experimental rate laws

Question 1

4 methods to determine if rate law is correct

Answer 1

1. integration method
2. isolation method
3. differential method
4. half lives

Question 2

integration method on first order rate law

Answer 2

rate law: r = k(1st) [A]
differential form: d[A]/dt = -k(1st)[A]
(minus as A is a reactant, decreases w time)
integrate: ln[A] = -k(1st)t + ln[A]0

Question 3

what needs to be known to determine a first order rate constant?

Answer 3

absolute conc NOT needed, only some value proportional to conc
plot ln[A] vs t for straight line, y-int ln[A]0

Question 4

integration method on 2nd order rate law
A –> products

Answer 4

d[A]/dt = -k(2nd)[A]^2
integrate by separation: 1/[A] = k(2nd)t + 1/[A]0

Question 5

assumptions for determining rate law for
[A] + [B] –> products

Answer 5

rate law: r = -k2nd[A][B]
[A] and [B] related by stoic
if at t=0, set [A]=[B], then for all subsequent times they remain equal because 1:1, hence simplify to
r= -k(2nd)[A]^2
integrate as previous

Question 6

what is the isolation method and when is it used?

Answer 6

for more complex rate laws that are difficult to integrate by hand
a method of simplifying by assuming one reagent is in great excess so its conc doesn’t change and conc of other reagent drops to 0

Question 7

define pseudo first order rate constant

Answer 7

K(eff)
after assuming one reagent [A] significantly in excess
r = -k(eff)[B]
eg. where k(eff) = k(3rd)[A]^2

Question 8

shortcomings of the isolation method

Answer 8

1. large XS may make reaction inconveniently fast
2. conditions may alter the mechanism of a complex reaction

Question 9

when and how is the differential method used to analyse rate laws?

Answer 9

if the rate law is of the form r = k[A]^n

find n by plotting logs
ln(r) = ln(k) + n*ln[A]
graph has slope n

drawback is having to plot rates which is much harder to measure than conc

Question 10

define half life

Answer 10

time taken for the conc of a specified reagent to fall to half its initial value

Question 11

prove that first order half life independent of initial conc

Answer 11

start w integrated rate law
ln[A] = -k(1st)t + ln[A]
at t=t(1/2), [A] = [A]0/2

–> t(1/2) = ln2 * 1/k(1st)
[A]0 does not appear

Question 12

half life expression for second order reaction

Answer 12

t(1/2) = 1/k(2nd) * 1/[A]0

DOES depend on initial conc

Question 13

name some ways of measuring concentration

Answer 13

light absorbance
conductivity measurements
gas pressure
electrochemistry