# Stoichiometry

The stoichiometry (from gr. Στοιχεῖον stoicheion "basic material" and μέτρον metron "measure") is a basic mathematical aid in chemistry . With their help, the actual proportions ( reaction equation) and amounts of substance are calculated from the qualitative knowledge of the reactants and products of a reaction . In chemical colloquial language, stoichiometry does not describe the (mostly trivial ) calculation, but the result.

In practice, reactions in the laboratory are often carried out “unstoichiometrically”: at least one reactant is used in excess and is consequently not completely converted. In equilibrium reactions , this can shift the equilibrium to the side of the products, which is particularly important when one of the reactants is significantly more expensive than the others.

## Basics

The calculation bases of modern stoichiometry are based (also viewed historically) on the following laws:

The laws of stoichiometry are derived from the knowledge of the structure of matter from atoms and molecules .

## Terms

### Stoichiometric balance

The stoichiometric calculations are about calculating the amount of starting material (s) (reactants) that must be used in a chemical reaction. The calculation can be reversed so that knowing the amount of reactant (s) one can determine the amount of product (s).

In order to be able to balance any reaction, a more general symbol notation is used . For example, for a simple chemical reaction it is:

${\ displaystyle \ left | \ nu _ {1} \ right | A_ {1} + \ left | \ nu _ {2} \ right | A_ {2} = \ left | \ nu _ {3} \ right | A_ {3} + \ left | \ nu _ {4} \ right | A_ {4}}$

where the stoichiometric ratios (also called stoichiometric coefficients ) are for which the German standard DIN 32642 "Symbolic description of chemical reactions" also recommends the designation "stoichiometric number". ${\ displaystyle \ nu _ {i}}$

Since different reaction equations can be set up for a reaction

${\ displaystyle \ mathrm {\ CO + {\ tfrac {1} {2}} \ O_ {2} \ longrightarrow \ CO_ {2}}}$   or   ,${\ displaystyle \ mathrm {\ 2 \ CO + \ O_ {2} \ longrightarrow \ 2 \ CO_ {2}}}$

the stoichiometric ratios must be determined before the balancing. The following applies:

• The reaction equation with the smallest whole numbers as ratios is always chosen as a reference.
• Reactants always get a negative stoichiometric ratio.
• Products always have a positive stoichiometric ratio.
• Accompanying substances that do not themselves take part in the reaction (e.g. catalysts) are assigned the stoichiometric ratio 0.

During the reaction, the proportions [more precisely the mole fraction (s)] of the reactants change to the extent that the stoichiometric ratios dictate it. The stoichiometric balance for the reactants i and k results as:

${\ displaystyle {n_ {i, 0} -n_ {i} \ over - \ nu _ {i}} = {n_ {k, 0} -n_ {k} \ over - \ nu _ {k}}}$

Simple reshaping gives the discontinuous process, called record operation

${\ displaystyle {n_ {i, 0} -n_ {i} \ over n_ {k, 0} -n_ {k}} = {\ nu _ {i} \ over \ nu _ {k}}}$

and accordingly for the continuous process, called flow operation

${\ displaystyle {{\ dot {n}} _ {i, 0} - {\ dot {n}} _ {i} \ over {\ dot {n}} _ {k, 0} - {\ dot {n }} _ {k}} = {\ nu _ {i} \ over \ nu _ {k}}}$

With: ${\ displaystyle {\ dot {n}} = {dn \ over dt}}$

### Turnover (X i )

The conversion X i is a term used in chemical reaction engineering, which indicates what proportion of the original starting material i used was converted into other chemical substances by chemical reaction when it left the reactor . Expressed somewhat more mathematically: The conversion (degree) X i is the proportion of the converted amount of component i based on its originally used amount n i, 0 , where n i is the remaining amount of component i:

${\ displaystyle X _ {\ mathrm {i}} = {n _ {\ mathrm {i, 0}} -n _ {\ mathrm {i}} \ over n _ {\ mathrm {i, 0}}} = 1- {n_ {\ mathrm {i}} \ over n _ {\ mathrm {i, 0}}}}$

If several starting materials are involved, the degree of conversion is based on the convention that is limiting or that is in deficit.

### Yield (Y P )

The yield Y P is a term used in chemical reaction engineering that indicates the amount of a product P based on the key component (k), i.e. the substance that is present in a smaller amount than would correspond to the stoichiometry of the reaction.

The following applies to discontinuous record operation:

${\ displaystyle Y_ {P} = {n_ {P} -n_ {P, 0} \ over n_ {k, 0}} \ cdot {\ left | v_ {k} \ right | \ over v_ {P}}}$

For a continuous flow or flow operation, the following applies accordingly:

${\ displaystyle Y_ {P} = {{\ dot {n}} _ {P} - {\ dot {n}} _ {P, 0} \ over {\ dot {n}} _ {k, 0}} \ cdot {\ left | v_ {k} \ right | \ over v_ {P}}}$

### Selectivity (S P )

The selectivity S P of a chemical conversion or of a reactor is a term used in chemical reaction engineering which indicates which proportion of the total reactant converted was converted into the desired target product , taking into account the stoichiometry . As a rule, not all molecules of the starting material are converted into the desired product, since other products can also arise through subsequent or competitive reactions:

${\ displaystyle S_ {p} = {\ mathrm {formed \; amount} \, (k) \ over \ mathrm {converted \; amount} \, (i)} = {(n_ {p} -n_ {p, 0}) \ cdot \ left | v_ {k} \ right | \ over (n_ {k, 0} -n_ {k}) \ cdot v_ {p}} = {Y_ {p} \ over X_ {i}}}$

### Conversion, yield and selectivity

If you combine the definitions for conversion, yield and selectivity with one another, you get a simple relationship between the three variables:

${\ displaystyle Y_ {P} = X_ {i} \ cdot S_ {P}}$

This means that if there is only one possible reaction (S = 1), the yield Y is automatically equal to the conversion X.