1. Rate/velocity of Chemical Reaction:
Rate =ΔCΔt=molelittime=mole lit -1time-1=mole dm-3 time-1.
2. Types of Rates of Chemical Reaction:
For a reaction R⟶P
Average rate = Total change in concentration Total time taken
Rinstantaneous =limt→0 ΔcΔt=dcdt=-dRdt=d[P]dt
3. Rate Law (dependence of rate on concentration of reactants):
Rate =k conc.or der→ differential rate equation for rate expression.
Where k= Rate constant = specific reaction rate = rate of reaction when concentration is unity.
unit of k=(conc)1- order time-1
4. Order of Reaction:
m1A+m2B⟶ products.
R∝ApB q
Where p may or may not be equal to m1 & similarly q may or may not be equal to m2.
p is order of reaction with respect to reactant A and q is order of reaction with respect to reactant B and
p+q is overall order of the reaction.
5. Molecularity of a Reaction:
It is defined as the number of molecules colliding with each other in an elementary reaction. For example: A→B reaction has molecularity =1
For an elementary reaction, Molecularity = Order.
For a complex reaction, Molecularity has no meaning. However, Molecularity of Rate determining step (RDS) can be approximately used to determine the overall rate of reaction.
6. Integrated Rate Laws:
C0 or 'a' is initial concentration and Ct or a-x is concentration at time 't'
(i) For Zero Order Reaction:
Rate =k[conc.]0=constant
Rate =k=C0-C tt or Ct=C0- kt
Unit of k= mol lit -1sec-1, Time for completion of reaction=C0k
at Half life time t12, Ct=C0 2, so kt12=C02
⇒t12=C02k ∴t12∝C0
(ii) For First Order Reaction:
For a 1st order reaction is A⟶ Products.
t=2.303klogaa-x o r k=2.303tlogC0Ct
⟹ t12=ln2k=0.693k= Independent of initial concentration.
tAvg. =1k=1.44 t12
Graphical representation:
t=-2.303klogCt+2.303klogC0
(iii) Second Order Reaction:
2nd order Reactions are of two types
A + A ⟶ products a a 0 a-x a-x x ∴dxdt=k(a-x )2 ⇒1a-x-1a=kt | A + B ⟶ products. a b 0 a-x b-x x dxdt=ka-xb-x k=2.303a-blogba-xab-x |
(iv) Pseudo first order reaction:
∴For A+B⟶ Products Rate =KA1B1
k=2.303ta-blogba-xa b-x
Now if 'B' is taken in large excess b >>a
⇒k=2.303b tlogaa-x
'b' is very large can be taken as constant.
⇒kb=2.303tlogaa-x ⇒k'=2.303tlogaa-x
k'=kb is pseudo first order rate constant.
7. Methods to determine Order of a Reaction:
(i) Initial rate method:
r=kAaB bCc
if b= constant and c= constant
then for two different initial concentrations of A we have
r01=kA01a, r02=kA02a ⇒r01 r02=A01A02a
(ii) Using integrated rate law: It is a method of trial and error.
(iii) Method of half-lives:
For nth order reaction t12∝1R0n- 1
(iv) Ostwald Isolation Method:
rate =kAaBbCc=k0Aa
If B and C is taken in excess.
8. Methods to monitor the Progress of the First Order Reaction:
(i) Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature or by measuring total volume of mixture under constant pressure and temperature.
An→Δ nA
∴ k =2.303tlogP0n-1nP0-Pt {Formula is not applicable when n=1, the value of n can be fractional also}.
Here, Po and Pt represent the total pressure exerted by the system of gas at the starting of the reaction and at the reference time respectively.
(ii) By titration method:
H2O 2l→ H2Ol+O2 g
a00a-xxx2
∴ a∝V0 a-x∝Vt
⇒k=2.303tlogV0Vt
(iii) Study of acid hydrolysis of an ester:
RCOOR'l+H2Ol→ H+aq. RCOOH+R'O H
V∞= Volume of NaOH used at t=∞.
Vt= Volume of NaOH used at reference time.
V0= Volume of NaOH used at t=0
k=2.303tlogV∞-V0 V∞-Vt
(iv) By measuring optical rotation produced by the reaction mixture:
RCOOR'l+H2Ol →H+aq. RCOOH+R 'OH
θ∞=Optical rotation produced by the mixture at time t=∞.
θ0=Optical rotation produced by the mixture at t=0.
θt=Optical rotation produced by the mixture at reference time.
k= 2.303tlogθ0-θ∞θt- θ∞
9. Effect of Temperature on Rate of Reaction:
T.C. = Kt+10Kt=2 to 3 (for most of the reactions)
Arrhenius theory of reaction rate:
ΣHR=Summation of enthalpies of reactants.
ΣHP= Summation of enthalpies of products.
ΔH= Enthalpy change during the reaction.
Ea1= Energy of activation of the forward reaction.
Ea2= Energy of activation of the backward reaction.
ΣHP> ΣHR→ endothermic.
ΣHP< ΣHR→ exothermic.
ΔH=ΣHP- ΣHR= enthalpy change:
ΔH=ΣHP- ΣHR
Ethreshold =Ea1 + ΣHR =Ea2+ΣHP
Arrhenius equation:
k=Ae-EaRT
r=kconc.n
dlnkdT=EaRT2
logk=-Ea2.303R1T+logA
If k1 and k 2 be the rate constant of a reaction at two different temperature T1 and T2 respectively, then we have:
logk2k1=Ea2.303R1T1-1T2
Ink=lnA-EaRT
T→∞,K→A
10. Reversible Reactions:
kf=A f e-Ea RT
kb=Abe-EbRT
Keq=kfk b=AfAbe-Ea-EbRT
In K eq=-ΔHRT+lnAf Ab
Parallel 1st Order Reaction:
BC=k 1k2⇒Ea=Ea1k1+Ea2k2 k1+k2.
x=kfa kf+kb1-e-kf+kbt
REVERSIBLE 1ST ORDER REACTION: A⇌kbkfB
kf+kb=1tlnxeq.x eq-x
SEQUENTIAL 1ST ORDER REACTION: A→k1B→k2C
At=Aoe-k1t
Bt=k1a k2-k1e-k1t-e-k2t tBmax=1k1-k2 lnk1k2
tBmax= Time taken by B to reach the maximum concentration
CASE-I:
k1≫k2
CASE-II:
k2≫k1