CP14: Activation Energy from Temperature and Time

A temperature investigation times the same small reaction extent at each measured mixture temperature. Pearson’s supporting context uses a bromide–bromate(V) reaction and a colour endpoint; use the laboratory’s approved formulation and controls. The reaction can generate bromine, so the ventilation, reagent quantities and disposal instructions are essential. Do not improvise a stronger mixture or a sealed heated vessel.

Bromine produced by the reaction is initially consumed by phenol to form 2,4,6-tribromophenol: C₆H₅OH + 3Br₂ → C₆H₂Br₃OH + 3HBr. Once the fixed phenol amount has reacted, further bromine bleaches methyl red. In this clock, methyl red therefore signals that chemical threshold; its disappearance is not being used as an ordinary acid–base titration end point. The phenol amount and indicator conditions must remain comparable between temperatures.

Equilibrate reactant portions in the bath before mixing and measure the actual mixture temperature. Keep initial concentrations, total volume, endpoint chemistry and mixing consistent. Repeats at each temperature reveal timing scatter. Very short clock times give large relative manual-timing uncertainty and may be a poor basis for a precise gradient.

Arrhenius gives ln k = ln A − Ea/(RT). If the fixed-threshold time has k proportional to 1/t under the same other conditions, ln(1/t) against 1/T has gradient −Ea/R. Equivalently, ln t against 1/T has gradient +Ea/R. Pearson’s supporting sheet uses the latter positive-gradient form. The logarithm base, reciprocal temperature and plotted quantity must all be stated.

Convert Celsius to kelvin before taking reciprocals. If the horizontal axis is 1000/T rather than 1/T, the numerical gradient is divided by 1000: multiply it by 1000 before the corresponding Ea calculation. A base-ten logarithm requires the 2.303 conversion factor and cannot be treated as a natural log without adjustment.

Use a gradient from a justified best-fit line rather than one pair of noisy neighbouring readings. Apply the sign appropriate to the chosen vertical axis and use R = 8.314 J mol⁻¹ K⁻¹; convert the result to kJ mol⁻¹ if requested. A positive-gradient ln t plot does not imply a negative activation energy.

The result assumes the same effective mechanism and the proportionality between inverse time and k across the temperature range. Temperature drift, evaporation, changing threshold or significant reactant depletion can weaken that assumption. Repeats, better temperature equilibration and objective endpoint detection address different limitations. A straighter software line alone does not establish that every chemical condition stayed controlled.

Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.