1. Core Graphing Standards & Exam Conventions
Plotting and interpreting experimental graphs carries heavy mark weight in OxfordAQA Paper 5. Examiners enforce strict technical criteria for graph construction:
Axis Scaling & Plotting Standards
- Grid Occupancy: Plotted data points must occupy at least 50% of the grid in both horizontal (x) and vertical (y) dimensions. Awkward scale divisions (such as 3, 7, or 9 small squares per unit) are heavily penalized.
- Axis Labelling: Axes must be labelled with the full physical quantity name and unit separated by a solidus or slash (e.g.
Time / s,Volume / cm3,ln k). - Point Plotting: Plot points using a small sharp 'x' or a circled dot. Points must be plotted within half a small grid square of true values.
Lines of Best Fit & Anomalies
- Smoothness: Draw a single, thin, continuous straight line or smooth curve with a transparent ruler or steady hand. Never draw "dot-to-dot" jagged lines.
- Balance: An equal distribution of data points should lie above and below the line of best fit.
- Anomalous Points: Identify outliers that deviate markedly from the general trend. Circle anomalies and disregard them when positioning the line of best fit.
2. Reaction Rate Graphs & Tangent Construction
In kinetics (RP3 and RP7), experimental progress is tracked by measuring either the decrease in reactant concentration or the increase in product volume over time.
- Instantaneous Rate (at time t): The reaction rate at a specific point in time. Measured by drawing a tangent to the curve at time t and finding its gradient.
- Gradient Formula: Gradient = delta y / delta x = (change in concentration or volume) / (change in time).
When calculating a gradient from a tangent, examiners demand that your gradient triangle is large (hypotenuse must cover at least 50% of the drawn tangent line). Reading coordinates from a tiny triangle magnifies reading errors and loses precision marks.
3. Arrhenius Plots & Activation Energy Determination
The Arrhenius equation models how rate constants increase exponentially with absolute temperature:
Taking the natural logarithm of both sides converts this relationship into standard linear form (y = mx + c):
Linear Transformation Terms
- Dependent Variable (y-axis): ln k (or ln(1/t) in disappearing cross experiments where rate proportional to 1/t).
- Independent Variable (x-axis): 1/T, where temperature T must be in Kelvin (K). Typically plotted with scale 10^-3 K^-1.
- Gradient (m): Gradient = -Ea / R. Because gradient is negative, -Ea / R is negative, yielding a positive activation energy Ea.
- y-intercept (c): c = ln A, giving pre-exponential factor A = e^c.
Unit Conversion Trap (R = 8.314)
The gas constant R has units of J K^-1 mol^-1. Therefore, calculating Ea directly from the gradient gives:
Examination questions almost always request Ea in kJ mol^-1. You must divide by 1000:
4. Titration Curve Inflection Points & Indicator Selection
In acid-base titrations (RP1 and RP9), continuous pH measurement yields titration curves that reveal the strength of acids and bases, the volume required for neutralisation, and the acid dissociation constant (Ka).
| Titration Combination | Initial pH | Vertical Inflection Jump | Equivalence Point pH | Suitable Indicator |
|---|---|---|---|---|
| Strong Acid + Strong Base | pH ~ 1 | pH 3 to 11 (wide vertical section) | pH 7.0 | Either Methyl Orange (pH 3.1-4.4) or Phenolphthalein (pH 8.3-10.0) |
| Weak Acid + Strong Base | pH ~ 3 | pH 7 to 11 (vertical in alkaline range) | pH ~ 8.5 - 9.0 | Phenolphthalein (color change occurs entirely within steep jump) |
| Strong Acid + Weak Base | pH ~ 1 | pH 3 to 7 (vertical in acidic range) | pH ~ 5.0 - 5.5 | Methyl Orange (color change occurs entirely within steep jump) |
| Weak Acid + Weak Base | pH ~ 3 | No sharp vertical jump (inflection is gradual) | pH ~ 7.0 | No indicator suitable; must use a calibrated digital pH meter |
[HA] = [A-]
Ka = ([H+] * [A-]) / [HA] = [H+]
Therefore: pH at half-neutralisation = pKa
To find Ka: Ka = 10^(-pH)
5. Colorimetry & Beer-Lambert Calibration Curves
Colorimetry provides a quantitative, non-destructive optical method to determine the concentration of colored solutions (such as transition metal ions, iodine in kinetics clock reactions, or food dyes).
where A = Absorbance (dimensionless), epsilon = molar absorptivity (dm3 mol-1 cm-1), c = concentration (mol dm-3), and l = path length of cuvette (cm).
When path length and wavelength are kept constant, Absorbance is directly proportional to concentration (A proportional to c).
Calibration Protocol
- Prepare a standard stock solution of known concentration.
- Carry out serial dilutions to produce a series of 5 solutions of known concentration (e.g. 0.02, 0.04, 0.06, 0.08, 0.10 mol dm-3).
- Select the complementary colored filter that gives maximum light absorption (e.g. use a red/orange filter for blue copper(II) sulfate solutions).
- Zero the colorimeter with a cuvette containing pure distilled water (the blank).
- Measure the absorbance of each standard solution and plot Absorbance against Concentration.
- Draw a straight line of best fit through the origin (0, 0).
Determining an Unknown Concentration
To determine the concentration of an unknown sample:
- Measure the absorbance of the unknown under identical conditions and filter selection.
- Locate the measured absorbance on the vertical y-axis of the calibration graph.
- Move horizontally across to intersect the linear calibration line.
- Drop down vertically to the horizontal x-axis and read off the unknown concentration directly.
6. Worked Graph Calculation Problem
Problem: An experiment investigating the rate of the reaction between peroxodisulfate and iodide ions at various temperatures yielded the following linearized Arrhenius data. A plot of ln k on the vertical axis against 1 / T (in K^-1) on the horizontal axis produced a straight line with coordinates:
- Point 1:
(1/T) = 3.10 * 10^-3 K^-1,ln k = -2.15 - Point 2:
(1/T) = 3.45 * 10^-3 K^-1,ln k = -4.95
Given the gas constant R = 8.314 J K^-1 mol^-1, calculate the activation energy (Ea) for this reaction in kJ mol^-1.
Step 1: Calculate the gradient of the Arrhenius line (m)
Gradient m = delta y / delta x
m = (-4.95 - (-2.15)) / ((3.45 * 10^-3) - (3.10 * 10^-3))
m = -2.80 / (0.35 * 10^-3)
m = -8000 K
Step 2: Relate gradient to activation energy
m = -Ea / R
-8000 = -Ea / 8.314
Ea = 8000 * 8.314 = 66,512 J mol^-1
Step 3: Convert to kJ mol^-1 and apply significant figures
Ea = 66,512 / 1000 = 66.5 kJ mol^-1 (3 significant figures)
Final Answer: Ea = +66.5 kJ mol-1
7. Practice Exam Questions
Question 1: In an Arrhenius plot of ln k against 1/T, the line of best fit has a gradient of -6500 K. What is the activation energy in kJ mol^-1? (R = 8.314 J K^-1 mol^-1)
Show Answer & Explanation
Correct Answer: B
m = -Ea / R, so Ea = -(-6500) * 8.314 = 54,041 J mol^-1 = +54.0 kJ mol^-1.
Question 2: During a weak acid titration with 0.10 mol dm^-3 NaOH, the equivalence point occurs at 24.80 cm^3 with an inflection at pH 8.8. At what volume of added NaOH does pH = pKa?
Show Answer & Explanation
Correct Answer: B
The half-neutralisation point occurs at exactly half the equivalence volume (24.80 / 2 = 12.40 cm^3), where [HA] = [A-] and pH = pKa.