Interpret data, including graphs, from rate of reaction experiments

Cambridge IGCSE Chemistry 0620 – Rate of Reaction

Objective (AO1, AO2, AO3)

Interpret experimental data (tables, graphs, calculations) from rate‑of‑reaction investigations and explain how the five key factors affect the rate of a chemical reaction.

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1. What is the rate of a reaction?

The rate of a chemical reaction is the change in amount (or concentration) of a reactant or product per unit time.

Rate = \(\displaystyle\frac{\Delta[\text{A}]}{\Delta t}\) or \(\displaystyle\frac{\Delta V}{\Delta t}\) or \(\displaystyle\frac{\Delta m}{\Delta t}\)

• \([\text{A}]\) = concentration (mol L⁻¹) or amount (mol, g, cm³).
• \(t\) = time (s).
• Typical units: mol s⁻¹, cm³ s⁻¹, g s⁻¹ or mol L⁻¹ s⁻¹.

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2. Collision theory & activation energy (supplementary)

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3. Factors that influence the rate of reaction

Factor	Effect on rate (with example)
Concentration (or pressure) of reactants	More particles per unit volume → more collisions per second. Example: Doubling the concentration of \(\ce{HCl}\) in the reaction \(\ce{NaCl + HCl → NaCl + HCl}\) roughly doubles the rate. For gases, increasing pressure has the same effect as increasing concentration because the number of gas‑phase collisions rises.
Temperature	Increases average kinetic energy → larger fraction of molecules possess energy ≥ \(E_a\). Empirical rule: The rate roughly doubles for every 10 °C rise in temperature (for many reactions). Example: The reaction between \(\ce{Mg}\) and \(\ce{HCl}\) proceeds noticeably faster at 50 °C than at 20 °C.
Surface area of a solid	Smaller particles expose more surface → more sites for collisions. Example: Powdered calcium carbonate reacts much faster with \(\ce{HCl}\) than a single chunk of the same mass.
Catalyst	Provides an alternative pathway with a lower activation energy. The catalyst is not consumed; it appears unchanged at the end of the reaction. Example: Manganese(IV) oxide (\(\ce{MnO2}\)) speeds up the decomposition of \(\ce{H2O2}\).
Nature of the reactants	Reactivity depends on bond strength, ionic vs. covalent character, etc. Example: Acids react rapidly with active metals (e.g., \(\ce{Zn}\)), whereas gases such as \(\ce{N2}\) are inert at room temperature because the N≡N bond is very strong.

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4. Practical methods for investigating rate (AO3)

Method	What is measured	Typical set‑up (apparatus)
Volume of gas collected (e.g., \(\ce{CO2}\), \(\ce{H2}\))	\(\Delta V\) over time	Gas syringe or measuring cylinder attached to the reaction flask via a delivery tube; stop‑watch; thermometer to record temperature.
Loss of mass of a solid	\(\Delta m\) over time	Analytical balance, weighing boat (or crucible), stop‑watch; the solid is weighed before the reaction and at regular intervals.
Change in pressure (closed system)	\(\Delta P\) over time	Sealed reaction vessel, pressure sensor or manometer, thermometer; pressure is recorded at set time intervals.
Colour change (spectrophotometry)	\(\Delta\) absorbance over time	Colourimeter or spectrophotometer, cuvettes, stop‑watch; the absorbance of the reaction mixture is measured at regular intervals.
Titration of a product	Volume of titrant used per time interval	Burette, pipette, suitable indicator, stop‑watch; aliquots are taken at set times and titrated immediately.

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5. Calculating the rate from experimental data

5.1 Using the gradient of a straight‑line graph

If a measured quantity (volume, mass, pressure, absorbance) varies linearly with time, the gradient \(\displaystyle\frac{\Delta y}{\Delta x}\) is the average rate.

Gradient = \(\frac{y_2-y_1}{x_2-x_1}\) = \(\frac{\Delta\text{quantity}}{\Delta t}\)

5.2 Converting to moles s⁻¹ (or concentration s⁻¹)

For gases collected at room temperature and pressure Cambridge uses the molar volume:

\(24\ \text{dm}^3\ \text{mol}^{-1}\) ≈ \(24\,000\ \text{cm}^3\ \text{mol}^{-1}\)

Thus:

\[ \text{Rate (mol s}^{-1}) = \frac{\Delta V\ (\text{cm}^3)}{\Delta t\ (\text{s})}\times\frac{1\ \text{mol}}{24\,000\ \text{cm}^3} \]

5.3 Worked example – volume‑time data

Time (s)	Volume of \(\ce{CO2}\) (cm³)
0	0
10	12
20	24
30	36

Gradient (ΔV/Δt) = \(\frac{12\ \text{cm}^3}{10\ \text{s}} = 1.2\ \text{cm}^3\text{s}^{-1}\).

Convert to moles s⁻¹:

\[ \text{Rate} = 1.2\ \frac{\text{cm}^3}{\text{s}} \times \frac{1\ \text{mol}}{24\,000\ \text{cm}^3} = 5.0\times10^{-5}\ \text{mol s}^{-1} \]

If the reaction occurs in 0.500 L of solution, the change in concentration per second is:

\[ \Delta[\ce{CO2}] = \frac{5.0\times10^{-5}\ \text{mol s}^{-1}}{0.500\ \text{L}} = 1.0\times10^{-4}\ \text{mol L}^{-1}\text{s}^{-1} \]

5.4 Limiting‑reactant & % yield example (Mg + 2 HCl)

Data (mass of Mg remaining):

Time (s)	Mass of Mg remaining (g)
0	0.500
20	0.460
40	0.420
60	0.380
80	0.340

Mass of Mg lost in the first 20 s = 0.500 g – 0.460 g = 0.040 g.

Moles of Mg lost:

\[ n_{\ce{Mg}} = \frac{0.040\ \text{g}}{24.3\ \text{g mol}^{-1}} = 1.65\times10^{-3}\ \text{mol} \]

Reaction: \(\displaystyle \ce{Mg + 2HCl -> MgCl2 + H2}\)
1 mol Mg produces 1 mol \(\ce{H2}\). Hence moles of \(\ce{H2}\) formed = \(1.65\times10^{-3}\) mol.

Using the molar volume (24 000 cm³ mol⁻¹):

\[ V_{\ce{H2}} = 1.65\times10^{-3}\ \text{mol}\times24\,000\ \text{cm}^3\text{mol}^{-1}=39.6\ \text{cm}^3 \]

If the experiment actually collected 35 cm³, the percentage yield is:

\[ \%\,\text{yield}= \frac{35}{39.6}\times100 = 88\% \]

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6. Interpreting different types of graphs (AO2)

6.1 Straight‑line (constant rate)

• Gradient = constant rate.
• Extrapolate the line to the origin to check whether the reaction started at \(t=0\) (useful for confirming that the measured quantity truly begins from zero).

6.2 Curved graph (rate changes with time)

• The gradient at any point gives the instantaneous rate.
   Use the “tangent‑line” method or calculate \(\Delta y/\Delta x\) over a small interval.
• Typical for reactions where reactant concentration falls, causing the rate to decrease (e.g., first‑order reactions).

6.3 Initial‑rate method

Plot the *initial* rate (taken from the first few data points) against a variable such as concentration, pressure or temperature. The shape of the plot reveals the order with respect to that variable:

• Linear → first order.
• Quadratic → second order.
• Horizontal → zero order.

6.4 Extrapolation & best‑fit line (noisy data)

When experimental points are not perfectly collinear, draw a straight line of best fit through them. State the uncertainty in the gradient (e.g., “\(0.85\pm0.05\ \text{cm}^3\text{s}^{-1}\)”). This satisfies AO3 – evaluating the reliability of the result.

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7. Summary checklist (useful for revision)

• Define rate and write the appropriate formula.
• State the five factors that affect rate and give a concrete example for each.
• Explain, using collision theory, why each factor influences the frequency or energy of collisions.
• Identify the correct practical method for a given type of measurement (volume, mass, pressure, colour, titration).
• Calculate a rate from raw data:
  1. Find the gradient (Δy/Δx).
  2. Convert to moles s⁻¹ (or concentration s⁻¹) using the molar volume or solution volume.
  3. If required, relate the result to limiting‑reactant or % yield.
• Interpret straight‑line and curved graphs, using the tangent‑line method for instantaneous rates and the initial‑rate method for reaction order.
• Comment on the reliability of your result (repeatability, sources of error, uncertainties).