To simply their calculations, chemists created a standard unit for the number of atoms of a particular compound involved in a reaction or some other chemical process. They define one mole (mol) as the quantity of any substance that has the same number of fundamental units as 12 grams of carbon-12, which is is Avogadro's number (6.022 × 10^{23}). The SI (metric) system of measurement defines a millimole (Mmol) as one-thousandth of a mole. You generally calculate the number of moles of a substance by weighing the amount you have on hand. If you want to convert to Mmol, multiply by 10^{3} (1,000).

#### TL;DR (Too Long; Didn't Read)

One mole is equal to Avogadro's number of particles of a particular compound. A millimole (Mmol) is one-thousandth of a mole.

## How to Calculate Moles

Atomic masses are measured in atomic mass units (AMU). One AMU is exactly 1/12 the mass of the nucleus of a carbon-12 atom in its ground state. One mole of a substance is defined to be equal to Avogadro's number of particles of that substance. According to this definition, the weight of one mole of a substance in grams is the same number as the weight of an individual particle of that substance in AMU. For example, the atomic weight of carbon-12 is 12 AMU, so one mole of carbon-12 weighs 12 grams.

Consider a container full of hydrogen gas (H_{2}). Each particle in the container is a molecule consisting of two hydrogen atoms, so you need only know the atomic mass of hydrogen to calculate the molecular weight. Most versions of the periodic table list the atomic mass of each element under its symbol. For hydrogen, which has a single proton in its nucleus, it's 1.008 AMU, which is an average of all the naturally occurring isotopes of hydrogen. Consequently, the atomic mass of hydrogen gas is 2.016 AMU, and one mole of hydrogen gas weighs 2.016 grams. To find the number of moles in your sample, you would weigh the sample in grams and divide that weight by the molecular weight of hydrogen gas in grams. For example, a sample weighing 15 grams of pure hydrogen gas contains 7.44 moles.

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## Converting to Mmol

Sometimes quantities under investigation are so small that expressing them in moles is cumbersome. Enter the millimole. By multiplying the number of moles by a thousand, you can convert a very small number to a more manageable one. This is especially convenient when dealing with volume units in the order of milliliters.

**1 mol =1,000 Mmol**

## Solution Concentration

Chemists use molarity as a measure of concentration of a particular compound in solution. They define molarity as the number of moles per liter. You convert molarity to millimolarity by multiplying by 1,000. For example, a 1 mol (molar, also written as M) solution has a concentration of 1 mole per liter. This is equivalent to a 1,000 Mmol (millimolar, also sometimes written as mM) solution, which is one that contains 1,000 Mmol per liter.

## Example

**A solution contains 0.15 grams of calcium carbonate. How many millimoles is that?**

The chemical formula of calcium carbonate is CaCO_{3}. The atomic weight of carbon (C) is approximately 12 AMU, that of oxygen (O) approximately 16 AMU and that of calcium (Ca) approximately 40 AMU. Each molecule of calcium carbonate thus weighs 100 AMU, which means that one mole weighs approximately 100 grams. A weight of 0.15 grams represents 0.15 g ÷ 100 g/mol = 0.0015 moles. This is equivalent to 1.5 Mmol.

**What is the molarity and millimolarity of this much calcium carbonate in 2.5 liters of solution?**

Molarity is defined as the number of moles per liter, so divide the number of moles by 2.5 to get the molarity: 0.0015 ÷ 2.5 =

**0.0006 M**

Multiply by 1,000 to get the millimolarity =

**0.6 mM**

Note that you arrive at the same result for millimolarity if you divide the number of millimoles by the volume of solution.