Chemca Formula Sheet - Chemical Kinetics

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EXAM MASTER FORMULA SHEET

Chemical Kinetics

High-Yield Content for JEE Main, Advanced & NEET

1. Rate of Reaction & Rate Law

Average & Instantaneous Rate:

For reaction: \( aA + bB \longrightarrow cC + dD \)

\[ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt} \]

Rate Law Expression:

\[ \text{Rate} = k[A]^x [B]^y \]

Order (\(n\)) = \(x + y\)

Unit of Rate Constant (\(k\)):

\[ (\text{mol L}^{-1})^{1-n} \text{ s}^{-1} \]

\(n\) = Order of reaction

2. Integrated Rate Equations

Order	Rate Equation (\(k\))	Half-life (\(t_{1/2}\))	Unit of \(k\)
Zero	\( [A]_0 - [A]_t = kt \)	\( \frac{[A]_0}{2k} \)	\( \text{mol L}^{-1} \text{s}^{-1} \)
First	\( k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t} \)	\( \frac{0.693}{k} \)	\( \text{s}^{-1} \)
Second	\( \frac{1}{[A]_t} - \frac{1}{[A]_0} = kt \)	\( \frac{1}{k[A]_0} \)	\( \text{L mol}^{-1} \text{s}^{-1} \)
n-th	\( \frac{1}{(n-1)} \left[ \frac{1}{[A]_t^{n-1}} - \frac{1}{[A]_0^{n-1}} \right] = kt \)	\( t_{1/2} \propto \frac{1}{[A]_0^{n-1}} \)	-

Note: For First Order, \( t_{75\%} = 2 \times t_{50\%} \) and \( t_{99.9\%} \approx 10 \times t_{50\%} \).

3. Arrhenius Equation

\[ k = A \cdot e^{-E_a/RT} \]

\(A\) = Pre-exponential factor | \(E_a\) = Activation Energy | \(R\) = 8.314 J/K·mol

Two-Temperature Form (Calculation):

\[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right] \]

Temperature Coefficient (\(\eta\)):

\( \frac{k_{T+10}}{k_T} \approx 2 \text{ to } 3 \)

Fraction of effective collisions (\(f\)):

\( f = e^{-E_a/RT} \)

4. Collision Theory & Catalysis

Rate Equation (Collision Theory): \[ \text{Rate} = P \cdot Z_{AB} \cdot e^{-E_a/RT} \]

\(Z_{AB}\) = Collision frequency, \(P\) = Orientation factor (Probability factor)

Molecularity vs Order

• Order: Experimental, can be fractional/zero.
• Molecularity: Theoretical, only for elementary reactions, always a whole number.

Role of Catalyst

Provides an alternate pathway with lower Activation Energy (\(E_a\)). It does not change \(\Delta H\) or equilibrium constant.

5. Methods to Determine Order

Initial Rate Method

Observe change in initial rate by varying initial concentrations of one reactant at a time.

Half-life Method

Relation: \( t_{1/2} \propto a^{1-n} \). By measuring \(t_{1/2}\) at different initial concentrations, \(n\) can be calculated.

Ostwald Isolation Method

Take all reactants except one in large excess to isolate the order with respect to the isolated reactant.

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