Rate Laws

• Determine the rate law and order of a chemical reaction from experimental data.

Include: various reaction orders, rate versus concentration graphs.

Additional KEY TermsRatio

A + B CRate is proportional to changes in A and B

Rate Law helps us calculate the rate of a REACTION not a reactant.

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 changes on reaction rate.

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.

Order

Reaction

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

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

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

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

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

Calculating Rate Law

Several ways to determine the rate law:

• differential rate law - uses calculus

• integrated rate law – uses graphing software

• initial rates method – uses data tables

Determining rate law:

Measure the effect of changes in concentration of one reactant on rate, while keeping the other reactant constant.

Ratio Approach

8 = 2 4

2 = 1 2

Using ratios: A + B → products

Rate2 k [A]2x

[B]2y

Rate1 k [A]1x

[B]1y

18.0 α 0.3 x 0.2 y

2.0 0.1 0.2 x = second order

9.0 α [3]x 1

9.0 α [3]x

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] y

α

same

=

Using ratios: A + B → products

Rate3 k [A]3x

[B]3y

Rate1 k [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

2.0 α [2]y

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 = k[A]x[B] y

α=

2

8.0 α 4 [2]y

y1

Using ratios: A + B → products

Rate2 α [A]2x

[B]2y

Rate1 [A]1x

[B]1y

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…..

2

9.0 α 9 [1]y

1 α [1]y

Can’t have multiple answers…pick new trials.

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]You might pick bad trials y

2

Common Sense Approach

2x

Rate2 k [H2O2]2x

[HI]2y

Rate1 k [H2O2]1x

[HI]1y

0.0152 α 0.1 x 0.2 y

0.0076 0.1 0.1 x = first order

2.0 α 1 ּ [2]y

2.0 α [2]y

=

same

same

1

2

1

rate = k[H2O2] [HI]rate = k[H2O2] [HI]

yx 11

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

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.

a. Write the rate law for this reaction.

rate = k[A][B]2

1 2 0

Rate2 k [A]2x

[B]2y

[C]2z

Rate1 k [A]1x

[B]2y

[C]2z =

Rate2 [A]2x

Rate1 [A]1x=

samesame

samesame

samesame

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.

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 mol/Ls

d. Calculate the concentration of A in Trial #6.

rate = k[A][B]2

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

CAN YOU / HAVE YOU?

• Determine the rate law and order of a chemical reaction from experimental data.

Include: various reaction orders, rate versus concentration graphs.

Additional KEY TermsRatio