Chemical Kinetics: Class 12 NCERT Guide to Reaction Rates

Understanding the Rate of a Chemical Reaction

The rate of a chemical reaction tells us how quickly reactants are consumed or products formed. It is expressed as the change in concentration per unit time. For a reaction $R \rightarrow P$, if $[R]_1$ and $[R]_2$ are reactant concentrations at times $t_1$ and $t_2$, then the average rate of disappearance of $R$ is:

$$\text{Average rate} = -\frac{\Delta [R]}{\Delta t} = -\frac{[R]_2 - [R]_1}{t_2 - t_1}$$

The negative sign indicates the concentration of $R$ decreases. Similarly, the average rate of appearance of product $P$ is:

$$\text{Average rate} = \frac{\Delta [P]}{\Delta t}$$

Units are usually mol L$^{-1}$ s$^{-1}$ or mol L$^{-1}$ min$^{-1}$. Instantaneous rate is the rate at a specific moment, found by taking the derivative:

$$\text{Instantaneous rate} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$$

Graphically, it is the slope of the tangent to the concentration vs time curve at that instant.

Calculating Reaction Rates: Examples and Formulas

Let's apply formulas to calculate average rates:

Example 1: For $R \rightarrow P$, $[R]$ changes from 0.03 M to 0.02 M in 25 minutes.

Average rate:

$$= -\frac{0.02 - 0.03}{25} = \frac{0.01}{25} = 4 \times 10^{-4} \text{ M/min}$$

Converting to seconds:

$$25 \text{ min} = 1500 \text{ s}$$

$$\text{Rate} = \frac{0.01}{1500} = 6.67 \times 10^{-6} \text{ M/s}$$

Example 2: For $2A \rightarrow$ Products, $[A]$ decreases from 0.5 to 0.4 mol L$^{-1}$ in 10 minutes.

Rate of disappearance of $A$:

$$-\frac{0.4 - 0.5}{10} = 0.01 \text{ mol L}^{-1} \text{ min}^{-1}$$

Since 2 moles of $A$ react, rate of reaction:

$$= \frac{1}{2} \times 0.01 = 0.005 \text{ mol L}^{-1} \text{ min}^{-1}$$

These calculations are crucial for Class 12 NCERT exams.

Rate Laws and Reaction Order Explained

The rate law expresses how the reaction rate depends on reactant concentrations. It is written as:

$$r = k [A]^m [B]^n$$

where:

• $r$ is the rate,
• $k$ is the rate constant,
• $m$ and $n$ are the orders with respect to reactants $A$ and $B$.

The overall reaction order is the sum $m + n$.

Example: For rate law $r = k [A]^{1/2} [B]^2$, the order with respect to $A$ is 0.5, and with respect to $B$ is 2.

Overall order = 0.5 + 2 = 2.5

Understanding reaction order helps predict how changing concentrations affect the rate.

Effect of Stoichiometry on Reaction Rate Expressions

In reactions where reactants and products have different stoichiometric coefficients, rates must be adjusted to maintain consistency.

For example, in:

$$2HI \rightarrow H_2 + I_2$$

The rate of disappearance of $HI$ is twice the rate of appearance of $H_2$ or $I_2$.

Rate expressions:

This ensures the reaction rate is the same regardless of which species concentration change is measured.

Factors Influencing Reaction Rates in Chemical Kinetics

Several factors affect how fast a chemical reaction proceeds:

• Concentration: Higher reactant concentration usually increases rate.
• Temperature: Raising temperature increases kinetic energy, speeding up reactions.
• Catalysts: Substances that lower activation energy, increasing rate without being consumed.
• Surface Area: More surface area of solids increases reaction rate.
• Nature of Reactants: Ionic reactions are generally faster than covalent ones.

Understanding these factors helps in controlling reactions in labs and industries.

Comparing Average and Instantaneous Rates

Both rates are important: average rate gives an overall speed, while instantaneous rate reveals reaction speed at any moment.