Calculating Moles 101 (Stoichiometry 101)

[Insurgent]

The most important piece of information to know here is that the molecular weight (mw) of a chemical is the weight that contains a specific number of molecules of that said chemical. For basic elements, the molecular weight is found on the periodic table. Here is a periodic table with molecular weights of basic elements:


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Example: Iodine & Iodine Crystals

Take Iodine (I) for example. The molecular weight shown on the periodic table for an Iodine atom is 126.90 (it's near the bottom of the green section). That means that 1 mole of Iodine atoms weighs 126.90 grams on Earth.

What does this mean? It means there are 6.02214199 × 10^23 iodine atoms in 126.90 grams (1 mole) of iodine atoms. I would write the number out, but there would be 23 digits after the number 6. BTW that number is called Avogadro's Number.

There is a catch. Iodine doesn't come as single atoms. Iodine crystals are actually a molecule made from (2) Iodine atoms. That's why the formula for Iodine crystals is I2. So if there are (2) atoms of Iodine in (1) Iodine molecule, then the molecular weight of I2 (Iodine crystals) is:

126.90 x 2 = 253.80 g


That means 1 mole of I2 (Iodine crystals) weighs 253.80 grams. That also means that there are 6.02214199 × 10^23 molecules of I2 in 253.80 grams of Iodine crystals.

Why is this useful? You can calculate the number of moles in a given weight of a chemical. If you have 100 g of iodine, you can calculate the number of moles like this:

100g I2 / 253.80 g per mole I2 = 0.394 moles of I2
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Example: Hydriodic Acid - 57% HI

This periodic table can also be used to calculate the molecular weight (grams per mole) of any molecule. Take HI (Hydriodic Acid), for example. You can see from the formula that (1) molecule of Hydriodic Acid is made up of (1) atom of Hydrogen (H) and (1) atom of Iodine (I). You can look up the induvidual molecular weights for Hydrogen and Iodine on the periodic table. Here they are:

M.W. of Hydrogen = 1.0079 g
M.W. of Iodine = 126.90 g


To calculate the molecular weight of HI, the weights of the two atoms are simply added together like this:

126.90 + 1.0079 = 127.9079 g


So 1 mole of Hydriodic Acid (HI) weighs 127.9079 g. One can't exactly weigh out 100 g of pure HI. HI is a gas. One can learn about other topics in chemistry to figure out how many moles of a gas are in a known volume at a known temperature and pressure. See Ideal Gas Law.

Many gasses are measured as a % weight dissolved in a liquid. That's where the 57% HI comes from. 57% HI means that 57% of the weight is HI and the other 43% is water. If one has 100g of 57% HI, then one has 57 g of HI gas dissolved in 43 g of water. The moles of HI can be calculated from these numbers. Hypothetically one has 100 g of 57% aqueous HI, and we know the molecular weight of HI is 127.9079 g:
100g HI solution x .57 = 57 g HI in solution (for 57% solution)
57 g HI / 127.9079 g per mole = 0.446 moles HI (in 100 g 57% solution)

We could also say that there are 0.446 x 6.022x10^23 = 2.69x10^23 molecules of HI in 100 g of 57% HI, but this isn't realistically as useful as moles. Most chemistry folks just calculate reactions based on moles, not molecules. See the next example.
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Lye + HCl Neutralization (NaOH + HCl => NaCl + H2O)

If 6254 molecules of NaOH reacts with 6254 molecules of HCl to yeild 6254 molecules of both H2O and NaCl, who cares? We know that 1 mole of NaOH rects with 1 mole of HCl to yield 1 mole of water and 1 mole of Salt (NaCl), and that is good enough.

For the following reaction:

NaOH + HCl => NaCl + H2O


We can calculate the correct weights of each chemical to exactly react everything. This is a primary use for calculating moles. As the reaction shows, the molecules react on a 1 to 1 basis. 1 molecule of NaOH for each Molecule of HCl. From the periodic table:

Molecular Weights in grams
Sodium (Na) = 22.990
Oxygen (O) = 15.999
Hydrogen (H) = 1.0079
Chlorine (Cl) = 35.453


One thing you should know at this point is that the weights we are pulling from the periodic table are actually called atomic wieghts because they are for atoms, not molecules. Anyway, from these atomic weights, the molecular weights can be calculated.

Molecular Weight Calculations (rounded to 3 digits):

NaOH has Na x 1, O x 1, & H x1:
(22.990 x 1) + (15.999 x 1) + (1.0079 x 1) = 39.997 g per mole

HCl has H x 1, & Cl x 1:
(1.0079 x 1) + (35.453 x 1) = 36.461 g per mole


So for a 1 mole reaction we need 1 mole of NaOH and 1 mole of HCl. The NaOH is easy; one would just measure out 33.997 g of NaOH (Sodium Hydroxide). The HCl (Hydrochloric Acid) isn't as simple because it is a gas. HCl can be found at most hardware stores as a 32% aqueous solution. Since we need 36.461 g (1 mole) of HCl we must calculate the weight of 32% HCl that contains 36.461 g (1 mole) of HCl. Here is how it's done:

36.461 / .32 = 113.941 g


So 113.941 g of 32% HCl.aq containes exactly 1 mole or 36.461 g of HCl. The rest of the solution is water. This means that there will be an extra 77.48 g (113.941 - 36.461) of water added to the reaction, as well.

The product of this reaction, as shown at the start of the example, is 1 mole of NaCl (Sodium Cloride, Salt) and 1 mole of water + the additional 77.48 g of water added.

H2O Molecular weight: (1.0079 x 2) + (15.999 x 1) = 18.015 g


The additional moles of water added at the beginning (with the aqueous HCl) is calculated like this:

77.48 g H2O / 18.015 g per mole H2O = 4.30 moles H2O


So the product of this reaction is really 1 mole of NaCl and 5.30 moles of H2O. Most of the NaCl would be dissolved in the water. This could be written as:

NaOH + HCl + 4.30*H2O => NaCl + 5.30*H2O

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Example: NaH2PO2 + HCl => H3PO2 + NaCl


Atomic WeightsSodium (Na) = 22.990
Hydrogen (H) = 1.0079
Phosphorus (P) = 30.974
Oxygen (O) = 15.999
Chlorine (Cl) = 35.453

Molecular Weights
NaH2PO2: 22.990 + (1.0079 x 2) + 30.974 + (15.999 x 2) = 87.978
HCl: 1.0079 + 35.453 = 36.461
H3PO2: (1.0079 x 3) + 30.974 + (15.999 x 2) = 65.996
NaCl: 22.990 + 35.453 = 58.443

For 1 mole, each

87.978 g Sodium Hypophosphite in 50% solution
87.978 x 2 = 175.956 g of 50% NaH2PO2 solution

36.461 g HCl in 32% solution
36.461 / .32 = 113.941 g of 32% HCl solution (muriatic acid)

Yields
65.996 g of H3PO2 in water.

For 50% H3PO2 in water:
Reduce weight of water to 65.996 grams (about 66 mL)


In reality, reduce it to 50 mL or less, filter salt, and add back water to 66 mL to avoild a salt saturated solution

[Tungsten.Chromium]

Wonderful post!  Excellent explanation of the mole, a concept that always seems to confuse chemistry students.  The example walkthroughs are great! 
For anyone wanting to practice, here are some links that I found to be extremely helpful!


IDEAL STOICHIOMETRY
https://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiometry/e/ideal_stoichiometry

LIMITING REAGENT STOICHIOMETRY
https://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiometry/e/limiting_reagent_stoichiometry

[Σ]

Here is a little more technical information and examples. The examples are taken from Linus Pauling's General Chemistry. I highly recommend this book to anyone with even a slight interest in chemistry as it carries all the information other text books have but at a much more affordable price.

The precise definition of Avagadro's Number (N) or Avagadro's Constant is the number of Carbon-12 atoms in exactly 12 grams of carbon-12 holding the approximate value of 6.02 x 10²³. As mentioned earlier this is a very large number.

A mole of a given substance is defined as Avagadro's Number of molecules or atoms of that substance. In order to prevent confusion as to wether one is working with mole's of molecules or atoms the term gram-atom can be substituted for mole when taken in terms of atoms. Remember that regardless of if you are working with a mole of atoms or molecules Avagadro's number will not change since it is a constant representing the number of individual parts (molecules or atoms) comprising the given substance you are working with.

Consider a mole of water. The molecular weight of H₂O is 18.0153. This can be obtained by adding the atomic weights of the atoms in the molecule together. Given that H has an atomic weight of 1.00797 and O has an atomic weight of 15.9994 and since there are 2 hydrogen atoms for each molecule of water the equation will be:
2 x 1.00797 + 1 x 15.9994
Resulting in a molecular weight of 18.0153.
If represented in terms of a "gram-atom" the weights would be hydrogen: 2.01594g and oxygen: 15.9994g with the hydrogen having 2(6.02x10²³) atoms and the oxygen having the regular 6.02x10²³
From the definition of atomic weight and the mole we can see that a mole of water is 18.0153 g. Just to recap this means that in 18.0153 g of water there are 6.02 x 10²³ individual molecules.