Typical Graphs

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# Typical Graphs - PowerPoint PPT Presentation

Typical Graphs . Rate of Reaction = Chemical Kinetics. Δ [Concentration]. Δ Time. Rate of Rxn = = Slope. 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!.

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Presentation Transcript
Rate of Reaction = Chemical Kinetics

Δ [Concentration]

Δ Time

• Rate of Rxn = = Slope
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 Example

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

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

Average rate =

Average rate =

[.10 - .0905]

[50 – 0]

[C4H9Cl]

t

Reaction Rates

The average rate of the reaction over each interval is the change in concentration divided by the change in time:

= 1.9 x 10 -4

AVERAGE RATE CHANGES!
• It is not constant.
• What’s happening to the average rate?
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 Time

Practice Example p. 598 #14.4

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 tangentline to curve at a point “t”

@ t = 0, initial rate

Think of it this way!
• You drove 98 miles to Charlotte in 2 hours.
• Your average rate is 49 mi/hr.
Reaction Rates p. 561

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

• 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?

Steeper Slope

What’s happening over time?

Slope is decreasing.

Rate is decreasing.

Reaction is slowing.

Reaction Rates

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

• 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.
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 = 2

First 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 INTERVAL

INSTANTANEOUS = @ SPECIFIC TIME VALUE

-[C4H9Cl]

t

Rate =

=

[C4H9OH]

t

Reaction Rates and Stoichiometry

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

• 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 ofC4H9OH.

1

2

[HI]

t

Rate = −

=

[I2]

t

Reaction Rates and Stoichiometry

What if the ratio is not 1:1?

2 HI(g)  H2(g) + I2(g)

aA + bB

cC + dD

= −

=

=

Rate = −

1

a

1

b

1

c

1

d

[C]

t

[D]

t

[A]

t

[B]

t

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