Rate Eqn.Rate Eqn. & & Order of RxnOrder of Rxn

C. Y. Yeung (CHW, 2009)

p.01

Rate Equation Rate Equation (Rate Law)(Rate Law)

the mathematical equation relating ththe mathematical equation relating the e rate of rxnrate of rxn to the to the [reactants][reactants]..

3A + 2B 3A + 2B C C

p.02

Examples:Examples:

raterate [A][A]xx[B][B]yy

order of rxn w.r.t. [A]order of rxn w.r.t. [A]

order of rxn w.r.t. [B]order of rxn w.r.t. [B]

p.03

raterate = =rate constantrate constant

(varies with temp.!!)(varies with temp.!!)

kk[A][A]xx[B][B]yy

Therefore, the rate equation shows that:Therefore, the rate equation shows that:

rate of rxn is affected byrate of rxn is affected by [reactants] [reactants]

rate of rxn is affected byrate of rxn is affected by temperature temperature

* usually, order of reaction = * usually, order of reaction = 0, 1 0, 1 oror 2 2..

p.04

rate = k [A]rate = k [A]mm[B][B]nn

Example:Example:

If [B] and temp. are kept constant, when If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 [A] doubles, rate of reaction increases 4 times. Find the value of m.times. Find the value of m.rate = k’ [A]rate = k’ [A]mm

raterate11 = k’ [A] = k’ [A]mm and rate and rate22 = k’ (2[A]) = k’ (2[A])mm

thenthenraterate11

raterate22==

k’ [A]k’ [A]mm

k’ (2[A])k’ (2[A])mm==

11

44

==11

441122

mm m = 2m = 2

the rxn is 2the rxn is 2ndnd order w.r.t. [A]. order w.r.t. [A].

p.05

If [B] and temp. are kept constant, when [A] If [B] and temp. are kept constant, when [A] doubles, rate of reaction increases 4 times. doubles, rate of reaction increases 4 times.

How to do it?How to do it?[A] [B] Initial

rate

Expt. 1 [A]01 [B] Rate1

Expt. 2 [A]02 [B] Rate2

Expt. 3 [A]03 [B] Rate3

….. ….. ….. …..

kept constantkept constant

tt

[A][A]

[A][A]0303

[A][A]0202

[A][A]0101

initial rate methodinitial rate method

Repeat expt. with constant [A] and different [B], find n!Repeat expt. with constant [A] and different [B], find n!

Plot Plot raterate vs vs [A] [A] ::

p.06Determination of k, m and n Determination of k, m and n

by by graphical methodgraphical method

rate = k’ [A]rate = k’ [A]mm

[A] [B] Initial rate

Expt. 1 [A]1 [B] Rate1

Expt. 2 [A]2 [B] Rate2

Expt. 3 [A]3 [B] Rate3

….. ….. ….. …..

raterate

[A][A]

m = 0m = 0

m = 1m = 1

m = 2m = 2

Only m could be found!Only m could be found!

p.07rate = k’ [A]rate = k’ [A]mm

log (rate) = m log [A] + log k’log (rate) = m log [A] + log k’

log (rate)log (rate)

log [A]log [A]

y = mx + cy = mx + c

m = 0m = 0

m = 1m = 1

m = 2m = 2

log k’log k’

i.e. Both k (=k’/[B]) and m could be found!i.e. Both k (=k’/[B]) and m could be found!

p.081992 Paper II, Q.2(a)1992 Paper II, Q.2(a)

p.09

1992 Paper II, Q.2(a) : Ans.1992 Paper II, Q.2(a) : Ans.

p.10

rate =rate =

Differential Rate Equation:Differential Rate Equation:

= k’ [A]= k’ [A]mm- d[A]- d[A]

dtdt

slope of tangent at a point on slope of tangent at a point on the conc. - time graph.the conc. - time graph.

(NOT accurate!)(NOT accurate!)

= k’= k’- d[A]- d[A]

dtdt

if m = 0if m = 0

= k’dt= k’dt- d[A]- d[A]

= k’ dt= k’ dt- d[A]- d[A] = k’t + C= k’t + C- [A]- [A]

when t = 0, [A] = [A]when t = 0, [A] = [A]00

C = - [A]C = - [A]00

[A] = - k’t + [A][A] = - k’t + [A]00

integrated rate eqn. integrated rate eqn. (zeroth order)(zeroth order)No calculation of No calculation of

tangent slope!tangent slope!

p.11

[A] = - k’t + [A][A] = - k’t + [A]00

ThereforeTherefore …. …. forfor Zeroth OrderZeroth Order RxnRxn

Monitor the variation of Monitor the variation of conc.conc. along with along with timetime by Chemical / Physical Method, by Chemical / Physical Method,

Time t1 t2 t3 t4

[A] [A]1 [A]2 [A]3 [A]4

[A][A]

tt

[A][A]00 slope = - k’slope = - k’

To conclude …. To conclude …. (1)(1)

p.12

Rate Equation shows that the rate of rxn Rate Equation shows that the rate of rxn is affected by is affected by conc. (order)conc. (order) & & temp (k)temp (k)..

Find the order of rxn (m, n) by Find the order of rxn (m, n) by Initial RatInitial Rate Method e Method (many combinations of [A] & [B]!)(many combinations of [A] & [B]!)

Plot Plot log (rate) = m log[A] + log k’log (rate) = m log[A] + log k’, , both both mm, , k’k’ and and kk could be found. could be found.

p.13

Initial Rate Method gives Initial Rate Method gives Differential Differential Rate EquationRate Equation, but , but mm and and kk may not be may not be accurately found from the initial rates accurately found from the initial rates (=slope of tangent)(=slope of tangent)..

Integrated Rate EquationIntegrated Rate Equation can give can give better better mm and and kk, as no calculation of , as no calculation of tangent is involved. tangent is involved.

To conclude …. To conclude …. (2)(2)

p.14

To collect data for Integrated Rate Eqn., To collect data for Integrated Rate Eqn., only only one combination of [A] & [B]one combination of [A] & [B] is nee is needed. Measure ded. Measure [A][A] at different at different tt..

To conclude …. To conclude …. (3)(3)

Integrated Rate Eqn. of Integrated Rate Eqn. of Zeroth OrderZeroth Order: : [A] = -k’t + [A][A] = -k’t + [A]00

Next ….Next ….p.15

Integrated Rate Eqn. of Integrated Rate Eqn. of 11stst and 2 and 2ndnd Order Order

To study whether the decomposition of To study whether the decomposition of HH22OO22 is 1 is 1stst order w.r.t. [H order w.r.t. [H22OO22]. ]. (expt. 8)(expt. 8)

AssignmentAssignmentp.16

Pre-lab [due date: 12/2(Thur)]Pre-lab [due date: 12/2(Thur)]

p.47 Q.1-6 [due date: 12/2(Thur)] p.47 Q.1-6 [due date: 12/2(Thur)]