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## Order of reaction-

### Solution )

#### i) For first order reaction-

t  = 1 hour  , a =1 mole, x = 3/4 mole

K= 2.303 / t [log (a/a-x)]

K = 2.303 / 1 [log  1 /( 1 – 3/4)]

K = 2.303  [log 1 /( 1/4)]

K = 2.303 (log 4)

log 4 = 0.6020

K = 2.303 x 0.6020

#### ii) For  second order reaction –

a=1 mole , x = 3/4 mole , t = 1 hour

K =1/t [x/a(a-x)]

K =1/1 [(3/4)/1(1 – 3/4)]

K = 1/ 1 [ (3/4)/( 1/4)

### Solution )

a=100 , x = 20,  t = 500 sec.

K =1/t [x/a(a-x)]

K = 1/ 500  [20/100 (100 – 20)

K = 1/ 500 (20/ 100 x 80)

K=20 / 500 x 100 x 80

#### K = 5 x 10-6 litre mole-1 sec-1

a = 100 , x = 60

t =1/K [x/a(a-x)]

t  = 1/ 5 x 10 -6  [60/100 (100 – 60)

t = 1/ 5 x 10 -6 (60/ 100 x 40)

t = 60 / 5 x 10 -6 x 100 x 40

### Solution-

(i) K = 6.2 x 10 -4 sec-1 ,

[N2O5] = 2.5 mole / litre

Rate  = K [N2O5] = 6.2 x 10 -4  x 2.5

### Rate =1.55 x 10-3  mole litre-1sec-1 Ans

(ii)

K = 6.2 x 10 -4 sec-1 ,

[N2O5] = 0.50  mole / litre

Rate  = K [N2O5] = 6.2 x 10 -4  x 0.50

### Rate = 3.1 x 10-4  mole litre-1sec-1 Ans

(iii) Rate = 4.2 x 10 -3 mole litre-1sec-1

K = 6.2 x 10 -4 sec-1 ,

[N2O5] = Rate / K

= 4.2 x 10 -3/ 6.2 x 10 -4

### Solution –

Rate = K[A] [B] 2/3

order of reaction = 1 + 2/3

### order of reaction = 1.67 Ans.

#### Unit of rate –

Rate = dx/dt= (mole/litre)/ time

### unit of rate = mole litre-1 time -1 Ans.

#### Unit of rate constant –

Rate = K [A] [B]2/3

K = (mole litre-1 time -1)/ (mole litre-1)(mole litre-1)2/3