Chemical Kinetics — Revision Notes

⚡ 30-Second Revision

Rate of Reaction: — Change in concentration per unit time. $\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt}$.
Rate Law: — $\text{Rate} = k[A]^x[B]^y$.
Order of Reaction ($n$): — $x+y$. Experimental. Can be 0, fractional, integer.
Molecularity: — Number of species in elementary step. Theoretical. Always 1, 2, or 3.
Units of $k$: — $(\text{mol L}^{-1})^{1-n} \text{ s}^{-1}$.
Zero-Order:

- Rate: $k$ - Integrated: $[A]_t = [A]_0 - kt$ - Half-life: $t_{1/2} = \frac{[A]_0}{2k}$

First-Order:

- Rate: $k[A]$ - Integrated: $\ln[A]_t = \ln[A]_0 - kt$ or $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$ - Half-life: $t_{1/2} = \frac{0.693}{k}$ (independent of $[A]_0$)

Arrhenius Equation: — $k = A e^{-E_a/RT}$ or $\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$.
Catalyst: — Lowers $E_a$, increases rate, does not change equilibrium.

2-Minute Revision

Chemical kinetics studies reaction rates and mechanisms. The rate of reaction is the change in concentration over time, normalized by stoichiometry. Factors like concentration, temperature, catalysts, and surface area influence this rate.

The rate law, $\text{Rate} = k[A]^x[B]^y$, is experimentally determined, where $k$ is the rate constant and $x, y$ are reaction orders. The overall order ($n=x+y$) can be zero, fractional, or integer, unlike molecularity (number of species in an elementary step, always 1, 2, or 3).

Integrated rate laws relate concentration to time: for zero-order, $[A]_t = [A]_0 - kt$; for first-order, $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$. Half-life ($t_{1/2}$) is the time for half reactant consumption; it's constant for first-order reactions ($0.

693/k$). The Arrhenius equation,$k = A e^{-E_a/RT}$, explains temperature dependence, where$E_a$is activation energy. Catalysts speed up reactions by lowering$E_a$ but do not affect equilibrium.

5-Minute Revision

Chemical kinetics is about the 'speed' and 'pathway' of reactions. The rate of reaction measures how fast reactants disappear or products appear, typically in $\text{mol L}^{-1} \text{s}^{-1}$. For $aA \rightarrow bB$, Rate $= -\frac{1}{a}\frac{d[A]}{dt}$. This rate is influenced by reactant concentration, temperature, catalysts, and surface area.

The rate law, $\text{Rate} = k[A]^x[B]^y$, is determined experimentally. Here, $k$ is the rate constant, specific to a reaction at a given temperature, and its units depend on the order of reaction ($n=x+y$). Order can be zero, fractional, or integer. For example, if $k$ has units of $\text{s}^{-1}$, it's a first-order reaction. Don't confuse order with molecularity, which is the number of species in an elementary step (always 1, 2, or 3) and is a theoretical concept.

Integrated rate laws connect concentration and time:

Zero-order: — $[A]_t = [A]_0 - kt$. Plot of $[A]$ vs. $t$ is linear with slope $-k$. Half-life $t_{1/2} = \frac{[A]_0}{2k}$ (depends on initial concentration).
First-order: — $\ln[A]_t = \ln[A]_0 - kt$ or $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$. Plot of $\ln[A]$ vs. $t$ is linear with slope $-k$. Half-life $t_{1/2} = \frac{0.693}{k}$ (independent of initial concentration).

Temperature dependence is described by the Arrhenius equation: $k = A e^{-E_a/RT}$. $E_a$ is the activation energy, the minimum energy for reaction. A higher temperature increases $k$ because more molecules overcome $E_a$. For two temperatures, $\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$. Remember to convert temperatures to Kelvin.

Catalysts speed up reactions by lowering $E_a$ (providing an alternative pathway) without being consumed. They do not alter the equilibrium constant or the overall $\Delta G$ of a reaction; they only help reach equilibrium faster. For NEET, practice numerical problems on integrated rate laws and Arrhenius equation, and conceptual questions on order vs. molecularity and catalyst properties.

Prelims Revision Notes

Chemical Kinetics: NEET Quick Recall Notes

1. Rate of Reaction:

Definition: Change in concentration of reactant/product per unit time.
Units: $\text{mol L}^{-1} \text{s}^{-1}$.
For $aA + bB \rightarrow cC + dD$: Rate $= -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$.
Average Rate: $\frac{\Delta C}{\Delta t}$. Instantaneous Rate: $\frac{dC}{dt}$.

2. Factors Affecting Rate:

Concentration: — Higher concentration $\rightarrow$ faster rate.
Temperature: — Higher temperature $\rightarrow$ faster rate (Arrhenius equation).
Catalyst: — Increases rate by lowering activation energy ($E_a$).
Surface Area: — Larger surface area (for solids) $\rightarrow$ faster rate.
Nature of Reactants: — Bond strengths, molecular complexity.

3. Rate Law & Order of Reaction:

Rate Law: — $\text{Rate} = k[A]^x[B]^y$ (experimentally determined).
Rate Constant ($k$): — Proportionality constant, temperature-dependent.
Order of Reaction ($n$): — Sum of exponents ($x+y$). Can be 0, 1, 2, 3, fractional, or negative. Determined experimentally.
Units of $k$ for $n$-th order: — $(\text{mol L}^{-1})^{1-n} \text{ s}^{-1}$.

* $n=0: \text{mol L}^{-1} \text{ s}^{-1}$ * $n=1: \text{s}^{-1}$ * $n=2: \text{L mol}^{-1} \text{ s}^{-1}$

4. Molecularity:

Definition: Number of reacting species in an elementary step.
Theoretical concept. Always an integer (1, 2, or 3). Never 0 or fractional.
For elementary reactions, molecularity = sum of stoichiometric coefficients of reactants.
Difference from Order: — Order is experimental, for overall reaction; molecularity is theoretical, for elementary steps.

5. Integrated Rate Laws & Half-life ($t_{1/2}$):

Zero-Order Reaction:

* Rate: $\text{Rate} = k$ * Integrated: $[A]_t = [A]_0 - kt$ * Plot: $[A]$ vs. $t$ is linear with slope $-k$. * Half-life: $t_{1/2} = \frac{[A]_0}{2k}$ (depends on initial concentration).

First-Order Reaction:

* Rate: $\text{Rate} = k[A]$ * Integrated: $\ln[A]_t = \ln[A]_0 - kt$ or $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$ * Plot: $\ln[A]$ vs. $t$ is linear with slope $-k$. * Half-life: $t_{1/2} = \frac{0.693}{k}$ (independent of initial concentration).

**Second-Order Reaction (for $\text{Rate} = k[A]^2$):**

* Integrated: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ * Plot: $\frac{1}{[A]}$ vs. $t$ is linear with slope $k$.

6. Arrhenius Equation:

$k = A e^{-E_a/RT}$

* $A$: Arrhenius factor (pre-exponential factor). * $E_a$: Activation energy (minimum energy for reaction). * $R$: Gas constant ($8.314 \text{ J mol}^{-1} \text{K}^{-1}$). $T$: Absolute temperature (Kelvin).

Two-point form: $\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$.
Plot: $\ln k$ vs. $1/T$ is linear with slope $-E_a/R$.

7. Catalysis:

Increases reaction rate by providing an alternative pathway with lower $E_a$.
Does not change $\Delta G$, $\Delta H$, or equilibrium constant ($K_{eq}$). Speeds up attainment of equilibrium.
Not consumed in the reaction.
Highly specific.

Vyyuha Quick Recall

To remember the graphical plots for reaction orders:

'Zero-A, First-LnA, Second-1/A'

Zero-A: — For Zero-order, plot [A] vs. time is linear.
First-LnA: — For First-order, plot ln[A] vs. time is linear.
Second-1/A: — For Second-order, plot 1/[A] vs. time is linear.

And for slopes:

'Zeros and Firsts are Negative, Seconds are Positive'

Zero-order slope: $-k$
First-order slope: $-k$
Second-order slope: $k$