Stoichiometry


Stoichiometry is the relationships between the quantities of reactants and products before, during and after chemical reactions.
Stoichiometry is based on the law of conservation of mass; the total mass of reactants must equal the total mass of products, so the relationship between reactants and products must form a ratio of positive integers. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be empirically determined, then the amount of the other reactants can also be calculated.
This is illustrated in the image here, where the unbalanced equation is:
Here, one molecule of methane reacts with two molecules of oxygen gas to yield one molecule of carbon dioxide and two molecules of liquid water. This particular chemical equation is an example of complete combustion. The numbers in front of each quantity are a set of stoichiometric coefficients which directly reflect the molar ratios between the products and reactants. Stoichiometry measures these quantitative relationships, and is used to determine the amount of products and reactants that are produced or needed in a given reaction.
Describing the quantitative relationships among substances as they participate in chemical reactions is known as reaction stoichiometry. In the example above, reaction stoichiometry measures the relationship between the quantities of methane and oxygen that react to form carbon dioxide and water: for every Mole of methane combusted, two moles of oxygen are consumed, one mole of carbon dioxide is produced, and two moles of water are produced.
Because of the well-known relationship of moles to atomic weights, the ratios that are arrived at by stoichiometry can be used to determine quantities by weight in a reaction described by a balanced equation. This is called composition stoichiometry.
Gas stoichiometry deals with reactions solely involving gases, where the gases are at a known temperature, pressure, and volume and can be assumed to be ideal gases. For gases, the volume ratio is ideally the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses of the reactants and products. In practice, because of the existence of isotopes, molar masses are used instead in calculating the mass ratio.

Etymology

The term stoichiometry was first used by Jeremias Benjamin Richter in 1792 when the first volume of Richter's was published. The term is derived from the Ancient Greek words , meaning 'element', and , meaning 'measure'. Ludwig Darmstaedter and Ralph E. Oesper have written a useful account on this.

Definitions

A stoichiometric amount or stoichiometric ratio of a reagent is the optimum amount or ratio where, assuming that the reaction proceeds to completion:
  1. All of the reagent is consumed
  2. There is no deficiency of the reagent
  3. There is no excess of the reagent.
Stoichiometry rests upon the very laws that help to understand it better, i.e., law of conservation of mass, the law of definite proportions, the law of multiple proportions and the law of reciprocal proportions. In general chemical reactions combine in definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter, nor transmute one element into another, the amount of each element must be the same throughout the overall reaction. For example, the number of atoms of a given element X on the reactant side must equal the number of atoms of that element on the product side, whether or not all of those atoms are involved in a reaction.
Chemical reactions, as macroscopic unit operations, consist of many elementary reactions, where a single molecule reacts with another molecule. As the reacting molecules consist of a definite set of atoms in an integer ratio, the ratio between reactants in a complete reaction is also in an integer ratio. A reaction may consume more than one molecule, and the stoichiometric number counts this number, defined as positive for products and negative for reactants. The unsigned coefficients are generally referred to as the stoichiometric coefficients.
Each element has an atomic mass, and considering molecules as collections of atoms, every compound has a molecular mass or formula mass, which when expressed in daltons is numerically equal to the molar mass in g/mol. By definition, the atomic mass of carbon-12 is exactly 12 Da, making its molar mass 12 g/mol. The number of chemical entities per mole in a substance is given by the Avogadro constant, exactly since the 2019 revision of the SI. Thus, to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole reaction.
Elements in their natural state are mixtures of isotopes of differing mass; thus, atomic masses and thus molar masses are not exactly integers. For instance, instead of an exact 14:3 proportion, 17.031 g of ammonia consists of 14.007 g of nitrogen and 3 × 1.008 g of hydrogen, because natural nitrogen includes a small amount of nitrogen-15, and natural hydrogen includes hydrogen-2.
A stoichiometric reactant is a reactant that is consumed in a reaction, as opposed to a catalytic reactant, which is not consumed in the overall reaction because it reacts in one step and is regenerated in another step.

Converting grams to moles

Stoichiometry is not only used to balance chemical equations but also used in "conversions" between quantities of a substance by dimensional analysis, e.g., converting from grams to moles using molar mass as the "conversion factor", or from grams to milliliters using density. For example, to express 2.00 g of NaCl as an amount, one would do the following:
In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one, with the resulting amount in moles, as shown in the following equation,

Molar proportion

Stoichiometry is often used to balance chemical equations. For example, the two diatomic gases, hydrogen and oxygen, can combine to form a liquid, water, in an exothermic reaction, as described by the following equation:
Reaction stoichiometry describes the 2:1:2 ratio of hydrogen, oxygen, and water molecules in the above equation.
The molar ratio allows for conversion between moles of one substance and moles of another. For example, in the reaction
the amount of water that will be produced by the combustion of 0.27 moles of is obtained using the molar ratio between and of 2 to 4.
The term stoichiometry is also often used for the molar proportions of elements in stoichiometric compounds. For example, the stoichiometry of hydrogen and oxygen in is 2:1. In stoichiometric compounds, the molar proportions are whole numbers.

Determining amount of product

Stoichiometry can also be used to find the quantity of a product yielded by a reaction. If a piece of solid copper were added to an aqueous solution of silver nitrate, the silver would be replaced in a single displacement reaction forming aqueous copper nitrate and solid silver. How much silver is produced if 16.00 grams of Cu is added to the solution of excess silver nitrate?
The following steps would be used:
  1. Write and balance the equation
  2. Mass to moles: Convert grams of Cu to moles of Cu
  3. Mole ratio: Convert moles of Cu to moles of Ag produced
  4. Mole to mass: Convert moles of Ag to grams of Ag produced
The complete balanced equation would be:
For the mass to mole step, the mass of copper would be converted to moles of copper by dividing the mass of copper by its molar mass: 63.55 g/mol.
Now that the amount of Cu in moles is found, we can set up the mole ratio. This is found by looking at the coefficients in the balanced equation: Cu and Ag are in a 1:2 ratio.
Now that the moles of Ag produced is known to be 0.5036 mol, we convert this amount to grams of Ag produced to come to the final answer:
This set of calculations can be further condensed into a single step:

Further examples

For propane reacting with oxygen gas, the balanced chemical equation is:
The mass of water formed if 120 g of propane is burned in excess oxygen is then

Stoichiometric ratio

Stoichiometry is also used to find the right amount of one reactant to "completely" react with the other reactant in a chemical reaction – that is, the stoichiometric amounts that would result in no leftover reactants when the reaction takes place. An example is shown below using the thermite reaction,
This equation shows that 1 mole of and 2 moles of aluminium will produce 1 mole of aluminium oxide and 2 moles of iron. So, to completely react with 85.0 g of , 28.7 g of aluminium are needed.

Limiting reagent and percent yield

The limiting reagent is the reagent that limits the amount of product that can be formed and is completely consumed when the reaction is complete. An excess reactant is a reactant that is left over once the reaction has stopped due to the limiting reactant being exhausted.
Consider the equation of roasting lead sulfide in oxygen to produce lead oxide and sulfur dioxide :
To determine the theoretical yield of lead oxide if 200.0 g of lead sulfide and 200.0 g of oxygen are heated in an open container:
Because a lesser amount of PbO is produced for the 200.0 g of PbS, it is clear that PbS is the limiting reagent.
In reality, the actual yield is not the same as the stoichiometrically-calculated theoretical yield. Percent yield, then, is expressed in the following equation:
If 170.0 g of lead oxide is obtained, then the percent yield would be calculated as follows: