5. Its also called fractional change method. The time
taken to complete one half of the reaction is
independent of initial concentration of the
reactant for a first order reaction, inversely
proportional to the initial concentration of the
reactant for a second order reaction, inversely
proportional to the square of the initial
concentration of the reactant for a third order
reaction. This is so, provided that the reactants
are all taken at the same initial concentration.
Thus in general for a reaction of nth order,
HALF LIFE METHOD
6. t0.5 α 1/ an-1
suppose we start with two independent reactions with initial
concentrations a1 and a2 . Let the corresponding times be t1 and t2,
respectively, then
t1 α 1/a1
n-1
and t2 α 1/a2
n-1
or t1/t2 = (a2/a1)n-1
or logt1/t2 = (n-1) log (a2/a1)
or n= 1+ log (t1/t2)/log (a2/a1)
From this equation the order of reaction, n can be calculated.
In case of gaseous reactions,the initial pressure (p) can be taken instead
of initial concentration (a), so that :
n= 1+ log (t1/t2 )/log (p2/p1)
7. GRAPHICAL METHOD
The reaction velocity in a first order reaction varies as one
concentration term,while in a second order reaction,the
reaction velocity is dependent on two concentration terms
and so on. Mathematically,we can express the reaction
velocity for a reaction of nth order as:
dx/dt=k(a-x)n ........( i )
where a is the initial concentration and x is the amount of
reactant at time t
If a straight line is obtained by plotting dx/dt and (a-x)n,then the
reaction is of nth order. In the case of zero order reaction, a
straight line is obtained by plotting x against t. For a first order
reaction, a straight line is obtained by plotting dx/dt against
(a-x).
9. Similarly, for a second order reaction, a
straight line is obtained by plotting dx/dt
against (a-x)2
(a-x)2
dx/dt
10. The values of dx/dt at different intervals of
time can be determined by plotting a curve
between x(the amount of substance
decomposed) and time t. The value of dx/dt at
a particular time corresponding to a particular
value of (a-x) is given by the slope of the curve
at that point.
11.
12. On taking logarithm of equation (i) we get,
log dx/dt= log k+n log (a-x)
A curve when plotted between log dx/dt and log
(a-x) will give a straight line, the slope of
which wil give the value of n, i.e., the order of
reaction.
