Chemical Kinetics - Formulas
All rates written as
conc
time
or
[A]
t
. Instantaneous rate is the slope of a concentration vs time plot and is
shown by the differential equation:
d[A]
dt
. Overall rates for forward reactions are shown as POSITIVE rates,
therefore, all reactants (which have negative rate of change) must have their rates negated
d[A]
dt
.
In general for the overall reation:
aA+bBcC+dD
!overall rxn rate
[A]
at=
[B]
bt=+[C]
ct=+[D]
dt
Note that each individual rate is divided by it’s coefficient in the balanced chemical equation.
Half-life (t1/2) : The time it takes for the concentration to drop to one half its current value during the course of
the reaction. Note that the “current value” is typically the initial starting value - but not always.
Rate Laws for: a A products (all the following equations assume that k is for the overall reaction)
Zero Order
First Order
Second Order
rate = ak
rate = ak[A]
rate = ak[A]2
€
[A]0−[A]t=akt
€
ln[A]0−ln[A]t=akt
€
ln [A]0
[A]
⎛
⎝
⎜ ⎞
⎠
⎟ =akt
€
1
[A]t
−1
[A]0
=akt
[A]t = -akt + [A]0
€
ln[A]t=−akt +ln[A]0
€
1
[A]t
=akt +1
[A]0
€
t1/2 =[A]0
2ak
€
t1/2 =ln2
ak
€
t1/2 =1
ak[A]0
Watch out for this! Make sure you know HOW k is defined for a reaction. It must be known WHICH component that the rate is
being expressed. Is it A? B? C? D? Many times k is given for the overall reaction. If that is the case then you must remember to scale
k by the coefficients (a, b, c, or d) given in order to get the right rates for each component. That is: k = ak´, etc… (this is discussed in
section 15.2 in your textbook)
Temperature dependence of rate (Arrhenius Equation)
k=Ae
Ea/RT
Here’s the straight line plot (y = mx + b) version:
ln k=
Ea
R✓1
T◆+ ln A
When finding the new k at a new T...
ln k2
k1⇥=Ea
R1
T1
1
T2⇥
Note this is the typical Arrhenius Equation where you have 2
specific rate consants at 2 specific temperatures. Remember
they come in pairs. Also note how the Arrhenius factor A, has
factored OUT of the equation.
Here is the version using half-lives instead of k’s
ln t1
t2⇥=Ea
R1
T1
1
T2⇥
This is still the Arrhenius Equation, EXCEPT we now show
TIME in place of rate constant. Time is inversely proportional
to rate so the positions are switched. Any common timed event
will work – half-life is the most common.
