Chapter 14: Chemical Kinetics – Study Notes

Chapter 14: Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates at which chemical reactions occur and the factors that affect these rates. Understanding kinetics is essential for controlling reactions in industrial, laboratory, and biological settings.

• Chemical kinetics focuses on how fast reactions proceed and the steps (mechanisms) by which they occur.

• Applications include slowing down undesirable reactions (e.g., food spoilage) and speeding up beneficial ones (e.g., industrial synthesis).

14.1 Factors That Affect Reaction Rates

Physical State of Reactants

The physical state (solid, liquid, gas) of reactants influences how readily they can interact and react.

• Surface area: Reactions involving solids proceed faster when the solid is finely divided, increasing surface area for contact.

• Example: Powdered sugar burns more rapidly than a sugar cube due to greater surface area.

Reactant Concentrations

The rate of a reaction generally increases as the concentration of reactants increases, because more particles are available to collide and react.

• Higher concentration → more frequent collisions → faster reaction rate.

• Example: Increasing the concentration of hydrogen peroxide speeds up its decomposition.

Reaction Temperature

Temperature has a significant effect on reaction rates. Raising the temperature increases the kinetic energy of molecules, leading to more frequent and energetic collisions.

• Higher temperature → faster reaction rate.

• Example: Food spoils faster at room temperature than in a refrigerator.

Presence/Concentration of a Catalyst

Catalysts are substances that increase the rate of a reaction without being consumed in the process. They provide an alternative pathway with a lower activation energy.

• Catalysts do not affect the equilibrium position, only the rate at which equilibrium is reached.

• Example: Enzymes act as biological catalysts in living organisms.

14.2 Reaction Rates

Defining Reaction Rate

The rate of a chemical reaction is the change in concentration of a reactant or product per unit time.

• Average rate: Change in concentration over a specific time interval.

• Instantaneous rate: Rate at a particular moment, given by the slope of the tangent to the concentration vs. time curve.

Formulas:

• Average rate over interval $9;\Delta t\u00039;$: $\text{Average Rate} = -\frac{\Delta [A]}{\Delta t}$

• For a general reaction $aA \rightarrow bB$: $\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt}$

Why Reaction Rates Change Over Time

• As reactants are consumed, their concentrations decrease, leading to fewer collisions and a slower reaction rate.

• Graphically, the concentration vs. time curve flattens as the reaction proceeds.

Measuring Reaction Rates

• Continuous monitoring (e.g., spectrophotometry) provides real-time data.

• Sampling at intervals (aliquots) is used for slower reactions.

• Possible tests: Measuring absorbance of visible/UV light, electrical conductivity, or gas pressure.

14.3 Concentration and Rates

Rate Laws

The rate law expresses the relationship between the reaction rate and the concentrations of reactants. It must be determined experimentally.

• General form: $\text{Rate} = k [A]^m [B]^n$

• $k$ = rate constant (depends on temperature and catalyst)

• $m$, $n$ = reaction orders (not necessarily equal to stoichiometric coefficients)

Determining Rate Laws

• Initial rates method: Measure the rate at the very beginning of the reaction, when product concentrations are negligible.

• Compare experiments with varying initial concentrations to deduce the order with respect to each reactant.

Example Table: Determining Reaction Order

The following table summarizes how changing reactant concentrations affects the reaction rate, allowing determination of reaction order.

Experiment	[A] (M)	[B] (M)	Initial Rate (M/s)
1	0.10	0.10	0.014
2	0.20	0.10	0.028
3	0.10	0.20	0.056

Additional info: The table above is a typical example used to determine the order of reaction with respect to each reactant by comparing how the rate changes when concentrations are varied.

Units of the Rate Constant

• The units of $k$ depend on the overall order of the reaction.

• For a first-order reaction: $[k] = \text{s}^{-1}$

• For a second-order reaction: $[k] = \text{M}^{-1}\text{s}^{-1}$

• For a third-order reaction: $[k] = \text{M}^{-2}\text{s}^{-1}$

Summary Table: Rate Law Orders and Units

Overall Order	Rate Law Example	Units of k
0	Rate = k	M s-1
1	Rate = k[A]	s-1
2	Rate = k[A]2 or k[A][B]	M-1 s-1
3	Rate = k[A]2[B]	M-2 s-1

Key Terms and Concepts

• Reaction rate: Change in concentration of a reactant or product per unit time.

• Rate law: Mathematical relationship between reaction rate and reactant concentrations.

• Order of reaction: Exponent of a reactant concentration in the rate law; indicates how the rate depends on that reactant.

• Rate constant (k): Proportionality constant in the rate law, specific to a given reaction at a given temperature.

• Catalyst: Substance that increases reaction rate without being consumed.

Example Problem

For the reaction: $2\text{N}_2\text{O}_5 (g) \rightarrow 4\text{NO}_2 (g) + \text{O}_2 (g)$

• Calculate the average rate of reaction and the average rate for NO2 formation over a given time interval.

• Use the formula: $\text{Average Rate} = -\frac{1}{2}\frac{\Delta [\text{N}_2\text{O}_5]}{\Delta t} = \frac{1}{4}\frac{\Delta [\text{NO}_2]}{\Delta t}$

Summary

• Chemical kinetics provides insight into how and why reactions occur at different rates.

• Key factors affecting rates include physical state, concentration, temperature, and catalysts.

• Rate laws must be determined experimentally and are essential for predicting and controlling chemical processes.