Introduction to Rate Kinetics and Physical Chemistry

Introduction to Chemical Kinetics

• Definition: Kinetics is the study of the rates of chemical processes and provides insight into reaction mechanisms.

• Stoichiometry Limitations: Equations like $2H_2(g) + O_2(g) \rightarrow 2H _2O(g)$ show reactant/product ratios but do not indicate reaction speed, the sequence of steps, or which bonds are broken and formed.

Defining and Measuring Reaction Rates

• Reaction Rate: Defined as the change in concentration of a substance per unit time interval.   * Formula: $\text{rate of a chemical reaction} = \frac{\text{change in concentration}}{\text{time interval}}$   * Mathematical Expression: $\frac{\Delta[]}{\Delta t}$

• Units: Concentration is measured in Molarity ($mol\,dm^{-3}$) and time in seconds $(s)$. The unit for rate is $mol\,dm^{-3}\,s^{-1}$.

• Types of Rates:   * Average Rate: Measured over a large time interval ($t \neq \Delta t$); it generally decreases as the reaction progresses.   * Instantaneous Rate: The rate of reaction at any specific time, $t$.

• Dependence: Rates can be measured by either the consumption of a reactant or the formation of a product.

Questions & Discussion: Calculating Rate

• Prompt: For the reaction $H_2(g) + I_2(g) \rightarrow 2HI(g)$, the starting concentrations for $H_2$, $I_2$, and $HI$ are $1.8$, $1.8$, and $0\,mol\,dm^{-3}$. After $10\,min$, the concentration of $HI$ is $2.0\,mol\,dm^{-3}$. What is the rate of formation for $HI$?

• Response:   * Step 1 (Change in Concentration): $\Delta[HI] = 2.0\,mol\,dm^{-3} - 0\,mol\,dm^{-3} = 2.0\,mol\,dm^{-3}$   * Step 2 (Time Conversion): $10\,min = 600\,s$   * Step 3 (Calculate Rate): $\text{Rate} = \frac{2.0\,mol\,dm^{-3}}{600\,s} = 0.0033\,mol\,dm^{-3}\,s^{-1}$

Factors Affecting Reaction Rates

Five fundamental factors influence the speed of a chemical reaction:

1. Reactant concentration

2. Temperature

3. Action of catalysts

4. Surface area

5. Pressure

Chemical Rate Laws

• Rate Law Expression: $Rate = k[A]^n [B]^m$   * $k$: The rate constant; a measure of intrinsic reactivity. It is independent of concentration but temperature-dependent.   * $n$ and $m$: The reaction orders for specific species; these must be determined experimentally and are not related to stoichiometry.   * Overall Order: The sum of the individual orders ($n + m$).

• Reaction Orders:   * Zero Order: Concentration changes have no effect on the rate.   * First Order: Doubling concentration doubles the rate; $k$ units are $s^{-1}$.   * Second Order: Doubling concentration quadruples the rate ($2^2 = 4$); $k$ units are $mol^{-1}\,dm^3\,s^{-1}$.   * $n^{th}$ Order: Doubling concentration causes a $2^n$ increase in rate.

Activation Energy and Transition States

• Activation Energy ($E_a$): According to Arrhenius, this is the minimum energy required to initiate a chemical reaction and break reactant bonds.

• Activated Complex: A "temporary species" (e.g., $A-B-C$) that exists in a transition state. It occurs at the moment kinetic energy is transformed into internal potential energy, with bonds simultaneously breaking and forming.