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12. Chemical kinetics

Reaction rates

kinetics: study of the rate of a reaction

rate

units

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molarity over time

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calculating

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always negative

example: what is the rate of NO₂ from 0 seconds to 50 seconds?

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Differential rate law

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only with reactants (not products)

k: rate constant (1/timeⁿ)

units change depending on the order

e.g. first order: 1/s

figure out by solving for k in equation (use M/s for rate)

[A]: concentration (M)

n: order of reaction

units: M/s or [M]

example: what are the rates of H₂ and H₂O?

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use ratios to solve

H₂ = - 4.0 M/s

H₂O = + 4.0 M/s

O₂ = 2.0 M/s

Changing reaction rates

concentration

temperature

pressure/volume

surface area

catalyst

Rate laws from experiment

order can only be determined/calculated by experiments

example: find order for each reactant, overall order, k

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three experiments, changing concentrations (only worry about reactants)

0.100 M and 0.0050 M

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0.100 M and 0.010 M

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0.200 M and 0.010 M

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pick two experiments where one concentration does not change and one does (e.g. 1 and 2)

NO₂⁻ molarity doubles

rate doubles

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pick two experiments where the other concentration changes

NH₄⁺ molarity doubles

rate doubles

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overall order: all individual orders added together

overall order: 1 + 1 = 2

k is a constant, so pick one experiment to plug in and solve for k

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example: find individual and overall orders

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0.10 M, 0.10 M, 0.10 M

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0.20 M, 0.10 M, 0.10 M

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0.20 M, 0.20 M, 0.10 M

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0.10 M, 0.10 M, 0.20 M

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solving for a

experiments 1 and 2: molarity doubles, rate doubles

a = 1

solving for b

experiments 2 and 3: molarity doubles, rate doubles

b = 1

solving for c

experiments 1 and 4: molarity doubles, rate quadruples

c = 2

overall order: 1 + 1 + 2 = 4

Integrated rate laws

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[A]: concentration at time t

k: rate constant

t: time (s)

[A]₀: initial concentration

lines up with line equation (y = mx+ b)

pick the graph with a straight line, then check units

half-life: the time it takes for half of the concentration of the reactants to decay

radioactive decay: first order

order

zero

first

second

rate law

rate = k

rate = k[A]

rate = k[A]²

integrated rate law

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plot needed to give a straight line

[A] vs. t

ln[A] vs. t

1/[A] vs. t

relationship of rate constant to slope of straight line

slope = - k

slope = k

half-life

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There are no rows in this table

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Reaction mechanisms

factors that determine reaction rate

collide with enough energy to break bonds

collide with the correct orientation

catalyst grabs reactants and puts them in the correct orientation

example:

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multiple steps that cancel to form reaction

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(slow)

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(fast)

reaction is as fast as the slowest step

look at slowest rate

write the reactants

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intermediate: molecule in the product of the first step and the reactant of the second step

very low concentration (does not exist for very long)

example: find rate law and intermediate

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(slow)

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(fast)

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intermediate: F

example (second step is slow)

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(fast)

reversible

think of it like an equals sign (A + B = C)

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(slow)

substitute first reaction into second reaction

A + B + D ⟶ E

rate = k[A][B][D]

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the higher the “hill” the slower the reaction

exothermic: high → low

endothermic: low → high

catalyst will shrink the size of the hill

number of hills = number of steps

catalysts never get used up in the reaction

present in both reactants and products

Reaction rates

Differential rate law

Changing reaction rates

Rate laws from experiment

Integrated rate laws

Reaction mechanisms

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