In Depth Notes on Reaction Rates and Rate Laws

UNIT 5 IMPORTANT INFORMATION

REACTION RATES & RATE LAWS

REACTION RATES

• A rate measures how fast a change occurs over time, specifically in chemical reactions is measured as a change in concentrations of reactants/products divided by change in time.
• Formula:
  $Rate = \frac{\Delta [A]}{\Delta t}$
• Example Reaction:
  $H<em>2(g) + I</em>2(g) \rightarrow 2 HI(g)$
• For a given time interval $t<em>1$ to $t</em>2$, the rate can be expressed as:
  $Rate = \frac{A[H<em>2]}{\Delta t} + \frac{A[I</em>2]}{\Delta t} + \frac{A[HI]}{\Delta t}$

Changes in Reactant & Product Concentration

• Reactants are consumed leading to a negative change.
• Products are formed leading to a positive change.

Average Rate of Change

• Formula:
  $\text{Average Rate} = \frac{[C]<em>{final} - [C]</em>{initial}}{t<em>{final} - t</em>{initial}}$

Instantaneous Rate of Change

• Obtained by drawing a tangent to the curve at a specific point and calculating the slope of that tangent.

Rate Laws

• Generally, for an elementary reaction, the reaction can be expressed as:
  $aA + bB \rightarrow cC + dD$
• Rate expression based on stoichiometry:
  $Rate = k[A]^n[B]^m$ where $n$ and $m$ are the orders of the reaction.

Order of Reactions

1. Zero-Order Reaction: If $n = 0$, the rate is constant and independent of concentration.

   • $Rate = k$(units of $k$: M/s)

2. First Order Reaction: If $n = 1$, rate is directly proportional to the concentration.

   • $Rate = k[A]^1$
   • Doubling concentration doubles the rate.

3. Second Order Reaction: If $n = 2$, rate is proportional to the square of the concentration.

   • $Rate = k[A]^2$
   • Doubling concentration quadruples the rate.

Factors Affecting Reaction Rates

• Collision Theory: For a reaction to occur, particles must collide with the correct orientation and sufficient energy.
• Increasing Temperature: Increases kinetic energy, hence the rate of reaction increases.
• Increasing Concentration: Higher concentration results in more collisions, increasing reaction rate.
• Increasing Surface Area: More area available for reaction leads to increased collisions.
• Using a Catalyst: Lowers activation energy, facilitating the reaction and increasing the rate.

Integrated Rate Laws

1. Zeroth Order:

   • $[A] = [A]_0 - kt$
   • Half-life: $t<em>{1/2} = \frac{[A]</em>0}{2k}$

2. First Order:

   • $ln[A] = ln[A]_0 - kt$
   • Half-life: $t_{1/2} = \frac{0.693}{k}$

3. Second Order:

   • $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$
   • Half-life: $t<em>{1/2} = \frac{1}{k[A]</em>0}$

Sample Problems Summary

1. Average rate calculations using concentration changes over time with specific examples provided.
2. Understanding of rate laws and experimental data leading to conclusions about reaction order and constants.
3. Application of collision theory to explain observed changes in reaction rates under various conditions.

CATALYSIS

• Catalysts change the mechanism of a reaction making it faster, and are not consumed in the overall reaction.

REACTION MECHANISMS

• Chemical reactions often proceed in multiple steps (elementary steps), with the slowest step being the rate-determining step.
• The reaction mechanism must sum to the overall balanced equation, and validate against experimental rate laws.
• Mechanism validation requires:
  1. Overall steps match.
  2. Rate law prediction matches observed data.