Chemical kinetics Lecture-6
Kinetic analysis of experimental data
Average rate -
$Average\hspace{2 mm} rate=-\frac{c_3-c_1}{t_3-t_1}$
$=-\frac{\Delta c}{\Delta t}$
Instantaneous rate
By drawing a tangent at that instant or that time point , $t_1$
Take the slope of the tangent
For products - $r_ {inst}=\frac{d[P]}{dt}$ $P\rArr product$
Initial rate of reaction
Key points
It is preferred to do the initial rate calculation based on product appearance
Initial rate calculation has to be done very close to the starting point of the reaction $\rarr$ within 5% of the reaction
Except chain reactions
The initial rate line or tangent will be the one which is the steepest
Dependence of reaction rate on concentration
The rate of reaction is in some way dependent on the concentration of the reactant remaining
Way dependent on the concentration of the reactant remaining
rate $\alpha$ $[reactant]^n$ $\dots$(1)
n$\rArr$ is a number which states exactly how the rate depends on [reactant]
Where n = order of the reaction rate = $k[reactant]^n$ $\dots$(2)
k is the constant of proportionality rate constant
If, n = 1 , first order reaction
n = 2 , second order reaction
n = 3 , third order reaction
n = 0, zero order reaction
n = 3/2 , fractional order
Rate of reaction including 2 reactants, A and B
Rate = $k[A][B]\dots(3)$
First order with respect to A
First order with respect to B
Total order of the reaction = 1 + 1 = 2
Rate = $K[A]^2[B]\dots(4)$
Second order with respect to A
Total order = 2+1 = 3
Rate of reaction including 2 reactants , A and B
$rate=k[reactant]^n \dots(5)$
$rate=k[reactant_1]^\alpha[reactant_2]^\beta \dots(6)$
These are referred to as rate expressions
Rate of reaction general reaction
$aA+bB+cC+….\rarr pP + qQ…..$
$rate = k[A]^\alpha [B]^\beta [C]^\gamma….\rarr(7)$
total order = $\alpha+\beta+\gamma+…$
$k\rArr$ experimental rate constant
One concentration form for each reactant
Each concentration term is raised to a particular power - $\alpha , \beta , \gamma…$
Kinetic analysis -
Find the value of $\alpha , \beta , \gamma…$
k rate constant at a certain temperature
Units of rate
$\frac{[concentration]}{time}$
unit of rate is $\frac{M}{time}$ or M $time^{-1}$
$\frac{molL^{-1}}{time}$ or $molL^{-1} time^{-1}$
$\frac{atm}{time}$ $\hspace{2mm}$ atm $time^{-1}$
If time is in seconds
$Ms^{-1}$ or $molL^{-1}s^{-1}$ or $atm s^{-1}$
Meaning of rate expression
Units of rate constant
Example
Solution
$rate = k[A]^1[B]^1$
$rate = k[A][B]$
overall order = 1+1 = 2
$k=\frac{rate}{[A][B]}$ $=\frac{molL^{-1} min^{-1}}{[molL^{-1}][molL^{-1}]} = L mol^{-1} min^{-1}$
Thank you