Kinetics - Rate Law

Concept: Determine reaction order with respect to A

• Rate law (simplified): $r = k [A]^n$ (assuming other reactants are constant or not involved in the rate-determining step)

• Goal: find the exponent $n$ that describes how the rate depends on $[A]$

Method: use initial-rate comparisons to cancel constants

• Compare trials where all factors except $[A]$ are held constant

• Constants cancel in ratios, leaving only the concentration terms and $n$

• Key ratio: $\frac{r<em>1}{r</em>2} = \left( \frac{[A]<em>1}{[A]</em>2} \right)^n$

Calculation steps

• Solve for $n$ from a pair of trials:
  $n = \frac{\log\left( \frac{r<em>1}{r</em>2} \right)}{\log\left( \frac{[A]<em>1}{[A]</em>2} \right)}$

• If more trials are available, check that the computed $n$ is consistent across pairs

Interpretation of results

• $n \approx 0$: zero-order in A (rate independent of $[A]$)

• $n \approx 1$: first-order in A

• $n \approx 2$: second-order in A

• Non-integer values indicate fractional or complex reaction order possibilities

Practical notes

• Use initial rates from each trial

• Ensure other reactants and conditions are held constant across the chosen trials

• The choice of trial pairs can be arbitrary; consistency across multiple pairs strengthens the result

• When comparing, remember to use natural logarithms or common logarithms consistently in the ratio