Chemical Kinetics: Rates of Chemical Reactions

Chemical Kinetics

Introduction to Chemical Kinetics

Chemical kinetics is t he branch of chemistry that studies the speed, or rate, at which chemical reactions occur. Understanding reaction rates helps chemists control and optimize chemical processes, both in the laboratory and in industry.

• Reaction rate: The speed at which reactants are converted to products in a chemical reaction.

• Key factors affecting reaction rates:

  • Reactant concentration

  • Temperature

  • Presence of catalysts

• Goal: To understand chemical reactions at the molecular level.

Defining Rate

What is a Rate?

A rate expresses how much a quantity changes over a given period of time. In chemistry, this typically refers to the change in concentration of a substance per unit time.

• Examples of rates in everyday life:

  • Speed of a car: miles per hour

  • Wages: dollars per hour

  • Pulse: heartbeats per minute

Reaction Rate

Definition of Reaction Rate

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. For reactants, the rate is negative (since their concentration decreases), and for products, it is positive (since their concentration increases).

• General formula for a reaction A → B:

$\text{Rate} = -\frac{\Delta [A]}{\Delta t} = \frac{\Delta [B]}{\Delta t}$

• The negative sign for reactants indicates a decrease in concentration over time.

Example: Rate for a Specific Reaction

For the reaction: $\mathrm{H_2(g) + I_2(g) \rightarrow 2HI(g)}$

$\text{Rate} = -\frac{\Delta [H_2]}{\Delta t} = -\frac{\Delta [I_2]}{\Delta t} = \frac{1}{2}\frac{\Delta [HI]}{\Delta t}$

• The coefficients in the balanced equation are used to relate the rates of change for each species.

Reaction Rate and Stoichiometry

General Rate Expression

For a general reaction: $aA + bB \rightarrow cC + dD$

$\text{Rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t}$

• This equation ensures that the rate is consistent regardless of which reactant or product is measured.

Key Points

• Reaction rate is always positive by convention.

• Stoichiometric coefficients are used to normalize the rates for each species.

Example: Applying Stoichiometry

For the reaction $2A + 3B \rightarrow 4C + D$:

$\text{Rate} = -\frac{1}{2}\frac{\Delta [A]}{\Delta t} = -\frac{1}{3}\frac{\Delta [B]}{\Delta t} = \frac{1}{4}\frac{\Delta [C]}{\Delta t} = \frac{\Delta [D]}{\Delta t}$

Summary Table: Rate Expressions for Reactants and Products

Species	Rate Expression	Sign
Reactant (A)	$-\frac{1}{a}\frac{\Delta [A]}{\Delta t}$	Negative
Reactant (B)	$-\frac{1}{b}\frac{\Delta [B]}{\Delta t}$	Negative
Product (C)	$\frac{1}{c}\frac{\Delta [C]}{\Delta t}$	Positive
Product (D)	$\frac{1}{d}\frac{\Delta [D]}{\Delta t}$	Positive

Additional info:

• Reaction rates are typically measured in units of molarity per second (M/s).

• Experimental determination of rates often involves monitoring concentration changes over time using techniques such as spectrophotometry.