Explain why the end point does not coincide with the equivalence point
when usingusing an acid-base visual indicator, Hin. Show the necessary
chemical equation

Indicators are generally weak acids in an equilibrium with water.  The
colour depends on the position of the equilibrium which in turn
depends on the total [H30+], that is on the pH of the solution to
which the indicator is added.
HIn(aq) + H2O(l) -----> H30+(aq) + In-(aq) 
colour 1                          colour 2 
The pH at which the colour changes depends on the acid dissociation
constant Ka, for the indicator known as the indicator constant KIn.
KIn = [H3O+][In-] / [HInd] 
The colour of the indicator changes from one colour to another at its
end point. At the end point  [HInd] = [In-]
Therefore, at the end point for an indicator (this is when half the
indicator is in acid form and half is in the form of its conjugate
base.):
KIn = [H3O+]   therefore log KIn = log[H3O+]   and   pKIn = pH 

To choose an indicator the pKIn value must be in the right pH range
for the titration being done. e.g. methyl orange pKIn = 5.1 for pH
range 4.2 - 6.3.
Strong acid and strong base - any indicator. 
Strong acid and weak base - low pH range 3.1- 4.4 e.g. methyl orange.
Weak acid and strong base - high pH range 8.3 - 10.0 e.g.
phenolphthalein.
Weak acid and weak base - narrow pH range, very hard choice. 
In each case pKIn must be matched to pH at equivalence point of
titration.
end point- mid way between 2 colours of indicator (a property of the
indicator)
equivalence point when the stoichiometric amounts of acid and alkali
have been added. End point and equivalence point must coincide for an
effective titration.


Take everything with a grain of skepticism.