in chemistry.

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.

start units, inches, end units, feet.  inches x (?/?) = feet.

Choose the ratio to cancel the units we DON’T want, and end up with the units we DO want.

To convert inches to feet, which of the above forms of the ratio should we use?

comparison between the two possible set ups with conversion ratios in between.  which one will cancel out?  We have inches x (12 inches/1 foot) = feet  or  inches x (1 foot/12 inches) = feet.  Which one will cancel?  The first way is incorrect.  The second way is correct.

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Use ONLY Horizontal Fraction Bars

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.

30 miles/hour written with a horizontal fraction bar.  30 miles/hour written with a diagonal fraction bar, but crossed out to emphasize that we should only use horizontal fraction bars in chemistry from now on.


showing a series of fractions, a/b, b/c, c/d, d/e, written with once with horizontal fraction bars and once with diagonal fraction bars.  It is obvious that the second writing leads to errors with long strings of factors as we have in chemistry.

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

Ratio #1: The Number of Particles in a Mole

(This value is always the same, regardless of the type of particle.)
6.022 x 10exp23 / mole
Ratio #2: The Volume of a Mole of Gas at STP

(This value is always the same, no matter which gas you have.)
22.4 Liters/mole
Ratio #3: The Molar Mass of a Specific Substance

(This value changes depending on which substance you have.)
? grams/mole of substance
Ratio #4: The Mole Ratio of Two Substances in a Chemical Equation

(This value changes depending on the coefficients in your chemical equation.)
? mole of substance A/? mole of substance B





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