DETERMINATION OF ORDER OF REACTION........

COMPILED BY TAKEEN KHURSHID

ORDER OF REACTION

• ORDER OF REACTION IS GIVEN BY THE NUMBER OF ATOMS OR MOLECULES WHOSE CONCENTRATION CHANGES DURING A CHEMICAL REACTION.

• Different methods for determining order of reaction:

INTEGRATION METHODHALF LIFE METHODGRAPHICAL METHODOSTWALD METHOD

INTEGRATION METHODHALF LIFE METHODGRAPHICAL METHODOSTWALD METHOD

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

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/a1n-1

and t2 α 1/a2n-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)

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).

(a-x)

dx/dtFir

st order

reacti

on

Similarly, for a second order reaction, a straight line is obtained by plotting dx/dt against (a-x)2

(a-x)2

dx/dt

seco

nd order reac

tion

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.

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.

The intercept on the axis of Y will give the value of log k.

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