The Chemistry Solution: Determining Rate Law from Experimental Data

Introduction

• Rate laws must be experimentally determined.
• Cannot deduce rate law from the stoichiometry of a reaction.
• Required to collect experimental data, often provided in lecture courses.

Experimental Setup

• Run the chemical reaction for a short time.
• Alter concentration of one reactant at a time to observe initial instantaneous rate.
• Determine how reaction rate changes with changes in concentration.

Determining Reaction Order

• Each reactant can be 0, 1st, 2nd, or 3rd order.
• Overall rate law depends on individual orders of reactants.

Example: Reaction A + B -> C

• Rate law format: rate = k[A]^x[B]^y
• Aim: Determine exponents x and y.

Determining Order for A

• Compare experiments where only [A] changes and [B] remains constant.
• Logical Approach:
  • Example: [A] doubles, rate doubles -> 1st order with respect to A.
  • If rate change mirrors concentration change, reaction is 1st order.
• Mathematical Approach:
  • Use proportionality to cancel terms and solve for x.
  • Example calculation shows x = 1 for A (1st order).

Determining Order for B

• Compare experiments where only [B] changes and [A] remains constant.
• Example: [B] doubles, rate quadruples -> 2nd order with respect to B.
• Mathematical Approach:
  • Solve for y using proportionality, example shows y = 2 for B (2nd order).

Calculating the Rate Constant (k)

• Use known reaction rate data to solve for k.
• Rate constant should be consistent across all experiments.
• Example calculation shows k = 0.0875 with appropriate units.

Additional Example

• Similar process applied to another reaction A + B -> C.
• Determining Order for A:
  • [A] triples, rate increases by factor of 9 -> 2nd order.
• Determining Order for B:
  • [B] changes, no rate change -> 0 order.
• Calculate k, example shows k = 3.75 x 10^(-3) with units.

Key Points

• Reaction orders are typically integers in general chemistry.
• Orders may indicate more complex kinetics if non-integers.
• Understanding exponents for 1st, 2nd, and 3rd order reactions:
  • 1st order: rate change = concentration change.
  • 2nd order: rate change = square of concentration change.
  • 3rd order: rate change = cube of concentration change.

Conclusion

• Tutorial on determining rate laws from experimental data highlights process and calculations to determine reaction orders and rate constant.
• Encourages practice with provided or hypothetical examples to reinforce learning.