chemical kinetics part 1: reaction rates - chemistry …courses.chem.psu.edu/chem112/fall/lecture...

CH112 FA10 LRSVDS 1

Dr. Lori Stepan Van Der Sluys

Section 002, MWF 9:05-9:55 am

Email: [email protected]

Office Hours:

! "Email for appointment or

! "______________________________

REQUIRED MATERIALS

Required: Brown, LeMay, Bursten & Murphy; Chemistry: The Central

Science, 11th ed., 2009.

Required: Chem 112 FA09 Student Packet

Required: non-programmable scientific calculator

Optional: Volume 2 for Chem 112; partial text

Optional: Wilson Solutions to Exercises in Chemistry, The Central Science,

11th ed.

CH112 LRSVDS Kinetics 2-3 2

Chemical Kinetics part 1: Reaction Rates Overview of Kinetics •"Rates of reaction

average rates instantaneous rates

•"Dependence of rate on concentration

rate constant

rate laws order of the reaction

•"Dependence of rate on time

First order

Second order

Half-life

•"Dependence of rate on temperature

Activation Energy Ea Activated Complex

Arrhenius Equation

•"Reaction Mechanisms

•"Catalysis and Enzymes


EXPRESS REACTION RATES

“What is the rate of this reaction?”

We can express the rate of reaction in terms of:

1.

2.

Rate = OR

Stoichiometry of a reaction tells us how these are related.

In General: aA + bB ! cC + dD

reactants products

(a, b, c, d are stoichiometric coefficients)

!

rate = "1

a

# A[ ]#t

= "1

b

# B[ ]#t

= +1

c

# C[ ]#t

= +1

d

# D[ ]#t

!

"#[C

4H

9Cl]

# t

C4H9Cl(aq) + H2O(l) ! C4H9OH(aq) + HCl(aq)!

!

+"[C

4H

9OH]

" t


Reaction Rates and Stoichiometry

!" A + B ! C

1." Given the rate of disappearance of A is 5M/s, what is the

rate of appearance of C?

2." What is the rate of disappearance of B?

!" 2A + B ! C

1." Given the rate of disappearance of A is 5M/s, what is the

rate of appearance of C?

2." What is the rate of disappearance of B?


Example Problem

2HI(g) ! H2(g) + I2(g) If 6 moles of HI in a 1 L flask are converted to I2 and H2 in 1 min., What is the rate of disappearance of HI?

What is the rate of appearance of H2?

1." Twice the rate of disappearance of HI?

2." 1/2 the rate of disappearance of HI?

HINT: is rate of appearance of H2 greater than or less than the rate of

disappearance of HI?

!

rate ="# HI[ ]#t

=

!

rate =+" H

2[ ]"t

=


WAYS TO MEASURE REACTION RATES

N2O4(g) ! 2NO2(g)

1 mole gas 2 moles gas

a) For gas reactions, can measure P or V changes if "ngas = +1, then [N2O4] # PN2O4 and [NO2] # PNO2

rate = "PNO2 = - "PN2O4

2"t "t

b)! Spectroscopic methods; are the colors different?

N2O4(g) colorless NO2(g) red-brown

Measure light absorption vs. time; Absorbance # [NO2]

rate = " [NO2] 2"t

•" Wavelength used corresponds to wavelength of light that is absorbed by the species of interest.

•" This is a general method since we can use any wavelength of light


FOUR FACTORS THAT AFFECT REACTION RATES

1.! The physical state of the reactants

2. The Concentration of reactants

3. The Temperature

4.! The Presence of a catalyst


Rate Law: the relationship between the _________

of a reaction and _________________ of its

reactants.

EFFECT OF CONCENTRATION

ON RATE

Rate varies as concentration varies:!


Rate Laws

For a general reaction:

aA + bB ! cC + dD reactants products

rate = -"[A] OR -"[B] OR +"[C] OR +"[D]

"t "t "t "t

The rate law is:

k is the rate constant •"

•"

x and y exponents are _____________ (Must be ! 0, not

necessarily integers)

Order of reaction = ________________ (Overall order of reaction = x + y)


Simple Rate Laws

For the following reaction, any of the following could be the rate

law, if it matches the experimental data:!

A + B ! C!

1.! If Rate = k[A]!

2.! If Rate = k[B]!

3.! If Rate = k[A][B]!


Reaction Orders

2 NO(g) + 2H2(g) ! N2(g) + 2H2O(g)

Rate =

Given the Rate Law: rate = k[NO]2[H2]

1." What order is the reaction in H2?

2." What order is the reaction in NO?

3." What is the overall reaction order?


DETERMINING THE RATE LAW

Method of “initial rates”:

Initially, we know [A] and [B] (and [C] = [D] =____)

initial rate = k1[A]ox [B]o

y

Strategy:

1.! Vary [A]0 and [B]0

2.! measure the initial rates

3.! observe the effect


Sample problem: data given for the reaction: A + B ! Z

[A]0 [B]0 initial rate

1) 1.0M 1.0M 0.8x10-2 M/s

2) 2.0 1.0 1.6x10-2

3) 2.0 2.0 6.4x10-2

4) 1.0 2.0 3.2x10-2 Rate = k [A]x [B]y

1.!What is x?

2.!What is y?

3.!What is the overall reaction order? 4.!What is the Rate Law?

5.!What is k? What are the units?


FYI

Solution to Sample Problem

1.! Compare Rate 1 to Rate 2

!

R1

R2

=k A[ ]

1

a

B[ ]1

b

k A[ ]2

a

B[ ]2

b=

A[ ]1

a

A[ ]2

a=

1M[ ]a

2M[ ]a

=1

2

!

Rate 1

Rate 2=

R1

R2

= 0.8 "10

#2M /s

1.6 "10#2

M /s =

1

2

Using the rate laws to compare rates:

a must be one for the relationship above to be true

!

" 1

2

#

$ % &

' (

a

= 1

2

Recall that [B] in trials 1 and 2 does not change so the ratio of ([B]1/[B]2 )b = 1

regardless of the value of the exponent.


FYI

Solution to Sample Problem continued

2. Compare Rate 2 to Rate 3

Using the rate laws to compare rates:

b must be two for the relationship above to be

true

!

Rate 2

Rate 3=

R2

R3

= 1.6 "10

#2M /s

6.4 "10#2

M /s =

1

4

!

R2

R3

=k A[ ]

2

a

B[ ]2

b

k A[ ]3

a

B[ ]3

b=

B[ ]2

b

B[ ]3

b=

1M[ ]b

2M[ ]b

=1

4

!

" 1

2

#

$ % &

' (

b

= 1

4


Determination of Rate Laws

aA + bB ! zZ

rate = k[A]x[B]y

Are x and y the same as a and b?

NOTE: Rate Law MUST be determined experimentally.

Exponents CANNOT be predicted from the overall reaction.

experiment $ rate law % mechanism

(exponents x, y)

Examples of Rate Laws:


Summary: Using experimental data to determine the rate law

!"Observe the effect of changing the initial concentration of the reactants on the initial rate of the reaction.

!" In most reactions the exponents are 0, 1, or 2 (can be a fraction or negative.)

!" Change in concentration of zero order reactants has no effect on the rate.

!" Doubling the concentration of first order reactants ___________ the rate.

!" Doubling the concentration of second order reactants increases the rate by 22=4 (____________ the rate).

!" Tripling the concentration of second order reactants increases the rate by 32=________.

!" For third order reactants, doubling the concentration increases the rate by 23=_______.


Using experimental data to determine the rate law

The following data were collected for the rate of disappearance of NO in the reaction below:

2 NO(g) + O2(g) ! 2NO2(g)

Exp [NO] [O2] Initial Rate (M/s)

1 0.0126 M 0.0125 M 1.41 & 10-2

2 0.0252 M 0.0250 M 1.13 & 10-1

3 0.0252 M 0.0125 M 5.64 & 10-2

(a)" What is the order in NO?

(b)" What is the order in O2?

(c)" What is the rate law for the reaction?

(d) What are the units of the rate constant?


Continued: Data were collected for the rate of

disappearance of NO in the reaction:

2 NO(g) + O2(g) ! 2NO2(g)

(e) What is the rate of disappearance of [O2] at the concentrations given in experiment 1?

Exp [NO] [O2] Initial Rate (M/s)

1 0.0126 M 0.0125 M 1.41 & 10-2


Summary

Measure the instantaneous rate of a reaction: this is a number!

Measure

the rate of loss

of a reactant

Or . . . the rate of appearance

of a product

Repeat the experiment to determine the concentration

dependence: Obtain the Rate Law

Differential rate Law: gives rate as a function of

concentration


Study Rate Law as a function of time We are studying a chemical reaction; for example

aA ! products

Measure the rate as a function of concentration

rate = -"[A] = k[A]x (the differential rate law)

" t

This is a differential equation; Integration gives [A] as a function of t

Differential Rate Law for 1st order reaction (x = 1):

Integrate to get:

or:

Rearrange:

(Different forms of the same equation)


FYI

If "[A] ! d[A] as "t ! 0 then

!

rate = "# A[ ]#t

= k A[ ] (First order rate law)

rearrange

!

" A[ ]A[ ]

= # k"t

!

d A[ ]A[ ]

= " kdt

Integrate: at t = 0, [A] = [A]0

!

d A[ ]A[ ]A[ ]

0

A[ ]

" = # k dt

0

t

"

ln A[ ] # ln A[ ]0 = ln

A[ ]A[ ]

0

= # kt

Integrated first order rate law: concentration as a

function of time


The Integrated First Order Rate Law

is a Linear Equation

ln[A] = - k t + ln[A]o

This is in the form of:

y = m x + b y = b =

x = m =

A plot of__________vs. ________ gives a straight line for

first order reactions.

time!

ln[A]! slope = -k!

ln[A]o!


CH3'N(C: CH

3 ' C ( N:

!

[A] = [A]0e"kt

PA

= P0e"kt

!n [A] = !n[A]0 - k t

!n (PA) = !n(P0) - k t

Make two plots using the reaction data:


INTEGRATED RATE LAW

2nd order reaction

2nd order reaction (x = 2):

differential

rate law

Integrate to get:

integrated 2nd

order rate law !

rate ="# A[ ]#t

= k A[ ] 2

!

1

A[ ]= k t +

1

A[ ] 0

[A]!

t!


FYI

If "[A] ! d[A] as "t ! 0 then !

rate = "# A[ ]#t

= k A[ ]2 Second order rate law

rearrange

!

" A[ ]

A[ ]2

= # k"t

!

d A[ ]

A[ ]2

= " kdt

Integrate: at t = 0 [A] = [A]0

!

"d A[ ]

A[ ]2

A[ ]0

A[ ]

# = k dt

0

t

#

1

A[ ] "

1

A[ ]0

= kt

Integrated second order rate law: concentration as a

function of time


NO2(g) ! NO(g) + ! O2(g)

Step 1: Measure [NO2] as a function of time

Collect data Calculate these

Time(s) [NO2](M) ln [NO2] 1/[NO2]

0.0 0.01000 - 4.610 100

50.0 0.00787 - 4.845 127

100.0 0.00649 - 5.038 154

200.0 0.00481 - 5.337 208

300.0 0.00380 - 5.573 263

Example : What is the rate law?

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0 100 200 300 400 500 600

TIME (SEC)

[NO

2]

(M)


Step 2 to Determine Order of Reaction:

Plot ln [NO2] vs. time Plot 1/[NO2] vs. time

Is either plot linear?

What is the rate law?

chemical kinetics part 1: reaction rates - chemistry …courses.chem.psu.edu/chem112/fall/lecture...

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