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3205-3208
6 Example 3 6 Solution Solution Solution Solution Solution Rationalised 2023-24 76 Chemistry The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration It is represented as t1/2 For a zero order reaction, rate constant is given by equation 3
1
3206-3209
6 Solution Solution Solution Solution Solution Rationalised 2023-24 76 Chemistry The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration It is represented as t1/2 For a zero order reaction, rate constant is given by equation 3 7
1
3207-3210
It is represented as t1/2 For a zero order reaction, rate constant is given by equation 3 7 [ ] [ ] R0 R k t − = [ ] [ ]0 1/2 1 R At , R 2 t =t = The rate constant at t1/2 becomes [ ] [ ] 0 0 1/2 1/2 R R k −t = [ ]0 1/2 R 2 t k = It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant
1
3208-3211
For a zero order reaction, rate constant is given by equation 3 7 [ ] [ ] R0 R k t − = [ ] [ ]0 1/2 1 R At , R 2 t =t = The rate constant at t1/2 becomes [ ] [ ] 0 0 1/2 1/2 R R k −t = [ ]0 1/2 R 2 t k = It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant For the first order reaction, [ ] [ ] 0 2
1
3209-3212
7 [ ] [ ] R0 R k t − = [ ] [ ]0 1/2 1 R At , R 2 t =t = The rate constant at t1/2 becomes [ ] [ ] 0 0 1/2 1/2 R R k −t = [ ]0 1/2 R 2 t k = It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant For the first order reaction, [ ] [ ] 0 2 303 R log R k t = (3
1
3210-3213
[ ] [ ] R0 R k t − = [ ] [ ]0 1/2 1 R At , R 2 t =t = The rate constant at t1/2 becomes [ ] [ ] 0 0 1/2 1/2 R R k −t = [ ]0 1/2 R 2 t k = It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant For the first order reaction, [ ] [ ] 0 2 303 R log R k t = (3 15) at t1/2 [ ] [ ]0 R R 2 = (3
1
3211-3214
For the first order reaction, [ ] [ ] 0 2 303 R log R k t = (3 15) at t1/2 [ ] [ ]0 R R 2 = (3 16) So, the above equation becomes [ ] [ ] 0 1/2 2
1
3212-3215
303 R log R k t = (3 15) at t1/2 [ ] [ ]0 R R 2 = (3 16) So, the above equation becomes [ ] [ ] 0 1/2 2 303 R log R/2 k t = or 1/2 2
1
3213-3216
15) at t1/2 [ ] [ ]0 R R 2 = (3 16) So, the above equation becomes [ ] [ ] 0 1/2 2 303 R log R/2 k t = or 1/2 2 303 log 2 t k  1/2 2
1
3214-3217
16) So, the above equation becomes [ ] [ ] 0 1/2 2 303 R log R/2 k t = or 1/2 2 303 log 2 t k  1/2 2 303 0
1
3215-3218
303 R log R/2 k t = or 1/2 2 303 log 2 t k  1/2 2 303 0 301 t k = × 1/2 0
1
3216-3219
303 log 2 t k  1/2 2 303 0 301 t k = × 1/2 0 693 t k = (3
1
3217-3220
303 0 301 t k = × 1/2 0 693 t k = (3 17) 2 pN O5 = 1
1
3218-3221
301 t k = × 1/2 0 693 t k = (3 17) 2 pN O5 = 1 5 – 2 × 0
1
3219-3222
693 t k = (3 17) 2 pN O5 = 1 5 – 2 × 0 512 = 0
1
3220-3223
17) 2 pN O5 = 1 5 – 2 × 0 512 = 0 476 atm Using equation (3
1
3221-3224
5 – 2 × 0 512 = 0 476 atm Using equation (3 16) i A 4 1 0
1
3222-3225
512 = 0 476 atm Using equation (3 16) i A 4 1 0 5 atm 2
1
3223-3226
476 atm Using equation (3 16) i A 4 1 0 5 atm 2 303 2
1
3224-3227
16) i A 4 1 0 5 atm 2 303 2 303 log 100slog 0
1
3225-3228
5 atm 2 303 2 303 log 100slog 0 476 atm 2
1
3226-3229
303 2 303 log 100slog 0 476 atm 2 303 0
1
3227-3230
303 log 100slog 0 476 atm 2 303 0 0216 4
1
3228-3231
476 atm 2 303 0 0216 4 98 10 s 100s p k t p         3
1
3229-3232
303 0 0216 4 98 10 s 100s p k t p         3 3
1
3230-3233
0216 4 98 10 s 100s p k t p         3 3 3 Half-Life of a Reaction Rationalised 2023-24 77 Chemical Kinetics A first order reaction is found to have a rate constant, k = 5
1
3231-3234
98 10 s 100s p k t p         3 3 3 Half-Life of a Reaction Rationalised 2023-24 77 Chemical Kinetics A first order reaction is found to have a rate constant, k = 5 5 × 10-14 s-1
1
3232-3235
3 3 Half-Life of a Reaction Rationalised 2023-24 77 Chemical Kinetics A first order reaction is found to have a rate constant, k = 5 5 × 10-14 s-1 Find the half-life of the reaction
1
3233-3236
3 Half-Life of a Reaction Rationalised 2023-24 77 Chemical Kinetics A first order reaction is found to have a rate constant, k = 5 5 × 10-14 s-1 Find the half-life of the reaction Half-life for a first order reaction is t1/2 = 0
1
3234-3237
5 × 10-14 s-1 Find the half-life of the reaction Half-life for a first order reaction is t1/2 = 0 693 k t1/2 = –14 –1 0
1
3235-3238
Find the half-life of the reaction Half-life for a first order reaction is t1/2 = 0 693 k t1/2 = –14 –1 0 693 5
1
3236-3239
Half-life for a first order reaction is t1/2 = 0 693 k t1/2 = –14 –1 0 693 5 5×10 s = 1
1
3237-3240
693 k t1/2 = –14 –1 0 693 5 5×10 s = 1 26 × 1013s Show that in a first order reaction, time required for completion of 99
1
3238-3241
693 5 5×10 s = 1 26 × 1013s Show that in a first order reaction, time required for completion of 99 9% is 10 times of half-life (t1/2) of the reaction
1
3239-3242
5×10 s = 1 26 × 1013s Show that in a first order reaction, time required for completion of 99 9% is 10 times of half-life (t1/2) of the reaction When reaction is completed 99
1
3240-3243
26 × 1013s Show that in a first order reaction, time required for completion of 99 9% is 10 times of half-life (t1/2) of the reaction When reaction is completed 99 9%, [R]n = [R]0 – 0
1
3241-3244
9% is 10 times of half-life (t1/2) of the reaction When reaction is completed 99 9%, [R]n = [R]0 – 0 999[R]0 k =     0 2
1
3242-3245
When reaction is completed 99 9%, [R]n = [R]0 – 0 999[R]0 k =     0 2 303 R log R t =       0 0 0 2
1
3243-3246
9%, [R]n = [R]0 – 0 999[R]0 k =     0 2 303 R log R t =       0 0 0 2 303 R log 0
1
3244-3247
999[R]0 k =     0 2 303 R log R t =       0 0 0 2 303 R log 0 999 R R t  = 2
1
3245-3248
303 R log R t =       0 0 0 2 303 R log 0 999 R R t  = 2 303 log103 t t = 6
1
3246-3249
303 R log 0 999 R R t  = 2 303 log103 t t = 6 909/k For half-life of the reaction t1/2 = 0
1
3247-3250
999 R R t  = 2 303 log103 t t = 6 909/k For half-life of the reaction t1/2 = 0 693/k 1/2 t t = 6
1
3248-3251
303 log103 t t = 6 909/k For half-life of the reaction t1/2 = 0 693/k 1/2 t t = 6 909 10 0
1
3249-3252
909/k For half-life of the reaction t1/2 = 0 693/k 1/2 t t = 6 909 10 0 693 k k   It can be seen that for a first order reaction, half-life period is constant, i
1
3250-3253
693/k 1/2 t t = 6 909 10 0 693 k k   It can be seen that for a first order reaction, half-life period is constant, i e
1
3251-3254
909 10 0 693 k k   It can be seen that for a first order reaction, half-life period is constant, i e , it is independent of initial concentration of the reacting species
1
3252-3255
693 k k   It can be seen that for a first order reaction, half-life period is constant, i e , it is independent of initial concentration of the reacting species The half-life of a first order equation is readily calculated from the rate constant and vice versa
1
3253-3256
e , it is independent of initial concentration of the reacting species The half-life of a first order equation is readily calculated from the rate constant and vice versa For zero order reaction t1/2 µµµµµ [R]0
1
3254-3257
, it is independent of initial concentration of the reacting species The half-life of a first order equation is readily calculated from the rate constant and vice versa For zero order reaction t1/2 µµµµµ [R]0 For first order reaction t1/2 is independent of [R]0
1
3255-3258
The half-life of a first order equation is readily calculated from the rate constant and vice versa For zero order reaction t1/2 µµµµµ [R]0 For first order reaction t1/2 is independent of [R]0 Example 3
1
3256-3259
For zero order reaction t1/2 µµµµµ [R]0 For first order reaction t1/2 is independent of [R]0 Example 3 7 Example 3
1
3257-3260
For first order reaction t1/2 is independent of [R]0 Example 3 7 Example 3 7 Example 3
1
3258-3261
Example 3 7 Example 3 7 Example 3 7 Example 3
1
3259-3262
7 Example 3 7 Example 3 7 Example 3 7 Example 3
1
3260-3263
7 Example 3 7 Example 3 7 Example 3 7 Solution Solution Solution Solution Solution Example 3
1
3261-3264
7 Example 3 7 Example 3 7 Solution Solution Solution Solution Solution Example 3 8 Example 3
1
3262-3265
7 Example 3 7 Solution Solution Solution Solution Solution Example 3 8 Example 3 8 Example 3
1
3263-3266
7 Solution Solution Solution Solution Solution Example 3 8 Example 3 8 Example 3 8 Example 3
1
3264-3267
8 Example 3 8 Example 3 8 Example 3 8 Example 3
1
3265-3268
8 Example 3 8 Example 3 8 Example 3 8 Solution Solution Solution Solution Solution Table 3
1
3266-3269
8 Example 3 8 Example 3 8 Solution Solution Solution Solution Solution Table 3 4 summarises the mathematical features of integrated laws of zero and first order reactions
1
3267-3270
8 Example 3 8 Solution Solution Solution Solution Solution Table 3 4 summarises the mathematical features of integrated laws of zero and first order reactions Table 3
1
3268-3271
8 Solution Solution Solution Solution Solution Table 3 4 summarises the mathematical features of integrated laws of zero and first order reactions Table 3 4: Integrated Rate Laws for the Reactions of Zero and First Order Order Reaction Differential Integrated Straight Half- Units of k type rate law rate law line plot life 0 R® P d[R]/dt = -k kt = [R]0-[R] [R] vs t [R]0/2k conc time-1 or mol L–1s–1 1 R® P d[R]/dt = -k[R] [R] = [R]0e-kt ln[R] vs t ln 2/k time-1 or s–1 or kt = ln{[R]0/[R]} Rationalised 2023-24 78 Chemistry Most of the chemical reactions are accelerated by increase in temperature
1
3269-3272
4 summarises the mathematical features of integrated laws of zero and first order reactions Table 3 4: Integrated Rate Laws for the Reactions of Zero and First Order Order Reaction Differential Integrated Straight Half- Units of k type rate law rate law line plot life 0 R® P d[R]/dt = -k kt = [R]0-[R] [R] vs t [R]0/2k conc time-1 or mol L–1s–1 1 R® P d[R]/dt = -k[R] [R] = [R]0e-kt ln[R] vs t ln 2/k time-1 or s–1 or kt = ln{[R]0/[R]} Rationalised 2023-24 78 Chemistry Most of the chemical reactions are accelerated by increase in temperature For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50oC, 5 h at 25oC and 10 days at 0oC
1
3270-3273
Table 3 4: Integrated Rate Laws for the Reactions of Zero and First Order Order Reaction Differential Integrated Straight Half- Units of k type rate law rate law line plot life 0 R® P d[R]/dt = -k kt = [R]0-[R] [R] vs t [R]0/2k conc time-1 or mol L–1s–1 1 R® P d[R]/dt = -k[R] [R] = [R]0e-kt ln[R] vs t ln 2/k time-1 or s–1 or kt = ln{[R]0/[R]} Rationalised 2023-24 78 Chemistry Most of the chemical reactions are accelerated by increase in temperature For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50oC, 5 h at 25oC and 10 days at 0oC You also know that in a mixture of potassium permanganate (KMnO4) and oxalic acid (H2C2O4), potassium permanganate gets decolourised faster at a higher temperature than that at a lower temperature
1
3271-3274
4: Integrated Rate Laws for the Reactions of Zero and First Order Order Reaction Differential Integrated Straight Half- Units of k type rate law rate law line plot life 0 R® P d[R]/dt = -k kt = [R]0-[R] [R] vs t [R]0/2k conc time-1 or mol L–1s–1 1 R® P d[R]/dt = -k[R] [R] = [R]0e-kt ln[R] vs t ln 2/k time-1 or s–1 or kt = ln{[R]0/[R]} Rationalised 2023-24 78 Chemistry Most of the chemical reactions are accelerated by increase in temperature For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50oC, 5 h at 25oC and 10 days at 0oC You also know that in a mixture of potassium permanganate (KMnO4) and oxalic acid (H2C2O4), potassium permanganate gets decolourised faster at a higher temperature than that at a lower temperature It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled
1
3272-3275
For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50oC, 5 h at 25oC and 10 days at 0oC You also know that in a mixture of potassium permanganate (KMnO4) and oxalic acid (H2C2O4), potassium permanganate gets decolourised faster at a higher temperature than that at a lower temperature It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3
1
3273-3276
You also know that in a mixture of potassium permanganate (KMnO4) and oxalic acid (H2C2O4), potassium permanganate gets decolourised faster at a higher temperature than that at a lower temperature It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3 18)
1
3274-3277
It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3 18) It was first proposed by Dutch chemist, J
1
3275-3278
The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3 18) It was first proposed by Dutch chemist, J H
1
3276-3279
18) It was first proposed by Dutch chemist, J H van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation
1
3277-3280
It was first proposed by Dutch chemist, J H van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation 3
1
3278-3281
H van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation 3 4 Temperature 3
1
3279-3282
van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation 3 4 Temperature 3 4 Temperature 3
1
3280-3283
3 4 Temperature 3 4 Temperature 3 4 Temperature 3
1
3281-3284
4 Temperature 3 4 Temperature 3 4 Temperature 3 4 Temperature 3
1
3282-3285
4 Temperature 3 4 Temperature 3 4 Temperature 3 4 Temperature Dependence of Dependence of Dependence of Dependence of Dependence of the Rate of a the Rate of a the Rate of a the Rate of a the Rate of a Reaction Reaction Reaction Reaction Reaction The order of a reaction is sometimes altered by conditions
1
3283-3286
4 Temperature 3 4 Temperature 3 4 Temperature Dependence of Dependence of Dependence of Dependence of Dependence of the Rate of a the Rate of a the Rate of a the Rate of a the Rate of a Reaction Reaction Reaction Reaction Reaction The order of a reaction is sometimes altered by conditions There are many reactions which obey first order rate law although they are higher order reactions
1
3284-3287
4 Temperature 3 4 Temperature Dependence of Dependence of Dependence of Dependence of Dependence of the Rate of a the Rate of a the Rate of a the Rate of a the Rate of a Reaction Reaction Reaction Reaction Reaction The order of a reaction is sometimes altered by conditions There are many reactions which obey first order rate law although they are higher order reactions Consider the hydrolysis of ethyl acetate which is a chemical reaction between ethyl acetate and water
1
3285-3288
4 Temperature Dependence of Dependence of Dependence of Dependence of Dependence of the Rate of a the Rate of a the Rate of a the Rate of a the Rate of a Reaction Reaction Reaction Reaction Reaction The order of a reaction is sometimes altered by conditions There are many reactions which obey first order rate law although they are higher order reactions Consider the hydrolysis of ethyl acetate which is a chemical reaction between ethyl acetate and water In reality, it is a second order reaction and concentration of both ethyl acetate and water affect the rate of the reaction
1
3286-3289
There are many reactions which obey first order rate law although they are higher order reactions Consider the hydrolysis of ethyl acetate which is a chemical reaction between ethyl acetate and water In reality, it is a second order reaction and concentration of both ethyl acetate and water affect the rate of the reaction But water is taken in large excess for hydrolysis, therefore, concentration of water is not altered much during the reaction
1
3287-3290
Consider the hydrolysis of ethyl acetate which is a chemical reaction between ethyl acetate and water In reality, it is a second order reaction and concentration of both ethyl acetate and water affect the rate of the reaction But water is taken in large excess for hydrolysis, therefore, concentration of water is not altered much during the reaction Thus, the rate of reaction is affected by concentration of ethyl acetate only
1
3288-3291
In reality, it is a second order reaction and concentration of both ethyl acetate and water affect the rate of the reaction But water is taken in large excess for hydrolysis, therefore, concentration of water is not altered much during the reaction Thus, the rate of reaction is affected by concentration of ethyl acetate only For example, during the hydrolysis of 0
1
3289-3292
But water is taken in large excess for hydrolysis, therefore, concentration of water is not altered much during the reaction Thus, the rate of reaction is affected by concentration of ethyl acetate only For example, during the hydrolysis of 0 01 mol of ethyl acetate with 10 mol of water, amounts of the reactants and products at the beginning (t = 0) and completion (t) of the reaction are given as under
1
3290-3293
Thus, the rate of reaction is affected by concentration of ethyl acetate only For example, during the hydrolysis of 0 01 mol of ethyl acetate with 10 mol of water, amounts of the reactants and products at the beginning (t = 0) and completion (t) of the reaction are given as under CH3COOC2H5 + H2O H  CH3COOH + C2H5OH t = 0 0
1
3291-3294
For example, during the hydrolysis of 0 01 mol of ethyl acetate with 10 mol of water, amounts of the reactants and products at the beginning (t = 0) and completion (t) of the reaction are given as under CH3COOC2H5 + H2O H  CH3COOH + C2H5OH t = 0 0 01 mol 10 mol 0 mol 0 mol t 0 mol 9
1
3292-3295
01 mol of ethyl acetate with 10 mol of water, amounts of the reactants and products at the beginning (t = 0) and completion (t) of the reaction are given as under CH3COOC2H5 + H2O H  CH3COOH + C2H5OH t = 0 0 01 mol 10 mol 0 mol 0 mol t 0 mol 9 99 mol 0
1
3293-3296
CH3COOC2H5 + H2O H  CH3COOH + C2H5OH t = 0 0 01 mol 10 mol 0 mol 0 mol t 0 mol 9 99 mol 0 01 mol 0
1
3294-3297
01 mol 10 mol 0 mol 0 mol t 0 mol 9 99 mol 0 01 mol 0 01 mol The concentration of water does not get altered much during the course of the reaction
1
3295-3298
99 mol 0 01 mol 0 01 mol The concentration of water does not get altered much during the course of the reaction So, the reaction behaves as first order reaction
1
3296-3299
01 mol 0 01 mol The concentration of water does not get altered much during the course of the reaction So, the reaction behaves as first order reaction Such reactions are called pseudo first order reactions
1
3297-3300
01 mol The concentration of water does not get altered much during the course of the reaction So, the reaction behaves as first order reaction Such reactions are called pseudo first order reactions Inversion of cane sugar is another pseudo first order reaction
1
3298-3301
So, the reaction behaves as first order reaction Such reactions are called pseudo first order reactions Inversion of cane sugar is another pseudo first order reaction C12H22O11 + H2O H+ → C6H12O6 + C6H12O6 Cane sugar Glucose Fructose Rate = k [C12H22O11] Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions 3
1
3299-3302
Such reactions are called pseudo first order reactions Inversion of cane sugar is another pseudo first order reaction C12H22O11 + H2O H+ → C6H12O6 + C6H12O6 Cane sugar Glucose Fructose Rate = k [C12H22O11] Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions 3 5 A first order reaction has a rate constant 1
1
3300-3303
Inversion of cane sugar is another pseudo first order reaction C12H22O11 + H2O H+ → C6H12O6 + C6H12O6 Cane sugar Glucose Fructose Rate = k [C12H22O11] Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions 3 5 A first order reaction has a rate constant 1 15 × 10-3 s-1
1
3301-3304
C12H22O11 + H2O H+ → C6H12O6 + C6H12O6 Cane sugar Glucose Fructose Rate = k [C12H22O11] Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions 3 5 A first order reaction has a rate constant 1 15 × 10-3 s-1 How long will 5 g of this reactant take to reduce to 3 g
1
3302-3305
5 A first order reaction has a rate constant 1 15 × 10-3 s-1 How long will 5 g of this reactant take to reduce to 3 g 3
1
3303-3306
15 × 10-3 s-1 How long will 5 g of this reactant take to reduce to 3 g 3 6 Time required to decompose SO2Cl2 to half of its initial amount is 60 minutes
1
3304-3307
How long will 5 g of this reactant take to reduce to 3 g 3 6 Time required to decompose SO2Cl2 to half of its initial amount is 60 minutes If the decomposition is a first order reaction, calculate the rate constant of the reaction