Data Analysis and Graph Questions

Data analysis questions test your ability to extract information from graphs, tables, and experimental results. These questions appear in all three papers and carry significant marks. This lesson covers how to read every type of graph you will encounter, interpret tables accurately, plot data correctly, and handle spectral data systematically.

Reading Graphs Accurately

Rate-Concentration Graphs

When given a concentration-time graph, the rate at any point is the gradient of the tangent at that point. To find the initial rate, draw a tangent at t = 0. Common errors include drawing the tangent too steeply or too shallowly, or measuring the gradient incorrectly.

To find the gradient:

Draw the tangent line (touching the curve at the required point)
Choose two points on the tangent line that are far apart (at least half the width of the graph)
Calculate Δy / Δx using these points
Include units (typically mol dm⁻³ s⁻¹)

Worked Example: A concentration-time graph shows [A] decreasing. At t = 20 s, you draw a tangent. Two points on the tangent are (10, 0.80) and (40, 0.20). Gradient = (0.20 - 0.80) / (40 - 10) = -0.60 / 30 = -0.020 mol dm⁻³ s⁻¹ Rate = 0.020 mol dm⁻³ s⁻¹ (rate is positive by convention)

Common mistake: Using points on the curve itself rather than points on the tangent line. The tangent is a straight line that touches the curve at one point — the gradient of this line gives the rate.

Determining Reaction Order from Graphs

Graph type	Straight line means	Order
[A] vs time	Constant rate of decrease	Zero order
ln[A] vs time	Straight line with negative gradient	First order
1/[A] vs time	Straight line with positive gradient	Second order

Worked Example: If plotting ln[A] against time gives a straight line, the reaction is first order with respect to A. The gradient equals -k (the rate constant), and the y-intercept equals ln[A]₀.

Rate-Concentration Graphs (Direct Plots)

When asked to determine order from initial rate data:

Observation	Order
Doubling [A] has no effect on rate	Zero order
Doubling [A] doubles the rate	First order
Doubling [A] quadruples the rate	Second order

Titration Curves

Titration curves show pH against volume of titrant added. Key features to identify:

Equivalence point — the steepest part of the curve (where pH changes most rapidly)
Half-equivalence point — halfway to the equivalence point, where pH = pKa for a weak acid
Buffer region — the relatively flat section before the equivalence point (where the solution resists pH change)
Initial pH — indicates whether the analyte is a strong or weak acid/base

graph TD
    A[Identify the type of titration] --> B{What is the initial pH?}
    B -->|pH ~1| C[Strong acid being titrated]
    B -->|pH ~3-4| D[Weak acid being titrated]
    B -->|pH ~13| E[Strong base being titrated]
    B -->|pH ~10-11| F[Weak base being titrated]
    C --> G[Equivalence point at pH 7]
    D --> H[Equivalence point above pH 7]
    E --> I[Equivalence point at pH 7]
    F --> J[Equivalence point below pH 7]
    G --> K[Use any indicator]
    H --> L[Use phenolphthalein]
    I --> M[Use any indicator]
    J --> N[Use methyl orange]

How to Read Key Values from a Titration Curve

Feature	How to find it	What it tells you
Equivalence point	Steepest section — midpoint of vertical region	Volume needed for complete neutralisation
Half-equivalence point	Half the equivalence volume	pH = pKa at this point
Buffer region	Flat section before equivalence	Where the solution resists pH change
Indicator range	Must span the steep section	Suitable indicator for this titration

Enthalpy Diagrams / Energy Profile Diagrams

Energy profile diagrams show the energy of reactants and products. Key readings:

Activation energy (Ea): Height from reactants to the peak (transition state)
Overall enthalpy change (ΔH): Difference between reactant and product energy levels
- Negative ΔH: products are lower (exothermic)
- Positive ΔH: products are higher (endothermic)
Catalysed reaction: Shows a lower peak (lower Ea) but the same ΔH

Worked Example: An energy profile shows reactants at 100 kJ, products at 40 kJ, and the peak at 180 kJ. Ea = 180 - 100 = 80 kJ ΔH = 40 - 100 = -60 kJ (exothermic)

Interpreting Tables of Data

When asked to describe or explain trends from a table:

State the trend clearly — "as X increases, Y increases/decreases"
Quote specific data points — use numbers from the table to support your answer
Identify anomalies — point out any values that do not fit the trend
Explain the trend if asked — link to underlying chemistry

Worked Example: A table shows melting points: Na 98°C, Mg 650°C, Al 660°C, Si 1414°C, P 44°C, S 115°C, Cl -101°C, Ar -189°C.

Describe: "Melting point increases from Na (98°C) to Si (1414°C), then decreases sharply from P (44°C) to Ar (-189°C)."

Explain: "Na to Al are metals with metallic bonding — melting point increases as charge density increases (Na⁺ to Al³⁺), strengthening the metallic bond. Si has a giant covalent structure requiring much energy to break its strong covalent bonds. P₄, S₈, Cl₂, and Ar have simple molecular structures with weak van der Waals forces, so melting points are low."

Key principle: Always quote numbers from the data. "The melting point increases" is weaker than "the melting point increases from 98°C to 660°C."

Plotting Graphs

If asked to plot data:

Choose appropriate scales (data should fill at least half the graph paper)
Label axes with quantity and units (e.g., "Concentration / mol dm⁻³")
Plot points accurately using crosses (×) — not dots or circles
Draw a line of best fit (straight line or smooth curve as appropriate)
Identify and circle any anomalous points (do not include them in the line of best fit)

Common Plotting Mistakes

Mistake	Why it loses marks	Correct approach
Awkward scales (e.g., 3s or 7s)	Hard to read intermediate values	Use 1, 2, 5, or 10 per division
Data fills only a small area	Reduces resolution	Choose scales so data uses >50% of paper
Joining dots with straight lines	Not a line of best fit	Draw a smooth curve or best-fit straight line
No axis labels or units	Cannot interpret the graph	Always include "quantity / unit"
Plotting dots instead of crosses	Harder to see precise position	Use × for each data point

Describing Trends

Use precise language:

"Increases" or "decreases" (not "goes up" or "goes down")
"Proportional" only if the graph is a straight line through the origin
"Linear" for straight-line relationships (not necessarily through the origin)
"Rate of increase slows" rather than "levels off" (be specific about what is happening)
"Reaches a plateau" or "approaches a maximum" for curves that flatten

Precision matters: "There is a positive correlation between temperature and rate" is acceptable but weak. "Rate approximately doubles for every 10°C increase in temperature" is much stronger because it quantifies the relationship.

Spectral Interpretation

Infrared (IR) Spectroscopy

Key absorptions to memorise:

Absorption (cm⁻¹)	Bond	Appearance	Found in
3200-3600	O-H (alcohol)	Broad	Alcohols, phenols
2500-3300	O-H (acid)	Very broad	Carboxylic acids
1700-1750	C=O	Sharp, strong	Aldehydes, ketones, acids, esters
3300-3500	N-H	Medium, 2 peaks for NH₂	Amines, amides
2850-3000	C-H	Medium	Most organic compounds

Mass Spectrometry

Molecular ion peak (M⁺): Gives the relative molecular mass
Fragmentation peaks: Show which bonds have broken

Worked Example: M⁺ at m/z = 74, peak at m/z = 45 (loss of 29 = CHO), peak at m/z = 29 (CHO⁺). Molecular formula could be C₃H₆O₂. The CHO loss suggests an ester or carboxylic acid. With M = 74, this is methyl ethanoate (CH₃COOCH₃) or propanoic acid (CH₃CH₂COOH).

NMR Spectroscopy

¹H NMR:

Number of peaks = number of different hydrogen environments
Integration (peak area) = relative number of hydrogens in each environment
Chemical shift (δ) = type of hydrogen environment
Splitting pattern = number of adjacent hydrogens (n+1 rule)

¹³C NMR:

Number of peaks = number of different carbon environments
Chemical shift = type of carbon environment

Systematic Approach to Unknown Identification

graph TD
    A[Start with mass spectrum] --> B[Find M⁺ → molecular mass]
    B --> C[Calculate molecular formula from M_r]
    C --> D[Calculate degrees of unsaturation]
    D --> E[Check IR spectrum]
    E --> F[Identify functional groups from absorptions]
    F --> G[Check ¹H NMR]
    G --> H[Count H environments from number of peaks]
    H --> I[Determine integration ratios]
    I --> J[Analyse splitting patterns]
    J --> K[Check ¹³C NMR for carbon environments]
    K --> L[Propose a structure consistent with all data]
    L --> M[Verify: does the structure explain all peaks?]

Worked Example: A compound has M⁺ = 60, a broad IR absorption at 2500-3300 cm⁻¹ and a sharp absorption at 1710 cm⁻¹. The ¹H NMR shows two peaks: a quartet at δ 2.4 and a triplet at δ 1.2 with integration ratio 2:3.

Analysis: M = 60, broad O-H + C=O suggests carboxylic acid. Molecular formula C₂H₄O₂ = 60 (but this is ethanoic acid with M = 60 and would show a singlet). Try C₃H₈... No, with COOH we need C₃H₆O₂ = 74... Actually M = 60 with COOH: CHO₂ = 45, leaving 15 = CH₃. So CH₃COOH (ethanoic acid, M = 60). But the NMR shows two environments with splitting...

Reconsider: M = 60, the quartet-triplet pattern with 2:3 ratio suggests CH₂CH₃. If CH₃CH₂COOH = propanoic acid, M = 74. This does not match. With M = 60 and the acid group: this is propan-1-ol? No. Let me re-examine: CH₃COOH (M=60), with ¹H NMR showing a singlet for CH₃ and a broad singlet for OH. The question must refer to a different compound.

This worked example demonstrates the iterative process — when data conflicts, re-examine your assumptions. The exam expects you to work through this systematically.