Reaction Kinetics lessons

Measuring rate

To measure a rate, track how much product forms as time passes. Then divide the change by the time it took.

Mean rate of reaction: \text{mean rate} = \frac{\text{change in amount}}{\text{time taken}}

If 30 cm³ of gas forms in 15 seconds, the mean rate is \frac{30}{15} = 2\ \text{cm}^3\text{/s}.

Three ways to follow a reaction, each playing live: mass lost on a balance, gas collected in a syringe, and a cross disappearing under a cloudy solution.

Pick the method that suits the reaction. Collect a gas in a syringe, weigh a flask as gas escapes, or time how long a solution takes to turn cloudy.

Practice: Calculate a mean rate

Read a table of gas volumes or mass lost and type the mean rate between two times.

Rate from a graph

Plot the amount of product against time and you get a curve. The steeper the curve, the faster the reaction.

The rate at one moment is the gradient of the curve there. Draw a straight tangent that just touches the curve, then divide its rise by its run.

A gas volume curve with a tangent that slides along it; the rise over run gives the rate at each moment.

The curve is steepest at the start, when there are the most reactant particles. It flattens out once a reactant runs out.

Practice: Read the rate graph

Questions about two runs of the same reaction plotted on one graph: which is faster, when each finishes, and the mean rate.

Collision theory

Collision theory says particles must collide to react. Most collisions do nothing, though.

A collision only works if the particles have enough energy and hit the right way round. The minimum energy needed is the activation energy, written E_a.

Three collisions play in turn: too slow, wrong way round, and fast and lined up. An energy bar compares each one with Ea.

A collision that makes products is a successful collision. The rate depends on how many successful collisions happen each second.

Practice: Will they react?

Sort described collisions into the ones that react and the ones that do not.

Energy profile diagrams

An energy profile plots energy as a reaction goes from reactants to products. The hump in the middle is the activation energy the particles must climb.

In an exothermic reaction the products sit lower, so energy is given out and \Delta H is negative. In an endothermic reaction the products sit higher, so \Delta H is positive.

An energy profile that switches between exothermic and endothermic, with Ea and the energy change marked.

Energy change: \Delta H = E_{\text{products}} - E_{\text{reactants}}

Measure E_a from the reactants up to the peak. Measure \Delta H from the reactants to the products.

Practice: Label the energy profile

Drag Reactants, Products, Activation energy and Energy change onto the numbered parts of an energy profile.

Practice: Read the energy values

Read Ea or the energy change, with its sign, off an energy profile with a scale.

Temperature

Heating a reaction speeds it up. The particles move faster and have more kinetic energy.

This works in two ways. Faster particles collide more often, and more of their collisions have at least E_a.

The second effect is much bigger. For many reactions, a rise of just 10 °C roughly doubles the rate.

The Maxwell-Boltzmann distribution

Particles in a gas do not all have the same energy. The Maxwell-Boltzmann distribution shows how many particles have each energy.

The curve starts at zero, rises to a peak, then tails off. Only the particles in the tail beyond E_a have enough energy to react.

Maxwell-Boltzmann curves at 20 °C and at a temperature you choose, with the share above Ea shaded and compared.

When the gas gets hotter, the peak moves right and gets lower. The area under the curve stays the same, because the number of particles has not changed.

Practice: Pick the curve

Pick which Maxwell-Boltzmann curve shows a hotter gas, a cooler gas or an added catalyst.

Concentration and pressure

A more concentrated solution has more reactant particles in the same volume. They collide more often, so there are more successful collisions each second.

For gases, raising the pressure does the same job. It squeezes the particles into a smaller space.

A live particle box: add reactant particles or squeeze the box and watch the collisions per second.

Neither change gives the particles more energy. The same share of collisions succeed, but there are more collisions.

Surface area

A solid can only react at its surface. Cutting it into smaller pieces exposes more surface, so more particles can hit it at once.

A cube cut into smaller and smaller cubes: the mass stays the same while the surface area, and the rate, grow.

A powder reacts much faster than one lump of the same mass. This is why fine flour or coal dust in the air can explode.

Practice: Why each factor works

Match each change to the reason it speeds up a reaction.

Practice: Slowest to fastest

Put four versions of the same experiment in order from slowest to fastest.

Catalysts

A catalyst speeds up a reaction without being used up. It gives the reaction a different route with a lower activation energy.

With a lower E_a, more particles have enough energy to react. The curve of energies itself does not change.

An energy profile with and without a catalyst, above the energy curve where the Ea line moves left and the shaded share grows.

Enzymes are the catalysts in living things. Industry uses catalysts too, such as iron in the Haber process and platinum in car exhausts.

Practice: What does each change do?

For one change at a time, say whether collisions per second, the activation energy and the share with enough energy go up, down or stay the same.

Rate equations

A rate equation links the rate to the concentration of a reactant. Square brackets mean concentration, so [A] is the concentration of A in \text{mol/dm}^3.

Rate equation: \text{rate} = k[A]^n

Here k is the rate constant and n is the order with respect to A. With an order of zero, the concentration makes no difference at all.

Pick an order and change [A]: the rate follows k[A] to that power on a graph, and doubling [A] shows the rate going up 1, 2 or 4 times.

In first order, doubling [A] doubles the rate. In second order, doubling [A] makes the rate four times bigger.

Finding the order from data

Orders come from experiments, not from the balanced equation. Change one concentration, keep everything else the same, and see what happens to the rate.

1. \text{Exp 1: } [A] = 0.10,\ \text{rate} = 2.0 \times 10^{-3} (the starting point)
2. \text{Exp 2: } [A] = 0.20,\ \text{rate} = 8.0 \times 10^{-3} ([A] doubled)
3. \frac{8.0 \times 10^{-3}}{2.0 \times 10^{-3}} = \textcolor{#0d9488}{4} (the rate went up 4 times)
4. 2^n = \textcolor{#0d9488}{4},\ \text{so } n = 2 (second order in A)

Ask how many times bigger the rate got when the concentration doubled. Times 1 means order 0, times 2 means order 1, and times 4 means order 2.

Practice: Find the orders

Read three experiments and type the order with respect to A and to B into the rate equation.

Practice: Use the rate equation

Use rate = k[A] or k[A] squared to work out a rate or the rate constant.

Reversible reactions and equilibrium

Some reactions can go both ways. The products can react to make the reactants again, and chemists show this with a pair of half arrows.

In a closed container, the forward reaction slows down as reactants are used up. The reverse reaction speeds up as products build up.

Particles flip between A and B at random; the counts level off while the flips carry on in both directions at the same rate.

Soon both reactions run at the same rate. This is dynamic equilibrium: the amounts stay level, but both reactions keep going.

Practice: Spot equilibrium

Tap the time on a concentration graph when equilibrium is reached.