### Stoichiometry

Stoichiometry is a measure of reactants and product in a given reaction. Jeremias Benjamin Richter first introduced the term in 1792. The principle of stoichiometry is based on four fundamental laws of reactions as follows:

a) Law of conservation of mass:Antoine Lavoisier first proposed it in 19th century. It states that for any closed system, which is closed for transfer of mass or energy, the mass of the system should remain constant over time, as the system cannot change quantity by itself unless it is added or removed.

b) Law of definite proportions:Proust proposed this law in 1806. It states that the chemical compound always contains exactly same proportion of elements by mass. In other words all samples of a given chemical compound have same elemental composition by mass.

c) Law of multiple proportions: John Dalton proposed this law in 1808 along the side of law of conversation of mass and law of definite proportions. It states if two elements form more than one compound between them, then the ratio of the masses of the second, which combine with a fixed mass of first element, will be ratios of small whole numbers.

This law fails with non-stoichiometric compounds and also doesn’t work well with polymers and oligomers.

d) Law of reciprocal proportions: Jeremias Richter in 1791 proposed this law. It states that the proportion in which elements combine across the number of different elements. If element A combines with element B and also with C, then, if B and C combine together, the proportion by weight in which they do so will be simply related to the weights of B and C which separately combine with a constant weight of A.

Stoichiometric amount or stoichiometric ratio is the ratio of reagents taking part in the reaction by taking into consideration reactions proceeds to completion. Further, stoichiometric reactant is a reactant that is consumed for reaction, which is different from catalytic reactant. Broadly, stoichiometry is not only used for balancing the equation but also used for unit conversions like grams to moles or from grams to milliliters.

Examples of use stoichiometry in balancing the equations:

2H2 + O2 2H2O ———– (1a)

Example for conversion of gram to moles: The molecular weight of a compound is expressed as gm/mole. Hence, one have to divide given mass of compound with its molecular weight to determine the quantity in moles as shown below

2 gm of NaCl contains: 0.034 moles of NaCl

2.00 g NaCl/ 58.44 NaCl mole-1

=0.034 mole

Stoichiometry can also be used to determine the concentration of product of reaction. For example, in a given reaction where 120 g of propane reacts with oxygen producing carbon dioxide and water. Following are the steps to be followed for determining yield of water produced.

a) Write and balance the reaction equation

C3H8 + 5O2 3CO2 + 4H2O ———– (1b)

b) Determination of mass of water produced

mH2O= (120/ 44.1) (4x 18.02)= 196 g

In some reactions there are limiting reagents which limits the amount of product is formed even though they are completely consumed during the reaction. On the other hand excess reactant is material that is left over once the reaction is stopped due to limiting reactant.

In a given reaction % yield of product = (practical yield/theoretical yield) x 100

Under ideal conditions the stoichiometric yield of product should be 100%. However, the efficiency is never 100%. For example in the given reaction of conversion of lead sulfate to lead oxide:

2PbS + 3O2 2 PbO + 2SO2

There is a possibility that amount of PbO produced is lesser then starting the material (PbS). Under these conditions mathematically PbS may serve as limiting reagent for production of PbO.

Stoichiometric coefficient is a value used to determine the number of molecules, which participates in a given reaction. For example in a given reaction of methane with oxygen to produce water an carbon dioxide. Stoichiometric coefficient of reactants CH4 and O2 is -1 and -2 whereas the stoichiometric coefficient of products CO2 and H20 is +1 and +2 respectively.

CH4 + 2O2 CO2 + 2H2O ———– (2a)

Mathematically stoichiometric coefficient of reaction system for an i-th component can be explained by equation

vi= DNi/ Dx, ———– (2b)

Where, vi= stoichiometric coefficient, DNi= number of molecules of i and x is the progress variable or extent of reaction. The extent of reaction is given by equation dx= dnB/vB, vB is stoichiometric number of reaction entity B (reactant or product) and nB is the corresponding amount.

Stoichiometry is also applied to reactions where product obtained is gas. This is also called as gas stoichiometry. But it is applicable only when gases produced is assumed to an ideal gas and pressure, temperature and volume of gas is also known. Mostly the standard (S) temperature (T) and pressure (P) is taken as 0Â°C and 1 bar is applied respectively for stoichiometric calculations if no specifications are provided. The ideal gas equation useful for the calculation is given as

PV= nRT ——– (3)