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Rate Laws
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· Determine the rate law from experimental data.
· Explain the effect of concentration on reaction rates.
· Derive rate law form a reaction mechanism.
· Predict a reaction mechanism from rate law.
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2A B
The rate is directly proportional to reactant A
Rate Law helps us calculate the rate of a reaction.
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where: k rate constant [A] concentration of Ax reaction order
Rate = k[A]x
**The rate constant (k) and the order (x) can only be determined experimentally**
It is an expression that shows the quantitative effect of concentration on reaction rate.
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Rate = k[A]x
The rate constant (k) is specific for each reaction at a specific temperature.
Temperature is the only factor to affect the rate constant.
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Order
Reaction
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The orders of a reaction (x and y) indicate how much each [reactant] affects the rate of a reaction.
A + B Products
Rate = k[A]x[B]y
Each reactant can affect the rate differently
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First order reaction ( x = 1)
The reaction rate is directly proportional to changes in reactant concentration.
[A] is doubled - rate doubles 2 = 21 [A] is tripled - rate triples 3 = 31
Rate = k[A]1x
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Second order reaction (x = 2)
The reaction rate is proportional to changes in reactant concentration squared.
Doubling [A] - increase rate 4x 4 = 22
Tripling [A] - rate increase 9x 9 = 32
Rate = k[A]2
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Zero order reaction (x = 0)
The rate does not depend on the [A]. • Changing [A] does NOT change the rate.
Third order reaction (x = 3)
The reaction rate is proportional to changes in reactant concentration cubed.
**NOT included in the rate law if determined to be zero order**
Rate = k[A]3
Rate = k
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Overall order of reaction is the sum of the orders:
x + y = overall reaction order
Rate = k[A][B]2
1st order + 2nd order = 3rd order overall
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Calculating Rate Law
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Several ways to determine the rate law:
• differential rate law - uses calculus
• integrated rate law – uses graphing software
• initial rates method – uses data tables
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Determining rate law:
Measure the effect of changes in concentration of one reactant on rate, while
H2O2 + 2 HI 2 H2O + I2
Rate Law is related to stoichiometry. BUT…
Usually cannot be determined from overall reaction.
keeping the other reactant constant.
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Common Sense Approach
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rate = k[H2O2] [HI]
rate = k[H2O2] [HI]
yx 11
1 H2O2 + 2 HI 2 H2O + I2
2x 2x2x
Doesn’t agree with stoichiometry
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3 A (g) + B (g) + 2 C (g) 2 D (g) + 3 E (g)
a. Write the rate law for this reaction.b. Calculate the value of the rate constant (k).c. Calculate the rate for Trial #5.d. Calculate the concentration of A in Trial #6.
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a. Write the rate law for this reaction. rate = k[A][B]2
1 2 0
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b. Calculate the value of the rate constant (k).
To find the value of k, we use that data from ANY trial.
rate = k[A][B]2
Don’t include units for k.
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c. Calculate the rate for Trial #5.
rate = k[A][B]2
rate = (200)(0.50 mol/L)(0.40 mol/L)2
rate = 16.0 mol/Ls
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d. Calculate the concentration of A in Trial #6.
rate = k[A][B]2
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Ratio Approach
8 = 2 4
2 = 1 2
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Using ratios: A + B → products
Trial [A] (mol/L) [B] (mol/L) Initial Rate (mol/Ls)
1 0.10 0.20 2.0
2 0.30 0.20 18.0
3 0.20 0.40 16.0
Rate = k[A]x[B] yRate = k[A]x[B] yRate α [A]x [B]y
Rate2 α [A]2x
[B]2y
Rate1 [A]1x
[B]1y
18.0 α [0.3]x [0.2]y
2.0 [0.1]x [0.2]y
18.0 α 0.3 x 0.2 y
2.0 0.1 0.2
9.0 α [3] [1]y
y = 0 or 1 or 2…..
3x 9x
x
9.0 α 9 [1]y1 α [1]y
22
Can’t have multiple answers…start over.
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Using ratios: A + B → products
Trial [A] (mol/L) [B] (mol/L) Initial Rate (mol/Ls)
1 0.10 0.20 2.0
2 0.30 0.20 18.0
3 0.20 0.40 16.0
Rate = k[A]2[B]Rate α [A]x [B]y
Rate3 α [A]3x
[B]3y
Rate1 [A]1x
[B]1y
16.0 α 0.2 2 0.4 y
2.0 0.1 0.2 y = first order
8.0 α [2]2 [2]y
8.0 α 4 [2]y
2.0 α [2]y
y1
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Tl[A]i
mol/L[B]i
mol/LInitial Rate(mol/Ls)
10.010
00.024
01.45 x 10−4
20.010
00.012
07.25 x 10−5
30.020
00.048
05.80 x 10−4
Rate = k[A] [B]
Rate α [A]x [B]y
Rate3 α [A]3x
[B]3y
Rate2 [A]2x
[B]2y
5.8 -4 α 0.2 x 0.048 1
7.25 -5 0.1 0.012
x = first order
8.0 α [2]x [4]1
8.0 α [2]x 4
2.0 α [2]x
y1x
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Conclusion: Everything in the Rate Law must be determined experimentally:
1. Write a basic rate law with all reactants
2. Determine the order for each reactant (1, 2, 0)
3. Re-write the rate law with the determined order of reaction for each
4. Solve any problems
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CAN YOU? / HAVE YOU?
· Determine the rate law from experimental data.
· Explain the effect of concentration on reaction rates.
· Derive rate law form a reaction mechanism.
· Predict a reaction mechanism from rate law.