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Entry Task: Nov 5th Wednesday

Sign off on Expression and Law wsGrab Integrated Law notes by door

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Agenda:

• Go through Expression and Law ws• Walkthrough NOTES Ch. 14 sec 3 – The change

in concentration with time (integrated – graph)

• Integrated Rate Law ws

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1. Given the reaction: 2A (g) --->B (g) + C (g)a. Express the rate of reaction in terms of the change in concentration of each of the reactants and products.

- 1 2

Δ[A] Δt

= 1 1

Δ[B] Δt

= 1 1

Δ[C] Δt

b. When [C] is increasing at 2.0 mol.L–1.s–1 , how fast is [A] decreasing? SHOW WORK!

= 1 1

Δ[2.0] Δt

- 1 2

Δ[A] Δt

= 2 1

Δ[2.0] Δt

Δ[A] Δt

4 mol.L-1s-1 =

A decreases twice as fast

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2. Given the reaction: 2D (g) + 3E (g) + F (g) ----> 2G (g) + H (g)

a. Express the rate of reaction in terms of the change in concentration of each of the reactants and products.

- 1 2

Δ[D] Δt

= -1 3

Δ[E] Δt

= 1 2

Δ[G] Δt

b. When [E] is decreasing at 0.10 mol.L–1.s–1, how fast is [G] increasing? SHOW WORK!

= - 1 3

Δ[0.10] Δt

1 2

Δ[G] Δt

= 2 3

Δ[0.10] Δt

Δ[G] Δt

0.067 mol.L-1s-1 =

2/3 as fast

= -1 1

Δ[F] Δt

1 1

Δ[H] Δt

=

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3. For the reaction 3 ClO – (aq) → ClO3 – (aq) + 2 Cl – (aq) doubling

the concentration of ClO – quadruples the initial rate of formation of ClO3-. What is the rate law for the reaction?

Rate = k [ClO –]2

4. The reaction C6H5N2Cl (aq) + H2O (l) → C6H5OH (aq) + N2 (g) + HCl

(aq) is first order in C6H5N2Cl and zero order in H2O. What is the rate law for this reaction?

Rate = k [C6H5N2Cl]

5. For the reaction H3PO4 (aq) + 3I – (aq) + 2 H+ (aq) → H3PO3 (aq) + I3

- (aq) + H2O (l) the rate law under certain conditions is given by Rate = k[H3PO4][I -][H+]2. What method(s) could be used if you want to double the reaction rate?

Double the concentration of H3PO4 or I-

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7. For the reaction 2 NO (g) + Cl2 (g) → 2 NOCl (g) If the concentration of NO is tripled, the rate of the reaction increases by a factor of nine. If the concentration of Cl2 is cut in half, the rate of the reaction is decreased to half the original rate. Find the order of reaction for each reactant and write the rate law for the reaction.

2nd

6. What is the overall order of reaction for each of the following? a) Rate = k[NO2]2 _______ b) Rate = k _______c) Rate = k[Br2] _______ d) Rate = k[NO]2[O2] ______

Zero1st 3rd

NO is a second order Cl2 is 1st order Rate = k [NO]2[Cl2]

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9. A reaction has the experimental rate law of Rate = k[A]2. a) What happens to the rate if the concentration of A is tripled?

b) What happens to the rate if the concentration if A is reduced to one third the initial concentration?

Rate = k

8. In the decomposition of ammonia on a platinum surface at 856°C , 2 NH3 (g) → N2 (g) + 3 H2 (g) , changing the concentration of NH3 has no effect on the rate. Write the rate law for the reaction.

Rate = k [3]2

Rate = k [1/3 ]2

Rate would increase by a factor of 9

Rate would decrease by a factor of 1/9

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10. For the reaction 2 A + B → C + D, if the concentration of A is doubled, the reaction rate doubles. If the concentration of B is halved, there is no change in the reaction rate. Determine the order of reaction with respect to each reactant and the overall order of reaction. Write the rate law for the reaction.

A would be 1st order and B is zero order

Rate = k [A]

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ChemicalKinetics

I can…

• Graph the relationship of time with amount of reactant concentrations and integrate this with rates of reactions.

• Determine the graphical relationship between time and the rate order.

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Equation SheetUnder thermochemistry and kinetics

1st order

2nd order

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Two Types of Rate Laws

1. Differential- Data table contains RATE AND CONCENTRATION DATA. Uses “table logic” or algebra to find the order of reaction and rate law

2. Integrated- Data table contains TIME AND CONCENTRATION DATA. Uses graphical methods to determine the order of the given reactant. K=slope of best fit line found through linear regressions

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Integrated Rate Law

• Can be used when we want to know how long a reaction has to proceed to reach a predetermined concentration of some reagent

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Graphing Integrated Rate Law

• Time is always on x axis• Plot concentration on y axis of 1st graph• Plot ln [A] on the y axis of the second

graph• Plot 1/[A] on the y axis of third graph• You are in search of a linear graph

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Zero order Reactions-Use A B as an example. What happens when we double [A], what happens to the rate of reaction that is zero order?

 

 

So does the concentration affect rate? Y/N____

What would the rate law be for a zero order?

The rate of reaction does not change

No

Rate = k

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ChemicalKinetics

Sketch a graph with rate on Y and concentration on X axis- Label axis!!

As concentration increases, the rate of reaction remains the same.

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

Integrated Rate laws

We look for straight lines. This provides a “clean” visual about the relationship of concentration and time.

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

So when we plot our data table and get a negative straight line it is ____________order!

Slope is negative (-k)

Zero

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First Order Reactions

AB in a reaction.

① Write the rate expression for reactant A. (sec. 1 stuff)

Rate = - ∆[A]∆t

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14.3- The Change of Concentration with Time

② Write the rate law for reactant A. (sec 2 stuff)

Rate = k[A]1

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14.3- The Change of Concentration with Time

Describe a First Order reaction.

Double the concentration the reaction doubles.

Low amount of reactant = low rate of reaction

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Sketch a graph with rate on Y and concentration on X axis- Label axis!!

As we double our concentration , the rate doubles. It’s a direct relationship.

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

Integrated Rate laws

We look for straight lines. This provides a “clean” visual about the relationship of concentration and time. This does not provide a straight line

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

Integrated Rate laws

We can manipulate the data to provide a straight line plot.

Change how we plot concentration.

Natural log x ConcentrationIn [A]

Slope is negative (-k)MAYHAN

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14.3- The Change of Concentration with Time

Take equations and and smash ① ②them together.

Rate = - ∆[A]∆t

= k[A]

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14.3- The Change of Concentration with Time

How do you use this equation to solve for concentration?

Using calculus to integrate the rate law for a first-order process gives us

ln[A]t

[A]0

= −kt

Where

[A]0 is the initial concentration of A.

[A]t is the concentration of A at some time, t, during the course of the reaction.

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Integrated Rate Laws

Manipulating this equation produces…

ln[A]t

[A]0

= −kt

ln [A]t − ln [A]0 = − kt

ln [A]t = − kt + ln [A]0

…which is in the form y = mx + b

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First-Order Processes

Therefore, if a reaction is first-order, a plot of ln [A] vs. t will yield a straight line, and the slope of the line will be -k.

ln [A]t = -kt + ln [A]0

Relate this equation to the slope.

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The decomposition of a certain insecticide in water at 12 C follows first-order kinetics with a rate constant of 1.45 yr1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 107 g/cm3. Assume that the average temperature of the lake is 12 ºC. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to

decrease to 3.0 10–7 g/cm3? PLUG & CHUG

Sample Exercise 14.5 Using the Integrated First-Order Rate Law

ln[insecticide]t -1 yr = 1.45 + (14.51)

k = 1.45 yr-1

ln [A]0 = [5.0 x 10-7g/cm3]

t = 1 year

ln [insecticide]t-1yr = [X]

-(1.45 yr-1)

SET IT UP

(1 year)ln [insectacide]t-1yr = + ln [5.0 x 10-7g/cm3]

Get rid of ln by ex on both sides

ln[insecticide]t - 1 yr = 15.96

[insecticide]t = 1 yr = e15.96 = 1.2 107 g/cm3 MAYHAN

ChemicalKinetics

The decomposition of a certain insecticide in water at 12 C follows first-order kinetics with a rate constant of 1.45 yr1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 107 g/cm3. Assume that the average temperature of the lake is 12 ºC. (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to

decrease to 3.0 10–7 g/cm3? PLUG & CHUG

Sample Exercise 14.5 Using the Integrated First-Order Rate Law

k = 1.45 yr-1

ln [A]0 = [5.0 x 10-7g/cm3]

t = X

ln [3.0 10-7]t = -(1.45 yr-1)

SET IT UPXln [3.0 10-7]t = + ln [5.0 x 10-7g/cm3]

Get X by itself- move to left side

-1.45 yr-1

=Xln [3.0 10-7]t - ln [5.0 x 10-7g/cm3]-1.45 yr

=0.35 years-15.02 - -14.51

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Practice ExerciseThe decomposition of dimethyl ether, (CH3)2O, at 510 ºC is a first-order process with a rate constant of 6.8 10–4 s–1:

(CH3)2O(g) CH4(g) + H2(g) + CO(g)If the initial pressure of (CH3)2O is 135 torr, what is its pressure after 1420 s?

Continued

Sample Exercise 14.5 Using the Integrated First-Order Rate Law

ln[torr]t = 0.9656 + (4.91)

k = 6.8 x 10-4-s-1

ln [A]0 = [135 torr]

t = 1420 s

ln [X torr]t = [X]

-(6.8 x 10-4)

SET IT UP

(1420 s)ln [X torr]t = + ln [135 torr]

Get rid of ln by ex on both sides

ln[torr]t = 3.94

[torr]t = e3.94= 51.4 torr MAYHAN

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14.3- The Change of Concentration with Time

Describe a second-order reaction.

When you double the reactant the rate increases by a power of 2, to quadruple the rate

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Sketch a graph with rate on Y and concentration on X axis- Label axis!!

The relationship is more pronounced. Double your concentration and the rate goes up by the power of 2.Hence- second order.

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

Integrated Rate laws

We look for straight lines. This provides a “clean” visual about the relationship of concentration and time. This does not provide a straight line

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ChemicalKinetics

Sketch a graph with concentration on Y and time on X axis- Label axis!!

Integrated Rate laws

We can manipulate the data to provide a straight line plot.

Change how we plot concentration.

1 divided by Concentration1/[A]

And the slope is positive (k)MAYHAN

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Second-Order Processes

Similarly, integrating the rate law for a process that is second-order in reactant A, we get

1[A]t

= kt +1

[A]0also in the form

y = mx + b

Provide the second order equation.

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Second-Order Processes

So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line, and the slope of that line is k.

1[A]t

= kt +1

[A]0

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14.3- The Change of Concentration with Time

What does second order reactions depend on?

A second order reaction is one whose rate depends on the initial reactant concentration

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Second-Order ProcessesThe decomposition of NO2 at 300°C is described by the equation

NO2 (g) NO (g) + 1/2 O2 (g)

and yields data comparable to this:

Time (s) [NO2], M

0.0 0.01000

50.0 0.00787

100.0 0.00649

200.0 0.00481

300.0 0.00380 MAYHAN

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Second-Order Processes• Graphing ln [NO2] vs. t

yields:

Time (s) [NO2], M ln [NO2]

0.0 0.01000 −4.610

50.0 0.00787 −4.845

100.0 0.00649 −5.038

200.0 0.00481 −5.337

300.0 0.00380 −5.573

• The plot is not a straight line, so the process is not first-order in [A].

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Second-Order Processes• Graphing ln

1/[NO2] vs. t, however, gives this plot.

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

0.0 0.01000 100

50.0 0.00787 127

100.0 0.00649 154

200.0 0.00481 208

300.0 0.00380 263

• Because this is a straight line, the process is second-order in [A].

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kt[A][A] 0 ln[A]0[A]

1kt

[A]

1

0ln[A]kt

s

M

s

1sM

1

t vs.[A] t vs.ln[A] t vs.[A]

1

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Practice with graphs- After creating regression graphs of various reactions, provide the rate

order for each graph.

What order is this reaction and what formula would I use to calculate various times/concentrations?

First order and ln[A] 0ln[A]kt

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ChemicalKinetics

Practice with graphs- After creating regression graphs of various reactions, provide the rate

order for each graph.

What order is this reaction and what formula would I use to calculate various times/concentrations?

Zero order and kt[A][A] 0

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ChemicalKinetics

Practice with graphs- After creating regression graphs of various reactions, provide the rate

order for each graph.

What order is this reaction and what formula would I use to calculate various times/concentrations?

Second order and

0[A]

1kt

[A]

1

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