Limiting reactant

Chemical reactions are usually carried out with the objective of preparing a desirable compound from a precious reactant.   In order to maximise conversion of the one reactant to the desirable product, It is commonplace to use an excess of other reactants.  The reactant present in limited amount limits the amount of reaction.

In order to predict the maximum amount of a particular product that will be formed from a mixture of reactants of given masses or concentrations and volumes, it is necessary to decide which reactant is the limiting one. 

This can be done by calculating the maximum amount in moles of reaction that would occur for the amount in moles of each reactant that has been added. 
The maximum amount of reaction is equal to the amount in moles added divided by the coefficient of that substance in the balanced equation for the reaction.
  
For a reaction aA + bB  cC + dD
where A,B,C and D are substances,
and a, b, c and d are the stoichiometric coefficients
 n(reaction) = n(A) =  n(B)
 a  b

The limiting reactant predicts the smallest amount in moles of reaction.
The other reactant is said to be present in excess.
 
In the example below NaOH is the limiting reactant because the amount in moles of reaction is smaller for this reactant because 2 mol NaOH are consumed for every 1 mol of H2SO4 reacting.
 
The amount in moles of other substances that are consumed or produced can be calculated by multiplying the known amount in moles of reaction by the coefficient of the substance.

In the example below the amount in moles of Na2SO4 that would be produced is equal to the maximum amount of reaction, but the amount in moles of H2O produced is twice the amount in moles of reaction.
 
Example using these ideas:
reaction H2SO4 + 2NaOH Na2SO4 + 2H2O
amount of reactants 5 mol H2SO4   7 mol NaOH        
 divide by the coefficient in the balanced equation  
maximum amount of reaction 5 mol reaction   3.5 mol reaction
(limiting reactant)
       
multiply by the coefficient in the balanced equation  
predicted amount of products         3.5 mol Na2SO4   7.0 mol H2O