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Reactivity How fast? The rate of chemical change : R2.2.10 Order of a reaction IB DP Chemistry Study Notes

Reactivity How fast? The rate of chemical change : R2.2.10 Order of a reaction IB DP Chemistry Study Notes - New Syllabus 2025

Reactivity How fast? The rate of chemical change – IB DP Chemistry- Study Notes

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Reactivity 2.2.10 – Reaction Order

Reactivity 2.2.10 – Reaction Order

The order of a reaction refers to how the rate of a chemical reaction depends on the concentration of one or more reactants.

  • The order with respect to a particular reactant is the power (exponent) to which the concentration of that reactant is raised in the rate equation.
  • The overall order of the reaction is the sum of the individual orders with respect to each reactant.

General Rate Equation:

\( \text{Rate} = k[A]^m[B]^n \)

  • \( k \) = rate constant (depends on temperature and catalyst)
  • \( [A], [B] \) = concentrations of reactants A and B
  • \( m \), \( n \) = orders of the reaction with respect to A and B respectively
  • Overall order = \( m + n \)

How to Determine Reaction Order:

  • It must be determined experimentally—it cannot be deduced from the balanced chemical equation (except in elementary steps).
  • The order of a reactant gives insight into how many particles of that reactant are involved in the rate-determining step of the reaction mechanism.

Types of Orders:

OrderDescriptionEffect on Rate
Zero OrderRate is independent of concentrationRate remains constant even if [A] changes
First OrderRate is directly proportional to concentrationIf [A] doubles, rate doubles
Second OrderRate is proportional to the square of concentrationIf [A] doubles, rate increases by a factor of 4

Importance in Mechanism:

  • The order helps determine how many molecules of a substance are involved in the slowest (rate-determining) step.
  • It is a vital link between experimental kinetics and reaction mechanisms.

Key Differences from Stoichiometry:

  • Reaction orders are found from experimental data, not chemical equations.
  • They are not always whole numbers — though for IB Chemistry, only integers (0, 1, 2) are assessed.

Example Rate Equation and Interpretation:

\( \text{Rate} = k[\text{NO}_2]^1[\text{O}_3]^0 \)

  • Order with respect to \( \text{NO}_2 \) = 1 (affects rate)
  • Order with respect to \( \text{O}_3 \) = 0 (no effect on rate)
  • Overall order = 1

Graphical Representations of Reaction Order

Graphical methods are useful for determining the order of a reaction from experimental data. There are two common types of graphs used:

  • Concentration–Time Graphs (to monitor how concentration changes over time)
  • Rate–Concentration Graphs (to relate reaction rate to reactant concentration)

1. Concentration–Time Graphs

OrderShape of [A] vs Time GraphInterpretation
ZeroStraight line with constant negative slopeRate is independent of [A]
FirstExponential decayRate is directly proportional to [A]
SecondSteeper exponential decayRate is proportional to [A]2

2. Rate–Concentration Graphs

OrderShape of Rate vs [A] GraphInterpretation
ZeroHorizontal straight lineRate is constant regardless of [A]
FirstStraight line through originRate ∝ [A]
SecondUpward-sloping curve (quadratic)Rate ∝ [A]2

How to Use the Graphs to Determine Order:

  • Plot [A] vs time → observe whether it’s linear or curved.
  • Plot rate vs [A] → shape of the curve tells the order directly.
  • If you suspect first order: plot ln[A] vs time. If linear, it’s first order.
  • If you suspect second order: plot 1/[A] vs time. If linear, it’s second order.

Graph Interpretation Tips:

  • Always measure rate from slope (gradient) of concentration–time graphs.
  • Use tangents on curved graphs for instantaneous rate at a specific time.
  • Data tables should be used alongside the graphs to calculate average rates or verify linearity.

Example:

Experimental data for a reaction is collected, and a graph of rate vs [A] is plotted. The plot is a curve that passes through the origin and becomes steeper as [A] increases.

▶️Answer/Explanation

The rate increases non-linearly with concentration, forming a curved plot that suggests a second-order relationship. Therefore, the reaction is second order with respect to A.

Note: For IB assessments, only integer values for reaction orders (0, 1, 2) will be considered. Non-integer orders or complex mechanisms are outside the syllabus.

Example:

A student collects the following data for a reaction between reactants P and Q:

[P] (mol/L)[Q] (mol/L)Initial Rate (mol/L·s)
0.100.100.020
0.200.100.040
0.100.200.080

Determine the order with respect to each reactant and write the rate equation.

▶️Answer/Explanation

Compare experiments 1 and 2: [P] doubles, [Q] constant → rate doubles → first order with respect to P

Compare experiments 1 and 3: [Q] doubles, [P] constant → rate quadruples → second order with respect to Q

Rate law: Rate = 𝑘 [ P ] 1 [ Q ] 2

Rate=k[P] 1 [Q] 2

Overall order = 1 + 2 = 3

Example :

A student collected the following data for a reaction involving reactant A:

[A] (mol/L)Rate (mol·L−1·s−1)
0.1\( 1 \times 10^{-3} \)
0.2\( 2 \times 10^{-3} \)
0.3\( 3 \times 10^{-3} \)
0.4\( 4 \times 10^{-3} \)

Determine the rate law for this reaction based on the given data.

▶️Answer/Explanation

We observe a direct linear relationship between the concentration of A and the rate of reaction.

  • When [A] doubles, the rate also doubles.
  • This indicates that the reaction is first order with respect to A.

Therefore, the rate law is:

\( \text{Rate} = k[A]^1 \)

Where:

  • \( k \) is the rate constant
  • \( [A] \) is the concentration of reactant A
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