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.
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
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