Stoichiometric Calculations Based on Chemical Formulas

You may wonder why it is necessary to quantify elements involved in chemical reactions. If by chance your cook puts extra salt in your favorite food, will you prefer eating it? Possibly not. Likewise, without a correct examination of stoichiometry, it is not possible to rule out what amount of elements is appropriate for any specific reaction. So, what is stoichiometry?

Here, in this content, you will get to know what stoichiometry means and what are stoichiometric calculations.

Let us start.

Stoichiometry

Stoichiometry refers to the evaluation of products and reactants taking part in any chemical reaction. The term “stoichiometry” is obtained from two Greek words, namely “stoichion” which determines element,s and “metry” which means measuring.

Moreover, stoichiometry is established on the law of conservation of mass where the entire mass of reactants is equivalent to the whole mass of products, which illustrates that relations among products and reactants’ quantities usually make a ratio of +ve integers. This shows that if you know the number of individual products, you can easily calculate the product amount.

Again, if the quantity of one reactant is known, and product quantity can be determined using an experiment, then the calculation of other reactants is also possible. This is represented in the following example of a balanced chemical reaction.

CH4 + 2O2 → CO2 + 2H2O

In this reaction, one mole of methane undergoes a reaction with two oxygen gas molecules to produce one carbon dioxide molecule and two water molecules. This chemical reaction is a perfect example of full combustion (burning).

Now that you have understood what is stoichiometry is, you must also know about reaction, composition, and gas stoichiometry.

The description of quantitative relationships among the elements while they participate in reactions is called reaction stoichiometry. For the above reaction example, reaction stoichiometry evaluates the relationship of amounts of methane and oxygen that react to give out water and carbon dioxide.

As atomic weight and moles have a relation between them, the ratios which are calculated by stoichiometry are used to measure quantities in terms of weight in a balanced equation. This process is known as composition stoichiometrarey.

Next, gas stoichiometry is concerned with the reactions that involve gases. In these reactions, gases have a known volume, pressure and temperature and hence assumed as ideal gases. The volume ratio of gases is the same according to Ideal Gas Law, but ratio of mass of one reaction has to be determined from reactants and products’ molecular masses. In real life, since isotopes exist, calculations of mass ratio are done using molar masses.

Now, as the discussion of what is meant by stoichiometry is completed, let us move further with stoichiometric calculations based on chemical formulas.

Chemical Equations

A chemical equation describes a chemical reaction that gives the quantities and identities of the products and the reactants. In a chemical equation, the starting compounds and reactants are on the left, the products and the final compounds are on the right. To balance a reaction, the number of elements on both sides of the equation should be equal. Various stoichiometry coefficients are used to adjust the number of elements on both sides of the reaction. The following are the various conversion factors and a few steps to solve stoichiometric problems.

• Balancing the given equation.

• Giving the unit as a mole to the substance.

• Calculating the number of moles.

Stoichiometric Formulas based on Chemical Reaction

The following are some of the terms used in Stoichiometry,

Formula Mass

Formula mass is defined as the sum of the atomic weights of the atoms in the given molecule of the substance. 

For example, the formula mass of Na₂S is calculated as 2(23) + 1(32) = 78.

Avogadro number

Avogadro’s number is the total number of particles in one mole of a substance. It is the number of atoms present in 12g of C-12. 

The value of the Avogadro number is 6.022 × 10²³.

Molar Mass

Molar mass is the sum of the total mass of all the atoms that constitute a molecule per mole.

Stoichiometric Calculations

The conversion factors in chemistry can be used to solve stoichiometric problems. Generally, solution of all stoichiometry issues can be found in just a few steps:

1. Balancing the equation

2. Converting substance units to moles

3. Using mole ratio to calculate moles of yielded substances in the reaction

4. Converting moles of needed elements to the required units.

Take a look at the following example of how rusting of iron takes place.

Fe + O2 → Fe2O3

Step 1

A chemical equation’s elemental parts never get lost or destroyed. The product of a reaction must correspond to the actual reagents. This fact is true not only for element types in the production but for the numbers as well. The unbalanced equation is:

Fe + O2 → Fe2O3

This chemical equation shows that two atoms of oxygen react with one atom of iron to form 2 atoms of iron and three atoms of oxygen. (The subscript value like 2 in O2 shows how many oxygen atoms are there in a molecule.) However, since the equation is unbalanced, the reaction is not real, because it demonstrates a reaction where one iron atom yields two atoms of iron.

Hence, balancing the equation is a must by putting coefficients before the substances to make sure that total number of atoms on the reactants’ side is similar to total number of substances on the product side. The balanced equation is:

4Fe + 3O2 → 2Fe2O3

On counting the atoms in this new balanced equation, you will see that on the arrow’s left side, there are four iron atoms and six oxygen atoms (3 x 2 = 6). On arrow’s right side, there are 4 iron atoms (2 x 2 = 4) and 6 oxygen atoms (2 x 3 = 6). Therefore, atoms on both left and right side match.

Step 2

The procedure of transforming units to moles demands for conversion factors. Below you will be able to see the most used and essential conversion factors that are used between moles and volumes of gases, moles and grams, moles and molecules and moles and solutions. You must remember that although these factors mainly convert other units to moles, they also can convert from moles to other units.

• Conversion of Grams to Moles

Gram formula mass of an element refers to one mole of an element’s mass. According to the definition, it is estimated in grams/mole and is evaluated by adding all the atomic weights of atoms of a compound. In the periodic table, atomic weights are provided in atomic mass units, but they depict gram formula mass. For example, one mole of carbon of 12 a.m.u has a weight of 12 grams.

As a conversion factor, GFM (gram formula mass) is used in stoichiometric evaluations by the following expression:

Moles = grams / gram formula mass

• Conversion of Volumes of Gas to Moles

With regards to the Ideal Gas Law PV = nRT, where n is number of moles, the equation can be rearranged to find a solution for n. So the equation can be written as:

n = PV / RT, where P = pressure in atm

V = volume in litres

T = temperature in Kelvin

R = gas constant which is equivalent to 0.0821 L - atm / mol – K

Hence, if P, T and V are given, moles of a compound in a gas can be found out. Furthermore, if a problem mentions that calculations should be done using Standard Temperature and Pressure (STP) where P = 1 atm and T = 273 K, the problems become easier. So, one mole of gas will occupy a volume of 22.4 litres at STP.

• Conversion of Individual Particle to Moles

The Avogadro number gives the conversion factor for converting particle number to moles. In general 6.02 x1023 particle formula units are there in one mole of a substance, where the formula unit determines whether that substance is a molecule, compound, atom or ion. Take a look at some formula unit examples below:

Compounds = Cu2S, NaCl

Molecules = N2, H2

Atoms = Fe, Na

Ions = Na+ (aq) Cl- (aq)

As 1 mole is equal to 6.02 x 1023 formula units, the conversion can be done using the following equation:

Moles = formula units / 6.02 x 1023

• Conversion of Solutions to Moles

It is comparatively simple to convert solution measures (molality and molarity) to moles.

The division of mole number of solute by litres of solvent is known as molarity. So after rearranging the equation, the following is obtained:

Moles = molarity x litres of solution

The division of mole number of solute by the number of solvent in kilograms is known as molality. Here also, after rearranging the equation, it is found:

Moles = Molality x kilograms of solution

Step 3

Considering the example of rusting of iron 4Fe + 3O2 -> 2Fe2 O3, the frontal coefficients of oxygen, iron and iron(III) oxide ratios govern the reaction. However, these numbers do not say that this reaction can only happen provided that there are exactly 3 oxygen moles and 4 iron moles that will yield 2 iron (III) oxide moles. Rather, it suggests that the reaction of oxygen and iron will stick to a ratio of 4 : 3. For instance, 2 iron moles undergo a reaction with 1.5 oxygen moles to form 1 iron (III) oxide mole.

Now, with the help of a balanced equation, units converted to moles and understanding mole ratio, calculation of the yields in a reaction in moles is possible.

Step 4

The last step calls for the conversion of moles to original units asked in a particular problem. So, it involves turning back the required conversion factors said above.

Solved Example

Problem: The equation N2 (g) + H2 (g) → NH3 (g) is at STP. Calculate the volume of H2 (g) required to produce 22 litres of NH3 (g).

Answer: After balancing the equation: N2 (g) + 3H2 (g) → 2NH3 (g)

Conversion to moles: (224 L of NH3 (g) x 1 mole) / 22.4 L = 10 moles of NH3 (g)

Mole ratio: (10 NH3 moles (g) x 3H2 moles (g)) / 2NH3 moles (g) = 15 moles of H2 (g)

Conversion to required unit: 15H2 moles (g) x 22.4 L / 1 mole = 336 L of H2 (g)