3.2. Rates of reaction

Defining and Tracking Rates of Reaction

Some reactions finish in the blink of an eye. If you mix aqueous solutions of silver nitrate and sodium chloride, a white precipitate of silver chloride forms instantly because the ions are already free in the water and react as soon as they meet. Other reactions creep along slowly. An iron nail can take months to rust, and limestone weathers over centuries. Rates depend on the reaction mechanism and conditions: energy barriers and access to reacting surfaces can make reactions slow.

Definition of rate of reaction

In Leaving Certificate chemistry, the rate of reaction is defined as the change in concentration per unit time of any one reactant or product.

The usual unit for rate is $\text{mol L}^{-1} \text{s}^{-1}$ (moles per litre per second). In our school laboratory, tracking concentration directly from second to second can be tricky, so we usually measure convenient physical changes instead. We might track the volume of gas produced over time (in $\text{cm}^3 \text{s}^{-1}$) or watch the mass of the flask drop on a balance (in $\text{g s}^{-1}$).

Common Laboratory Tracking Methods

• Gas collection: We collect a gaseous product in a gas syringe or by bubbling it into an inverted graduated cylinder filled with water. Reacting marble chips with hydrochloric acid gives carbon dioxide, while decomposing hydrogen peroxide over manganese(IV) oxide generates oxygen.
• Mass loss: When a dense gas like carbon dioxide escapes, we can place the conical flask straight onto a top-pan balance and log the mass drop at regular intervals. A loose plug of cotton wool in the flask neck lets the gas vent freely while catching any acid spray that might escape.
• Disappearing cross (turbidity): If a reaction precipitates an insoluble solid, we can time how long the mixture takes to turn opaque. Reacting sodium thiosulfate with dilute hydrochloric acid deposits solid yellow sulfur. By looking down through the liquid at a black cross drawn on paper beneath the flask, we record the exact time the cross disappears from view.

Analysing and Plotting Rate Graphs

For a typical gas-producing batch reaction at constant temperature, with no induction period, the volume collected against time has three main stages:

1. A steep initial slope at the start. Reactant concentrations are at their peak, so particles collide most frequently.
2. A curve that gradually flattens out. As reactants get used up, collisions happen less often and the reaction slows down.
3. A completely flat horizontal plateau. In a reaction that goes to completion, the limiting reactant has been used up and gas production stops.

Practical Rules for Graph Drawing

Examiners look for good graph habits:

• Put the independent variable, time, on the horizontal axis ($x$-axis) and your measured quantity, such as volume of gas or mass loss, on the vertical axis ($y$-axis).
• Label each axis clearly with the quantity and its unit, such as "Time / $\text{s}$" and "Volume of $\text{O}_2$ / $\text{cm}^3$".
• Choose a scale that spreads your points across more than half the grid in both directions, using sensible steps like 1, 2, 5, or 10 units per large square.
• Mark each data point with a neat, sharp pencil cross. Draw a smooth, single line of best fit rather than joining the points like a dot-to-dot puzzle.
• If one reading is clearly an outlier, circle it, leave it off your best-fit line, and do not distort the curve to reach it.

Three Ways to Calculate Rate from Graphs

• Average rate: This measures the speed over a set interval of time. Divide the total change in your measured quantity by the elapsed time:

• Instantaneous rate: This gives the exact rate at one specific second. Place a clear plastic ruler on the curve at the chosen time and draw a straight tangent line touching the curve at that single point. Form a large right-angled triangle along the tangent, read off the coordinates, and work out the slope:

• Initial rate: This is the reaction speed right at the start ($t = 0\text{ s}$). Draw your tangent line where the curve leaves the vertical axis at time zero and calculate its slope.

Collision Theory, Factors Affecting Rate, and Syllabus Limitations

Collision theory tells us that reactant particles must physically strike each other for a reaction to happen. Even so, most collisions in a container produce nothing; the particles bounce straight off each other without reacting. For a collision to actually make products (an effective collision), it has to meet two strict requirements:

1. Activation energy ($E_a$): The colliding particles must carry a minimum combined kinetic energy equal to or greater than the activation energy barrier. This provides the punch needed to break existing chemical bonds.
2. Correct collision orientation: The particles must strike each other at the right angle so the reacting atoms come directly into contact.

Factors That Control Reaction Rates

• Concentration: Adding more dissolved particles into each cubic centimetre crowds them closer together. This produces more collisions every second, which leads to more effective collisions per second.
• Pressure (in gases): Compressing a gas into a smaller container increases the number of gas molecules per unit volume. Just like raising the concentration of a solution, this boosts the collision frequency and speeds up the reaction.
• Surface area (solids): In a solid lump, only particles on the outside can collide with attacking molecules. Breaking the solid into tiny chips or grinding it into a powder exposes vastly more atoms, driving up collision frequency. This explains why combustible dusts, like flour in a mill or coal dust in a mine, can ignite explosively if a spark appears in a confined space.
• Temperature: Heating a mixture makes particles move a little faster, which slightly raises how often they collide. But the main reason heating speeds up a reaction so dramatically is that a far greater fraction of particles now possess kinetic energy equal to or greater than the activation energy ($E \ge E_a$). For many everyday reactions, raising the temperature by just $10\text{ }^\circ\text{C}$ roughly doubles the rate.
• Catalyst: Adding a catalyst creates a completely different reaction pathway that has a lower activation energy.

Syllabus Limitations of Collision Theory and Rate Models

Keep these qualifications in mind when applying the simple rate models:

• Concentration does not always alter the rate: Many reactions take place through several consecutive steps. The overall reaction speed is dictated by the slowest step in that sequence, called the rate-determining step. Changing the concentration of a reactant used only in a later fast step may leave the overall rate unchanged, provided that step remains fast and the mechanism is unchanged. Similarly, once every active site on a solid catalyst or enzyme is already busy (saturation), pouring in more reactant cannot speed things up.
• Orientation requirement: Even when particles collide with violent kinetic energy well above $E_a$, they will simply bounce apart if their reactive bonds are pointing the wrong way.
• Catalyst poisoning: Unwanted substances can bind to or block active sites on a catalyst (catalyst poisoning), reducing its activity. Poisoning may be reversible or permanent, depending on the catalyst and poison.

Comparing Energy Profiles: Catalysed and Uncatalysed Reactions

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It works by opening an alternative pathway with a lower activation energy ($E_a$). Because the catalyst is not used up, a tiny amount can convert huge quantities of reactant. Crucially, a catalyst does not alter the overall enthalpy change ($\Delta H$) of the reaction.

Rules for Sketching Energy Profile Diagrams

When sketching energy diagrams for exams:

• Put "Reaction progress" on the horizontal axis and "Energy" on the vertical axis.
• Draw flat horizontal lines for the reactant energy level and the product energy level.
• Draw the uncatalysed pathway with a tall hump. Label $E_a$ as the vertical energy gap from the reactant level to its peak.
• Draw a second, lower curve for the catalysed pathway, with the same reactant and product levels. In this simple profile, $E_{a,\text{cat}}$ is the vertical energy gap from the reactant level to the lower peak; it is not the curve itself.
• Label $\Delta H$ as the vertical gap between the reactant and product levels. This gap must remain identical whether a catalyst is present or not.

Exothermic Reactions

In an exothermic reaction, the reactants sit on a higher energy shelf than the products. The curve climbs up to clear the activation energy barrier ($E_a$) and then drops down below the starting level. The difference between reactants and products is negative ($\Delta H < 0$). The catalysed curve follows the same start and finish levels, but passes over a noticeably lower peak.

Endothermic Reactions

In an endothermic reaction, reactants sit on a lower shelf than products because the system takes in heat from the surroundings ($\Delta H > 0$). The curve climbs over a high activation barrier before settling onto the higher product shelf. The catalysed pathway begins and ends at the identical plateaus, but clears a lower barrier.

Reactions with an Intermediate Compound

In the illustrated two-step catalysed pathway, two lower peaks replace the single uncatalysed peak. The dip between them represents an intermediate. Other mechanisms may have a different number of steps and peaks.

Catalytic Mechanisms: Homogeneous, Heterogeneous, and Biological

We divide catalysis into two main types based on whether the catalyst and reactants share the same physical state.

Homogeneous Catalysis and Intermediate Formation

In homogeneous catalysis, the catalyst and the reactants exist in the exact same physical phase, such as all being dissolved in water. The catalyst reacts chemically with one reactant to make an unstable intermediate compound. This intermediate then reacts with another substance to yield the products and regenerate the original catalyst.

An example is the decomposition of aqueous hydrogen peroxide using dissolved iodide ions ($\text{I}^-$) as a catalyst:

The iodate(I) ion ($\text{IO}^-$) acts as the short-lived intermediate. Notice that iodide enters in step 1 and reappears unchanged in step 2.

A visual demonstration of this mechanism occurs when hydrogen peroxide oxidises potassium sodium tartrate in the presence of cobalt(II) chloride. The solution starts pink, turns dark green as an unstable intermediate complex forms, and then returns to its original pink colour once the reaction finishes and the cobalt(II) ions are regenerated.

Heterogeneous Catalysis and Surface Adsorption

In heterogeneous catalysis, the catalyst and the reactants are in different phases. The most common setup involves gaseous reactants passing over a solid transition metal catalyst. The process takes place in three stages:

1. Adsorption: Reactant molecules form temporary bonds onto active sites on the solid catalyst surface. This draws the molecules together, holds them in a favourable alignment, and stretches or weakens their internal bonds.
2. Reaction on the surface: The weakened reactant molecules react with one another on the surface, clearing a much lower activation energy barrier than in the gas phase.
3. Desorption: The new product molecules release their hold on the surface and diffuse away, freeing up the active sites for new reactant molecules.

Common practical examples include:

• Finely divided iron used in the Haber process to make ammonia: $\text{N}_2\text{ (g)} + 3\text{H}_2\text{ (g)} \rightleftharpoons 2\text{NH}_3\text{ (g)}$
• Vanadium(V) oxide ($\text{V}_2\text{O}_5$) in the Contact process to produce sulfur trioxide: $2\text{SO}_2\text{ (g)} + \text{O}_2\text{ (g)} \rightleftharpoons 2\text{SO}_3\text{ (g)}$
• Platinum, palladium, and rhodium in motor vehicle catalytic converters: $2\text{CO}\text{ (g)} + 2\text{NO}\text{ (g)} \rightarrow 2\text{CO}_2\text{ (g)} + \text{N}_2\text{ (g)}$

Lead compounds from leaded petrol can strongly block the active sites in catalytic converters, damaging their ability to clean exhaust fumes. Unleaded petrol avoids this source of poisoning.

Biological Catalysis: Enzymes

An enzyme is a biological catalyst; most enzymes are proteins. A protein enzyme folds into a three-dimensional shape with an active site suited to a particular substrate or closely related substrates.

For example, catalase, found in liver and potato tissue, breaks down harmful hydrogen peroxide into water and oxygen. Dropping raw liver into hydrogen peroxide produces instant, violent foaming.

Enzyme activity depends on temperature and pH:

• The optimum temperature depends on the enzyme and conditions; many human enzymes work well near body temperature. Sufficiently high temperatures can denature a protein enzyme by disrupting its folded structure and changing its active site, reducing activity. There is no universal denaturation threshold of 37 or 40 °C.
• Each enzyme has an optimum pH or pH range. Moving away from it can change charges at the active site and reduce activity; extreme pH can also disrupt the folded structure.

Laboratory Investigations: Measuring and Tracking Reaction Rates

The Leaving Certificate specification highlights several practical investigations that let you generate primary data and follow reaction rates in the laboratory.

Decomposition of Hydrogen Peroxide

We can follow the breakdown of hydrogen peroxide by collecting oxygen gas over time:

Apparatus and Method:

• Pour $50\text{ cm}^3$ of hydrogen peroxide into a conical flask and note its temperature.
• Weigh out $0.50\text{ g}$ of manganese(IV) oxide powder or granules.
• Add the solid to the flask, quickly push in the stopper connected to a gas syringe (or an inverted graduated cylinder filled with water), and start your stopwatch.
• Read the total volume of oxygen collected every 15 or 30 seconds until the gas volume stops increasing.
• Repeat the trial using $0.50\text{ g}$ of manganese(IV) oxide in a different particle size, keeping the volume, concentration, and starting temperature of the peroxide identical.

Observations and Sources of Error:

• The curve rises sharply at first and levels off to a horizontal plateau. The powdered catalyst gives a noticeably steeper initial slope than coarse granules because its larger surface area exposes more active sites. With the same initial amount of hydrogen peroxide (same volume and concentration), complete reaction and identical gas-collection conditions, both forms give the same final oxygen volume.
• A small burst of gas can escape during the delay between tipping in the powder and inserting the rubber bung. You can avoid this by suspending the solid in a tiny vial inside the flask on a thread and shaking it to start the reaction without opening the flask.
• Because this decomposition is exothermic, the flask warms up slightly, which can speed up the rate towards the middle of the run.

Sodium Thiosulfate and Hydrochloric Acid

To study how concentration affects speed, place the reaction flask over a paper card marked with a bold black cross. Add acid to the sodium thiosulfate solution, start the timer, and look straight down through the liquid until the precipitated sulfur obscures the cross completely. Because the flask dimensions and depth of solution remain fixed, a constant mass of sulfur is needed to obscure the cross each time. This means the reaction rate is proportional to $\frac{1}{t}$.

Plotting $\frac{1}{t}$ against sodium thiosulfate concentration produces a straight line that passes through the origin. This supports direct proportionality between rate and sodium thiosulfate concentration over the measured range, when temperature and other conditions are controlled.

Safety reminder: Sulfur dioxide is a sharp, choking gas that can trigger asthma attacks. Keep the lab well ventilated, dispose of mixtures into a sodium carbonate stop-bath right away, and wear eye protection throughout.

Key terms

Rate of reaction

The change in concentration per unit time of any one reactant or product.

Activation energy

The minimum energy that colliding particles must have in order to react.

Effective collision

A collision between reactant particles that produces a chemical reaction, requiring energy equal to or greater than the activation energy and the correct collision orientation.

Instantaneous rate

The rate of reaction at one specific moment in time, determined from the slope of the tangent drawn to the curve at that time.

Initial rate

The rate at the very start of the reaction (t = 0 s), found from the slope of the tangent to the curve at the point where it meets the vertical axis.

Average rate

The total change in a measured quantity over a stated time interval divided by the elapsed time.

Catalyst

A substance that increases the rate of a chemical reaction without being consumed in the reaction.

Homogeneous catalysis

Catalysis in which the reactants and the catalyst are in the same physical phase.

Heterogeneous catalysis

Catalysis in which the reactants and the catalyst are in different physical phases.

Adsorption

The temporary binding of reactant molecules to active sites on the surface of a solid catalyst.

Desorption

The detachment of product molecules from active sites on a solid catalyst surface into the surrounding fluid phase.

Catalyst poisoning

A substance blocking or interfering with catalyst active sites and reducing activity; the effect may be reversible or permanent.

Enzyme

A biological catalyst that speeds up specific biochemical reactions; most enzymes are proteins.

Rate-determining step

The slowest step in a multi-step reaction mechanism that dictates the overall rate of the reaction.