Overview
This lecture covers determining the activation energy of a reaction using the Arrhenius equation and data analysis from a temperature-dependent kinetics experiment involving crystal violet and sodium hydroxide.
Experiment Overview
- Crystal violet reacts with sodium hydroxide to go from purple to colorless.
- The reaction rate is monitored at four different temperatures to extract kinetic data.
- Concentration is determined from absorbance using molar absorptivity.
Kinetic Analysis Review
- Plot concentration vs. time, ln(concentration) vs. time, and 1/concentration vs. time to determine reaction order.
- Reaction is first order with respect to both crystal violet and hydroxide.
- The correct plot is ln(concentration) vs. time for first-order reactions.
- The rate constant (K_obs) is found as the negative slope from the appropriate plot.
- True rate constant K is calculated using K_obs divided by the hydroxide concentration to the first power.
Arrhenius Equation and Activation Energy
- To find activation energy, plot ln(K) vs. 1/T (T in Kelvin).
- Activation energy (Ea) is derived from the slope of this plot, using the Arrhenius equation.
- Temperature must be recorded before and after the reaction; use their average in calculations.
- Temperatures must be converted to Kelvin for calculations due to the gas constant's units.
- Slope from the plot gives –Ea/R; convert units as R is in J/(mol·K) and Ea is reported in kJ/mol.
Practical and Lab Considerations
- Use Excel for data analysis, graphing, and calculations.
- Remove invalid data points (absorbance >1 or <0.1) before analysis.
- Use ice water for low temperatures and a hot plate for high temperatures; exact measured temperatures are required.
- Mix reactants consistently and use parafilm for cuette inversion before measurement.
Key Terms & Definitions
- Activation Energy (Ea) — Minimum energy required for a reaction to proceed.
- Arrhenius Equation — Relates rate constant K to temperature and activation energy.
- First Order Reaction — Reaction rate depends linearly on one reactant.
- Molar Absorptivity — Constant linking absorbance and concentration.
- K_obs — Observed rate constant from kinetic plot.
- Kelvin (K) — Absolute temperature scale required for calculations.
Action Items / Next Steps
- Complete the experiment at four measured temperatures.
- Analyze data in Excel: calculate K, ln(K), 1/T (Kelvin), and plot ln(K) vs. 1/T.
- Remove any outlier absorbance values outside 0.1–1.0.
- Dress appropriately and follow lab safety procedures.