Chemical Kinetic Formulas

Going through the Chemical Kinetics Cheat Sheet you will have an overview of what Chemical Kinetics is exactly. Take your preparation to the next level by employing the Chemical Kinetic Formulae over here and solve the reactions quickly. Try to memorize the Simple Formulas on Chemical Kinetics provided as they form a stronger base during your study.

1. Rate of Reaction in the form of a Chemical reaction:
m₁A + m₂B + ……… → n₁P + n₂Q + n₃R + ……..
Rate of reaction = \(-\frac{1}{m_{1}} \frac{d[A]}{d t}=-\frac{1}{m_{2}} \frac{d[B]}{d t}=\frac{1}{n_{1}} \frac{d[P]}{d t}=\frac{1}{n_{2}} \frac{d[Q]}{d t}\)

2. Unit of Rate constant:
K = mol^1-Δn lit^Δn-1 sec^-1

3. First order reaction:
K = \(\frac{2.303}{t} \log _{10} \frac{a}{(a-x)}\)
& t_1/2 = \(\frac{0.693}{\mathrm{K}}\)
& [A]_t = [A]₀e^-kt (wilhelmy equation)
K = \(\frac{2.303}{t} \log \left(\frac{\mathbf{v}_{\infty}-\mathbf{v}_{0}}{\mathbf{v}_{\infty}-\mathbf{v}_{t}}\right) h\)
& K = \(\frac{2.303}{t} \log _{10}\left(\frac{P_{0}}{P_{0}-x}\right)\)
& K = \(\frac{2.303}{t} \log \left(\frac{r_{\infty}-r_{0}}{r_{\infty}-r_{t}}\right)\)
n = 1 + \(\frac{\log _{10}\left(t_{1 / 2}\right)_{1}-\log _{10}\left(t_{1 / 2}\right)_{2}}{\log _{10}\left(a_{2}\right)-\log _{10}\left(a_{1}\right)}\)

4. Second Order Reaction:
Case: (i) When concentration of A and B taking same.
K₂ = \(\frac{1}{t}\left(\frac{x}{a(a-x)}\right)\)

(ii) When concentration of A and B are taking different –
K₂ = \(\frac{2.303}{t(a-b)} \log \frac{b(a-x)}{a(b-x)}\)
t_1/2 = \(\frac{1}{\mathrm{K}_{2} \mathrm{a}}\)
&

5. Zero Order Reaction:
x = Kt & t_1/2 = \(\frac{\mathrm{a}}{2 \mathrm{K}}\)
The rate of reaction is independent of the concentration of the reacting substance.

6. Third Order Reaction:
K = \(\frac{1}{t} \cdot \frac{x(2 a-x)}{2 a^{2}(a-x)^{2}}\) & t_1/2 = \(\frac{3}{2 a^{2}}\)

7. Difference between Molecularity and Order of Reaction:

Molecularity	Order of Reaction
1. It is the number of molecules of reactants concentration terms taking part in elementary step of a reaction.	1. It is sum of power raised on the rate expression.
2. Molecularity is a theoretical value and is derived from mechanism.	2. Order of a reaction is experiment value derived from rate expression.
3. Molecularity can neither be zero nor fractional.	3. Order of a reaction can be zero, fractional for integer.
4. It is a assigned for each step of mechanism separately.	4. Order of a reaction may have negative value.
5. It is a assigned for each step of mechanism separately.	5. It is as singed for overall reaction.
6. It is independent of pressure and temperature.	6. It depends upon pressure and temperature.

8. Difference between Rate of Reaction & Rate constant:

Rate of reaction	Reaction rate constant
1. Rate of reaction is called as the change in concentration reactant or product per unit time.	1. Rate constant is the proportionality constant in the rate Saw equation. When molar concentration of reactants is taken as unity, its value is equal to rate of reaction.
2. Rate of reaction varies with concentration of the reactant.	2. Since it is proportionality constant for a articular reaction, it is independent of the concentration of the reactant.
3. Rate of reaction increases with increase in temperature.	3. Rate constant value also varies directly with the temperature.
4. The units of rate of reaction is mole litre-1 time-1.	4. The units of reaction rate constant depends upon the order of reaction i.e. its unit differs according to order of reaction.

9. Difference between Rate Law and Law of Mass Action:

Rate Law	Law of Mass action
1. It is an experimentally observed law.	1. It is a theoretical law.
2. It depends on the concentration terms on which the rate of reaction actually depends eg. for the reaction. aA + bB → Products Rate law, Rate = k[A]m[B]n	2. It is based upon the stoichiometry of the equation eg., for the reaction, aA + bB → Product Rate = k [A]a[B]b

10. Determination of order:
\(\frac{t_{2}}{t_{1}}=\left[\frac{a_{1}}{a_{2}}\right]^{n-1}\) [∵ t_1/2 ∝ \(\frac{1}{a^{n-1}}\)]
t(half life) ………….. a (Initial conc.)

11. Arrhenius equation:
k = Ae^-Ea/RT
& slope = \(\frac{-\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}\)
Temperature Coefficient = \(\frac{K a t\left(t+10^{\circ} C\right)}{K a t t^{\circ} C}=\frac{K_{35^{\prime} C}}{K_{25^{\prime} C}}\)

12. Positive catalyst increases the rate of reaction while, the negative catalyst decreases.

Process	Catalyst
1. Haber’s process for synthesis of ammonia	Iron Mo (promoter)
2. Contact process for manufacture of H2SO4	Pt, V2O5
3. Ostwald process for manufacture of HNO3	Pt gauze
4. Deacon’s process for manufacture of Cl2	Cu2Cl2
5. Bosch process for manufacture of H2	Fe2O3 + Cr2O3
6. Manufacture of vegetable ghee	Ni
7. Manufacture of C2H5OH from sucrose	Invertase, Zymase
8. Manufacture of C2H5OH from starch	Diastase, Maltase
9. Methanol from H2 and CO	ZnO & Cr2O3
10. Dehydrogenation of alkenes	H3PO4 on kieselguhr
11. Acetic acid by oxidation with air	V2O5

13. log\(\left(\frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}\right)\) = \(\frac{\mathrm{E}_{\mathrm{a}}}{2.303}\left(\frac{\mathrm{T}_{2}-\mathrm{T}_{1}}{\mathrm{T}_{1} \mathrm{T}_{2}}\right)\)

14. Energy of activation = Threshold energy – Energy of reactant
ΔE = E_p – E_R
Einstein

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