Typical Graphs

Rate of Reaction = Chemical Kinetics

• Rate of Rxn = = Slope

Δ [Concentration]Δ Time

Reaction Rates

Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time.

Watch This!

Par ExampleC4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)

In this reaction, [the concentration] of butyl chloride, C4H9Cl, was measured at various times.

Reaction Rates The average rate of

the reaction over each interval is the

change in concentration divided by the

change in time:

Average rate = [C4H9Cl]t

Average rate =[.10 - .0905][50 – 0]

= 1.9 x 10 -4

AVERAGE RATE CHANGES!

• It is not constant.

• What’s happening to the average rate?

Practice Example 14.1 p. 560

Reaction Rates • Note that the average

rate decreases as the reaction proceeds.

• This is because as the reaction goes forward, there are fewer collisions between reactant molecules.

Change of Rate over TimePractice Example p. 598 #14.4

a.YES! Linear Function with positive slope.

b. Yes! The slope = 0 indicating that the reaction is over evidenced by no change in [M].

Instantaneous Rate of Change• Instantaneous Rate of Change = slope of tangent

line to curve at a point “t”

@ t

= 0,

in

itial

ra

te

Think of it this way! • You drove 98 miles to Charlotte in 2 hours.

• Your average rate is 49 mi/hr.

• Your instantaneous rate is

Reaction Rates p. 561

• A plot of [C4H9Cl] vs. time for this reaction yields a curve like this.

• The slope of a line tangent to the curve at any point is the instantaneous rate at that time = RATE @ instant.

• Examine the slope at t = 0 vs. slope at t = 600 s.

• Which is greater?

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

Steeper Slope

What’s happening over time?

Slope is decreasing.Rate is decreasing.Reaction is slowing.

Reaction Rates

• All reactions slow down over time.

• Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning of the reaction.

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

How do calculate instantaneous rate?• NON-Calculus Method• Find slope of line at point:

HOW???• USE GRAPH!• Draw in tangent line • Calculate ~ slope •

• Approximation of actual slope of tangent line to curve @ t = seconds

• Calculus Method• In order to find the ACTUAL

slope of tangent line at t = X seconds

• MUST know function • DON’T know function• IF we knew the function,

THEN we could use the 1st derivative to find the actual instantaneous rate of change

Calculus Application

First Derivative = slope of tangent line to curve at t = 2First Derivative = Velocity

Let’s Practice p. 600 #14.21• (a) Calculate averages

between intervals of time. • (b) Calculate average rate

over entire time interval. • (c) Use LoggerPro to graph

data. Select natural exponent function.

• ANSWERS FOUND ON p. A-18 at back of book.

AVERAGE = OVER SPECIFIC TIME INTERVALINSTANTANEOUS = @ SPECIFIC TIME VALUE

Reaction Rates and Stoichiometry

• In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1.

• Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH.

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

Rate = -[C4H9Cl]t

= [C4H9OH]t

Reaction Rates and StoichiometryWhat if the ratio is not 1:1?

2 HI(g) H2(g) + I2(g)

Rate = − 12[HI]t

= [I2]t

Reaction Rates and Stoichiometry• To generalize, then, for the reaction

aA + bB cC + dD

Rate = −1a

[A]t = −

1b

[B]t =

1c

[C]t

1d

[D]t=

Sample Exercise 14.3 p. 563