new way chemistry for hong kong a-level book 2 1 rate equations and order of reactions increasing...

New Way Chemistry for Hong Kong A-Level Book 2

1

Rate Equations and Rate Equations and Order of ReactionsOrder of Reactions

Increasing concentration of reactants can increase Increasing concentration of reactants can increase the rate of reaction.the rate of reaction.

Is there any mathematical relationship between rate Is there any mathematical relationship between rate of reaction and concentration of reactants?of reaction and concentration of reactants?

YES!!!!!!YES!!!!!!

1414

Initial concentration / mol dm-3 Initial rate / mol dm-3 s-1

NO H2

0.0250 0.100 2.4 10-6

0.0250 0.050 1.2 10-6

0.0125 0.100 0.6 10-6

For the reaction:2NO(g) + 2H2(g) N2(g) + 2H2O (l)

Rate [H2(g)] when [NO(g)] is constant

Rate [NO2(g)]2 when [H2(g)] is constant

Rate [NO(g)]2 [H2(g)]

Rate = k[NO(g)]2 [H2(g)]


3

Rate Rate Equations and Equations and

Order of Order of ReactionsReactions

14.14.11


4

In general, for the reaction:

mA + nB products

(a rate equation)(a rate equation)

14.1 Rate Equations and Order of Reactions (SB p.25 NB p.8)

Rate Rate EquationEquation

• k = rate constant

• x = order of reaction with respect to reactant A

• y = order of reaction with respect to reactant B

• Overall order of reaction = x + y

Rate =

= k [A]x [B]y

m n


5

mA + nB products

14.1 Rate Equations and Order of Reactions (SB p.25)


Rate = k [A]x [B]y

• x and y are determined experimentally.experimentally.

• x and y may NOTNOT equal to m and n.

• x and y may not be whole numbers!!!

• Rate of reaction is independent of products’ concentration


6

14.1 Rate Equations and Order of Reactions (SB p.26)

Order of ReactionsOrder of Reactions

• Usually integers (0, 1, 2, … …)

• If x = 1

first order with respect to reactant A

• If y = 2

second order with respect to reactant B

• The overall reaction is a third order reaction.

Do Class Examples on p. 8


7

14.1 Rate Equations and Order of Reactions (SB p.25 NB p. 8)


• log rate = log k + x log[A] + y log[B]

• If B is kept large excess, its change in concentration will be negligible when compared with A.

log[B] ~ constant

log rate = c’ + x log[A]

when is log rate plotted against log[A]

straight line with slope = x

Rate = k [A]x [B]y


8

Zeroth, First anZeroth, First and Second Order d Second Order

ReactionsReactions

14.14.22

For the following reaction:

A product

[A] mol dm-3 Time (s)

1.00 0

0.80 10

0.70 20

0.65 30

0.53 40

: :

: :

How can we find out the order of reaction with respects to [A]?


10

Zeroth Order ReactionsZeroth Order Reactions

A products Rate = k [A]0 = k

14.2 Zeroth, First and Second Order Reactions (SB p.27 NB p.10)

e.g.

CH3COCH3(aq) + I2(aq) + H+(aq)

CH3COCH2I(aq) + I-(aq) + 2H+(aq)

Rate = k[CH3COCH3(aq)][H+(aq)][I2(aq)]0

The rate of reaction is independent of [I2]!!!

This means if we keep [CH3COCH3(aq)] and [H+(aq)] constant then measure the initial rate with various [I2(aq)], we will get the same initial rate.


11

Zeroth Order ReactionsZeroth Order Reactions14.2 Zeroth, First and Second Order Reactions (SB p.27)

[I2(aq)]


12

Zeroth Order ReactionsZeroth Order Reactions14.2 Zeroth, First and Second Order Reactions (SB p.27)

WHY???• The reaction is a multi-step reaction.• Only the slowest step affect the overall reaction rate.

A B

C

D

Iodine is not involved in the slowest step of the reaction.


13

Zeroth Order ReactionZeroth Order Reaction

[A] = -kt + [A]0

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37)

A product

Rate equation is:

A Plot of [A] against time will give a straight line

][

][ 00

dt ][

][

][

A

A

tkAd

dtkAd

kdt

AdRate


14

14.2 Zeroth, First and Second Order Reactions (SB p.28)

First Order ReactionFirst Order Reaction

2H2O2(aq) 2H2O(l) + O2(g)

Rate = k [H2O2(aq)]

• Though the stoichiometric coefficient of H2O2(aq) is 2

• Order of reaction with respect to H2O2

(aq) is 1 (determined experimentally)

• e.g Decomposition of H2O2(aq) to H2O and O2


15

First Order ReactionFirst Order Reaction

In A = -k1t + In [A]0

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.37 NB p. 9))

A product

Rate equation is:

A Plot of ln [A] against time will give a straight line

][

][ 0 1

1

1

0

][

][

][

][

][][

A

A

tdtk

A

Ad

dtkA

Ad

Akdt

AdRate


16

Half-life of First Order reactionHalf-life of First Order reaction


The time taken for half of the reactant to be converted to the product is known as the half-life of the reaction.

After time t,

[A] = [A]0

t is called the half life of the reaction.

2

1


17

Half-life of First Order ReactionHalf-life of First Order Reaction


ln[A] = -k1t + ln[A]0

k1t = ln[A]0 - ln[A]

][

][ln 0

1 A

Atk

If t = half-life (t0.5), then [A]0 = 2[A]:k1t0.5 = ln 2

15.0

2ln

kt t0.5 = constant


18

Half-life of a First Order ReactionHalf-life of a First Order Reaction


For a first order reaction:

• Half-life is a constant

Do Class Examples 1, 3 on p.10


19

Second Order ReactionSecond Order Reaction

14.5 Determination of Simple Rate Equations from Integrated Rate Equations (SB p.40 NB p.11)

A product

Rate equation is:

Integrating the above rate equation, obtain:

2]A[2t

[A]- Rate kd

d

0[A]

12[A]

1 tk

A plot of 1/[A] vs time will give a straight line


20

SummarySummary

Steps to determine the order of reaction

1. Plot a concentration-time graph

a straight line zeroth order

a curve with constant half life first order

Confirmation: ln[A] vs time straight line

2. Plot a second graph of vs time

a straight line second order

][

1

A

Do Q. 5 on p. 77Do Q. 14 on p. 80Q. 13 (more difficult)Do Q. 3 on NB p.17 Q. 2 on NB p. 21


21

Determination of Determination of Simple Rate Simple Rate Equations by Equations by

Graphical MethodGraphical MethodNotes p. 18Notes p. 18

14.4 – 14.514.4 – 14.5


22

14.4 Determination of Simple Rate Equations from Differential Rate Equations (SB p.32)

log (rate)-log (concentration) log (rate)-log (concentration) GraphGraph

rate = k[A]n

log (rate) = n log [A] + log k

• Plotting log (rate) against log [A], a straight line is obtained for any orders

• Slope of straight line = Order of reaction (n)

• y-intercept = log k

Do Q. 1 on NB p. 16


23

We need to plot two graphs:

(1) [A] vs time to find the rate at different [A]

(by slope to the curve)

(2) log (rate) vs log[A] to find the order and k


24


(a)Decide which curve in the following graph corresponds to

(i) a zeroth order reaction;

(ii) a first order reaction.

(a) (i)

(3)

(ii)

(2)


25


Isolation techniqueIsolation technique

When two or more substances react:

A + B products

• Order of reaction with respect to reactant A can be found by

• keeping concentration of B constant

(by using much excess B – isolation technique)

Rate = k[A]x[B]y Rate = k’ [A]x

Do Q. 1, 3 on p. 27Do Q 13 on p.80


26

The END

Q.13 on p. 80

t(s) v(cm3)

0 0

5 33

10 56

15 73

25 92

3600 110

5400 110

Products (not reactants)

vol. of N2 (a) in reactant/cm3

110

77

54

37

18

ln (a)

new way chemistry for hong kong a-level book 2 1 rate equations and order of reactions increasing...

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