RP3: Rate of Reaction with Temperature

1. Reaction Equation & Practical Aim

The aim of Required Practical 3 is to determine how the rate of a chemical reaction changes with temperature and calculate the experimental activation energy (Ea) using the Arrhenius relationship.

The reaction studied is between aqueous sodium thiosulfate and dilute hydrochloric acid:

Chemical Equation for Colloidal Sulfur Formation Na2S2O3(aq) + 2HCl(aq) → 2NaCl(aq) + SO2(g) + S(s) + H2O(l)

- Precipitate: Insoluble elemental sulfur (S) forms as a colloidal suspension, causing the transparent solution to turn progressively opaque and cloudy yellow.
- Gaseous By-Product: Toxic, choking sulfur dioxide (SO2) gas is released.

2. Disappearing Cross Experimental Protocol

The reaction rate is measured by timing how long it takes for a fixed amount of sulfur precipitate to obscure a printed black cross placed underneath the reaction vessel:

Mark a bold black cross (an 'X') on a square piece of white paper. Place a clean 100 cm3 conical flask directly on top of the cross.
Using a clean measuring cylinder, add 25.0 cm3 of 0.050 mol dm^-3 sodium thiosulfate solution to the conical flask.
In a separate boiling tube, measure 5.0 cm3 of 1.0 mol dm^-3 hydrochloric acid.
Place both containers into a thermostated water bath set to the target temperature (e.g. room temperature ~20 deg C, then 30, 40, 50, and 60 deg C).
Once both solutions reach thermal equilibrium with the bath, record the actual temperature of the thiosulfate solution with a thermometer.
Add the acid to the conical flask, swirl once to mix thoroughly, place back over the cross, and immediately start the stopwatch.
Look vertically down through the mouth of the conical flask from a fixed distance directly above the cross.
Stop the stopwatch the exact instant the black cross can no longer be seen through the murky suspension. Record the elapsed time (t) in seconds.
Immediately pour the contents of the flask into a sodium carbonate stop bath to neutralise the acid and dissolve SO2.

3. Water Bath Regulation & Thermal Pre-Equilibration

In kinetics experiments with temperature, uneven thermal gradients produce massive errors. In RP3, the following temperature control standards are mandatory:

Pre-Equilibration Protocol

Never heat sodium thiosulfate in a flask and add cold room-temperature hydrochloric acid. Mixing hot liquid with cold liquid drops the temperature instantly by 2 to 5 deg C, creating a fluctuating, non-isothermal reaction.

Remedy: Place both the thiosulfate flask and the boiling tube containing HCl into the same water bath for at least 5 minutes before mixing so both reactants start at the exact same temperature.

Measuring Mean Temperature

During the reaction, the liquid cools slightly toward room temperature. Record the temperature at the start (t = 0) and immediately after the cross disappears (t = end). Use the mean temperature for data plotting:

T_mean = (T_initial + T_final) / 2

4. Justification of Rate ∝ 1/t

In OxfordAQA Paper 5, candidates are regularly asked: "Explain why 1/t can be used as a measure of the initial rate of reaction in this experiment."

Theoretical Justification of 1/t 1. By definition, Rate = (change in concentration of product) / (time taken).
2. The black cross is obscured when a fixed, constant mass of sulfur precipitate has formed inside the flask.
3. Because the depth of liquid, flask geometry, and cross darkness are kept constant, the change in sulfur concentration (Δ[S]) is identical across all runs.
4. Therefore: Rate = constant / t ∝ 1 / t.
5. The reciprocal time (1/t, in s^-1) is directly proportional to the initial rate of reaction.

5. Calculating Activation Energy (Ea) via Arrhenius Plot

The Arrhenius equation links rate to temperature: k = A * e^(-Ea / RT). Because rate is proportional to 1/t, we can substitute rate into the natural logarithm form:

ln(1 / t) = (-Ea / R) * (1 / T) + constant

Variable / Parameter	Plotted Axis	Units	Examiner Attention Point
ln(1 / t)	Vertical y-axis	Dimensionless (negative values)	Values of ln(1/t) are negative (e.g. -3.2, -4.5) because t > 1 s. Ensure the y-axis accommodates negative values.
1 / T	Horizontal x-axis	K^-1 (typically scaled as 10^-3 K^-1)	Temperature must be converted from Celsius to Kelvin: `T(K) = theta(deg C) + 273.15`.
Gradient (m)	Line of best fit	Kelvin (K)	Gradient is negative: `m = -Ea / R`.
Activation Energy (Ea)	Calculated	J mol^-1 → convert to kJ mol^-1	`Ea = -m * 8.314 J mol^-1`. Divide by 1000 to report final answer in kJ mol^-1.

6. Sulfur Dioxide Hazard Control & Sodium Carbonate Stop Bath

Sulfur dioxide (SO2) is a toxic, choking gas that triggers severe respiratory irritation and acute bronchospasms in individuals with asthma.

Hazard Controls in the Laboratory

Fume Cupboards: Where possible, carry out the experiment inside an operating fume cupboard.
Small Quantities: Restrict solution volumes to 25 cm3 of dilute thiosulfate (0.050 M) to cap the maximum theoretical moles of SO2 produced at ≤ 0.00125 mol.
Room Ventilation: Keep laboratory windows open to ensure rapid atmospheric dispersion.

Sodium Carbonate Stop Bath Protocol

Prepare a large plastic container containing aqueous sodium carbonate (Na2CO3) with a dash of phenolphthalein indicator. Immediately after the cross disappears:

Pour the reaction mixture into the stop bath.
The basic carbonate rapidly neutralises the acid, terminating the reaction: Na2CO3 + 2HCl → 2NaCl + H2O + CO2.
It reacts with dissolved SO2 to form non-volatile sodium sulfite: SO2 + Na2CO3 → Na2SO3 + CO2, trapping the gas in solution.

7. Worked Activation Energy Problem

Worked Example: Calculating Ea from Disappearing Cross Timings

Problem: A student carried out RP3 at five different temperatures. A plot of ln(1 / t) on the y-axis against 1 / T (in K^-1) on the x-axis gave a straight line passing through:

Point 1: 1/T = 3.05 * 10^-3 K^-1, ln(1/t) = -2.85
Point 2: 1/T = 3.40 * 10^-3 K^-1, ln(1/t) = -5.02

Calculate the activation energy (Ea) for this reaction in kJ mol^-1. (R = 8.314 J K^-1 mol^-1).

Step 1: Calculate the gradient (m) of the Arrhenius line

m = delta y / delta x
m = (-5.02 - (-2.85)) / ((3.40 * 10^-3) - (3.05 * 10^-3))
m = -2.17 / (0.35 * 10^-3) = -6200 K

Step 2: Relate gradient to Ea

Gradient m = -Ea / R
-6200 = -Ea / 8.314
Ea = 6200 * 8.314 = 51,546.8 J mol^-1

Step 3: Convert to kJ mol^-1

Ea = 51,546.8 / 1000 = 51.5 kJ mol^-1 (3 significant figures)

Final Answer: Ea = +51.5 kJ mol-1

8. Practice Exam Questions

Question 1: What is the primary purpose of disposing of the reaction mixture into a sodium carbonate stop bath immediately after timing RP3?

A. To dissolve the sulfur precipitate so the flask can be re-used immediately. B. To neutralise acid and react with toxic sulfur dioxide gas, preventing it escaping into the laboratory. C. To bleach the yellow sulfur color so it does not stain the glass. D. To lower the activation energy of the remaining reactants.

Show Answer & Explanation

Correct Answer: B

Sodium carbonate neutralises excess HCl and reacts with dissolved SO2 to form non-volatile sodium sulfite (Na2SO3), preventing the escape of hazardous sulfur dioxide gas into room air.

Question 2: In RP3, why does a student pre-warm both the hydrochloric acid and the sodium thiosulfate solutions in the water bath before mixing?

A. To ensure that both solutions start at the same target temperature, preventing thermal shock and temperature drops upon mixing. B. To increase the volume of the solutions via thermal expansion. C. To dissolve any solid sulfur already present in the thiosulfate bottle. D. To activate the acid molecules before they encounter water.

Show Answer & Explanation

Correct Answer: A

Adding cold acid to warm thiosulfate lowers the overall temperature immediately. Pre-warming both reactants ensures the reaction runs at a constant, well-defined initial temperature.