For a reaction A + B → C the following kinetic data are obtained

Observation	[A]	[B]	Rate
1	0.1	0.2	0.01
2	0.2	0.2	0.04
3	0.2	0.8	0.08

 

The overall order of the reaction is

Concept:

Rate of a Reaction:

• The rate of a reaction is the velocity of a reaction.
• It is the amount of chemical change occurring with time.
• As the reaction continues, the amount or concentration of reactants decreases, and the concentration of products increases.

Thus it can be regarded as the rate of decrease of reactants or the rate of increase of products.

Rate Law:

• Rate law states that the rate of a reaction is proportional to the concentration of the reactants raised to the power of the order of the reaction.

In mathematical terms, we can say that

\( Rate = - (dc/dt) \); the rate of decrease of reactants

\(Rate= dx/dt\) ; the rate of increase of reactants

\(Rate = k[C]^n\) ; where 'k' = rate constant and 'n' = order of a reaction.

​Order of a reaction:

• The order of a reaction is the number of concentration terms on which the reaction rate depends.
• If multiple concentration terms are involved, then the order of a reaction is the sum of all powers.
• For example if -

\(- (dc/dt) = k[A]^x[B]^y ,\) then

\( order = x + y​\)

Calculation:

Given: 

The reaction is A + B→ C\(% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % GGUaGaaGimaiaaigdaaeaacaGGUaGaaGimaiaaisdaaaGaeyypa0Za % aiWaaeaadaWcaaqaaiaac6cacaaIXaaabaGaaiOlaiaaikdaaaaaca % GL7bGaayzFaaWaaiWaaeaadaWcaaqaaiaac6cacaaIYaaabaGaaiOl % aiaaikdaaaaacaGL7bGaayzFaaaaaa!4596! \frac{{.01}}{{.04}} = \left\{ {\frac{{.1}}{{.2}}} \right\}\left\{ {\frac{{.2}}{{.2}}} \right\}\)

Let the order of the reaction w.r.t A be 'n' and w.r.t B be 'm'.

\(\frac{{R_1}}{{R_2}} = \frac{{.01}}{{.04}} = \frac{{k[.1]^n[.2]^m}}{{k[.2]^n[.2]^m}}\)

\(\frac{{.01}}{{.04}} = \left\{ {\frac{{.1}}{{.2}}} \right\}^n \)

\(\left\{ {\frac{{.1}}{{.2}}} \right\}^2 = \left\{ {\frac{{.1}}{{.2}}} \right\}^n\)

Equating the powers as the bases are equal, we get 'n' = 2.

again, \(\frac{{R_2}}{{R_3}} = \frac{{.04}}{{.08}} = \frac{{k[.2]^n[.2]^m}}{{k[.2]^n[.8]^m}}\)

or,  \({.04\over.08}= \left\{ {\frac{{.1}}{{.4}}} \right\}^m\)

 \([{{.1\over .4}}]^{1\over2}= \left\{ {\frac{{.1}}{{.4}}} \right\}^m\)

Equating the powers as the bases are equal, we get 'm' = ½

Hence, the total order =  \(m + n = 2.5\)