Reaction Kinetics: The Iodination of Acetone – Rate Laws and Activation Energy

Reaction Kinetics

Introduction to Reaction Rates and Rate Laws

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that affect these rates. The rate law quantitatively expresses the relationship between the rate of a reaction and the concentrations of its reactants.

• General Reaction: $aA + bB \rightarrow cC + dD$

• General Rate Law: $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant, [A] and [B] are the concentrations of reactants, and m and n are the reaction orders with respect to A and B, respectively.

• The overall order of the reaction is $m + n$.

• The values of m and n must be determined experimentally; they cannot be deduced from the stoichiometry of the reaction.

Determining Reaction Order from Experimental Data

To determine the order of a reaction with respect to each reactant, the concentration of one reactant is varied while the others are held constant, and the effect on the reaction rate is measured.

• By comparing rates from different experiments, the exponents in the rate law can be found using ratios and logarithms.

• Example Calculation: If doubling [A] while keeping [B] constant doubles the rate, the reaction is first order in A.

• Mathematical Approach: $\frac{\text{Rate}_2}{\text{Rate}_1} = \left(\frac{[A]_2}{[A]_1}\right)^m$ Taking logarithms: $m = \frac{\ln(\text{Rate}_2/\text{Rate}_1)}{\ln([A]_2/[A]_1)}$

Example Table: Hypothetical Rate Study

The following table illustrates how experimental data can be used to determine reaction order:

Series	[A], M	[B], M	Rate, mol/min
1	0.10	0.10	0.012
1	0.20	0.10	0.024
2	0.10	0.10	0.012
2	0.10	0.20	0.012

Additional info: This table is used to show that the rate doubles when [A] is doubled (first order in A), but does not change when [B] is doubled (zero order in B).

Temperature Dependence and the Arrhenius Equation

The rate constant k is affected by temperature, described by the Arrhenius equation:

• $k = A e^{-E_a/(RT)}$

• Taking the natural logarithm: $\ln k = -\frac{E_a}{R}\left(\frac{1}{T}\right) + \ln A$

• Where Ea is the activation energy, R is the gas constant (8.314 J/mol·K), and T is the absolute temperature in Kelvin.

• An Arrhenius plot of $\ln k$ vs. $1/T$ yields a straight line with slope $-E_a/R$.

Iodination of Acetone: Experimental Study

Reaction and Rate Law

• Reaction: $\mathrm{CH_3COCH_3} + \mathrm{I_2} + \mathrm{H^+} \rightarrow \text{Products}$

• General Rate Law: $\text{Rate} = k[\mathrm{CH_3COCH_3}]^x[\mathrm{H^+}]^y[\mathrm{I_2}]^z$

• The exponents x, y, and z are determined experimentally.

Measuring Reaction Rate

• The instantaneous rate can be defined as: $\text{Rate} = -\frac{d[\mathrm{I_2}]}{dt}$

• In practice, the average initial rate is measured: $\text{Rate} = -\frac{\Delta[\mathrm{I_2}]}{\Delta t}$

• The disappearance of the blue starch-iodine complex is used as a visual indicator for the completion of the reaction.

Experimental Procedure Overview

• Prepare mixtures with varying concentrations of acetone, HCl, and I2 as specified in the experimental table.

• Mix solutions at controlled temperatures and measure the time for the blue color to disappear.

• Repeat trials for accuracy and calculate average times.

• Calculate initial concentrations based on solution volumes and concentrations, assuming additive volumes.

Table: Reaction Mixture Conditions

Mixture	Water (mL)	I2 (0.00100 M, mL)	HCl (0.500 M, mL)	Starch Indicator (mL)	Acetone (4.00 M, mL)	Total Volume (mL)
1	5.50	5.50	2.50	2.00	4.50	20.00
2	7.50	5.00	2.00	2.50	3.00	20.00
3	8.00	5.50	2.50	2.00	2.00	20.00
4	5.00	5.00	2.50	2.50	5.00	20.00

Additional info: Table values inferred from the procedure; actual values may vary slightly in the lab manual.

Calculations and Data Analysis

• Calculate the rate for each mixture using the measured time and change in [I2].

• Determine the reaction order with respect to each reactant by comparing rates between mixtures where only one reactant concentration changes.

• Write the experimentally determined rate law and specify the order for each reactant and the overall order.

• Calculate the rate constant k for each mixture and determine the average value.

Temperature Dependence and Activation Energy

• Repeat the reaction at different temperatures (0–35°C) using the same mixture composition.

• Calculate the rate constant k at each temperature.

• Construct an Arrhenius plot ($\ln k$ vs. $1/T$) and determine the activation energy $E_a$ from the slope: $\text{slope} = -\frac{E_a}{R}$

• Solve for $E_a$: $E_a = -\text{slope} \times R$

Sample Table: Arrhenius Plot Data

Temperature (°C)	Temperature (K)	1/T (K-1)	Rate (M/s)	k (M-1s-1)	ln k
5	278	0.00360	0.0005	0.10	-2.30
15	288	0.00347	0.0010	0.20	-1.61
25	298	0.00336	0.0020	0.40	-0.92
35	308	0.00325	0.0040	0.80	-0.22

Additional info: Table values are illustrative; actual experimental values will differ.

Lab Techniques and Safety

• Wear gloves and handle iodine solutions with care; wash skin thoroughly if contact occurs.

• Dispose of iodine-containing waste in designated containers and neutralize spills with 5% Na2S2O3 solution.

• Ensure accurate measurements and avoid cross-contamination.

• Maintain constant temperature for all solutions before mixing.

Sample Calculations and Questions

• Units of k: For a rate law $R = k[A]^{1/2}[B]^2$, units of k are: $\text{M s}^{-1} / (\text{M}^{1/2} \cdot \text{M}^2) = \text{M}^{-3/2} \text{s}^{-1}$

• Effect of Temperature: Reaction rate and rate constant k are affected by temperature; activation energy is not.

• Examples:

  • Platinum is a metal used in automobile catalytic converters.

  • Chlorine atoms (from CFCs) are catalysts in the destruction of ozone.

Summary Table: Key Concepts in Chemical Kinetics

Concept	Definition/Explanation
Rate Law	Mathematical relationship between reaction rate and reactant concentrations
Order of Reaction	Exponent of concentration term in rate law; determined experimentally
Rate Constant (k)	Proportionality constant in rate law; depends on temperature
Activation Energy (Ea)	Minimum energy required for reaction to occur
Arrhenius Equation	Describes temperature dependence of k: $k = Ae^{-E_a/(RT)}$
Arrhenius Plot	Plot of $\ln k$ vs. $1/T$; slope = $-E_a/R$