Calculating Chemical Reaction Quantities - Don't Forget Water of Crystallization!

Carrying out a chemical reaction by combining two or more substances to form new substances is generally performed quantitatively. For instance, take the reaction between sodium sulfate and barium chloride, which combine in solution to form sodium chloride (ordinary table salt) and barium sulfate (used as a contrast agent in x-ray diagnoses of the gastrointestinal tract).

Na₂SO₄ + BaCl₂ → 2 NaCl + BaSO₄ -- Equation 1
(A stoichiometric¹ reaction)

Now how much of each do we use? Well, it can be varied, but for simplicity's sake, lets consider combining one molecular weight of each item, which is the correct, easiest way to understand this reaction.

Calculating Reaction Quantities

The atomic weights in grams (rounded off for simplicity) of each of the constituent atoms is:

Sodium 23
Sulfur 32
Oxygen 16
Barium 137
Chlorine 35

Combining the atoms in correct proportion, we obtain for molecular weights:

Na₂SO₄ = 2 Sodium + 1 Sulfur + 4 Oxygen = 46 + 32 + 64 = 142 grams
BaCl₂ = 1 Barium + 2 Chlorine = 137 + 70 = 207 grams
NaCl = 1 Sodium + 1 Chlorine = 23 + 35 = 58 grams
BaSO₄ = 1 Barium + 1 Sulfur + 4 Oxygen = 137 + 32 + 64 = 233 grams

Checking for Correctness

Does this add up correctly? Using Equation 1, we see

142 + 207 → 2 (58) + 233 or
142 + 207 → 116 + 233
349 → 349

This looks good-our numbers match! Yet, despite our seeming correctness, we may actually be in error because of one factor we have not so far considered.

Water of Crystallization

There is a snare the new student of chemistry could fall victim to. That snare is forgetting what is called the "water of crystallization" (or, sometimes, "water of hydration"). Many ionic chemical substances produced from water solution crystallize out in solid form containing one or more molecules of water. Chemical manufacturing firms sometimes artificially remove that water, but frequently they do not. It is up to the individual carrying out a reaction to realize water is present. It must be included in all calculations of a quantitative nature.

Re-calculating Our Example

In the case of our reaction in equation one, we may actually have,

Na₂SO₄ • 10 H₂0 + BaCl₂ • 2 H₂0 → NaCl + BaSO₄

Sodium sulfate decahydrate is more commonly known as Glauber's salt. Yes, it actually contains ten molecules of water of crystallization per single molecule of sodium sulfate, and is solid! The bottle it comes in will indicate the correct formula. It is important, and needs to be taken into account. Do not forget to examine the label on the bottle. A similar situation exists with barium chloride. It often comes as the dihydrate.

Sodium chloride and barium sulfate do not possess water of crystallization. The twelve molecules of water released by the equation are normally not mentioned, as the reaction occurs in water as the solvent.

New Numbers for Our Reaction

To carry out this equation properly and completely then, we need to combine 322 grams (original 142 grams plus 180 grams water²) Glauber's salt with 243 grams (original 207 grams plus 36 grams water) barium chloride dihydrate in order to obtain the same 58 grams of sodium chloride and 233 grams of barium sulfate as products.

_¹The "Free Dictionary" defines stoichiometry as, "The quantitative relationship between reactants and products in a chemical reaction."
_² Water has a molecular weight of 18 grams. If there are ten water of crystallization molecules, this amounts to 180 grams.

References and Resources:

Shodor - Stoichiometry

The ChemCollective (Carnegie Mellon Institute) - Reaction Stoichiometry