NSW HSC Chemistry

Reactions that do not go to completion

Many reactions are treated as going one way until a reactant runs out, but a great many can also run backwards. A reaction that can proceed in both directions is reversible, and it is written with a double arrow, as in $\ce{N2O4(g) <=> 2NO2(g)}$. If a reversible reaction is left with nothing entering or leaving, the forward reaction gradually slows as reactants are used up and the reverse reaction speeds up as products build, until the two rates are equal. From then on the amounts of every substance stay constant, even though both reactions are still going. This is dynamic equilibrium.

The idea shows up in simple laboratory observations. Hydrated cobalt(II) chloride is pink and loses water on heating to give blue anhydrous cobalt(II) chloride, and adding water to the blue solid turns it pink again, so the change can be reversed by changing conditions. Iron(III) nitrate solution and potassium thiocyanate solution give a blood-red complex, $\ce{FeSCN^2+}$, but the colour does not deepen indefinitely however much of one reagent is added, because the reaction settles at a mixture of reactants and product. Burning magnesium and burning steel wool are the contrasting cases, because neither product turns back into its reactants under ordinary conditions: the magnesium oxide or iron oxide stays as it is, and the steel wool even gains mass as oxygen from the air joins the solid.

Open and closed systems

A closed system exchanges energy with its surroundings but not matter, while an open system can exchange both. Equilibrium in the sense used in this course can only be reached in a closed system, because in an open one a product can escape or a reactant can be added, and the two rates never balance.

Limestone shows the difference. In a sealed container, $\ce{CaCO3(s) <=> CaO(s) + CO2(g)}$ reaches equilibrium at a fixed temperature, because the carbon dioxide cannot leave. In an open kiln the gas is swept away, the reverse reaction never gets going and the decomposition runs to completion. Living things are open systems, which is why they are never at equilibrium with their surroundings: matter flows through them all the time.

Physical equilibria

Equilibrium is not only chemical. Water in a stoppered bottle at constant temperature reaches $\ce{H2O(l) <=> H2O(g)}$, where molecules leave the liquid and return to it at the same rate and the vapour pressure is constant. Dissolving works the same way: in a saturated solution with undissolved solute present, $\ce{NaCl(s) <=> Na+(aq) + Cl^-(aq)}$ is at equilibrium. Carbon dioxide in a sealed bottle of soft drink sits in equilibrium between the gas above the liquid and the dissolved gas, and opening the cap makes the system open, so gas leaves and bubbles form.

Static and dynamic equilibrium

A static equilibrium is one in which nothing is changing at all because nothing is happening at the particle level, such as a book at rest on a table where forces balance. A dynamic equilibrium is one in which opposite processes continue at equal rates, so the macroscopic properties (concentration, colour, pressure, pH) are constant while particles keep reacting.

The dynamic picture can be tested with isotopes. If a saturated solution of a salt containing a radioactive label is exposed to crystals of the same salt without the label, the label appears in the crystals, which could only happen if dissolving and crystallising were both still going on.

Features of a system at dynamic equilibrium

• It is closed, so nothing enters or leaves.
• The forward and reverse rates are equal.
• The macroscopic properties are constant.
• It can be reached from either direction, from reactants or from products, and the same equilibrium mixture results at a given temperature if the overall amounts are the same.
• It does not say the concentrations of reactants and products are equal. They may be very different.

A concentration-time graph for a reaction started with reactants only shows reactants falling and products rising, with both curves flattening to horizontal lines at the same moment. A rate-time graph shows the forward rate falling from its highest value and the reverse rate rising from zero until the two lines meet and stay together.

Collision theory and equilibrium

Collision theory says a reaction needs particles to collide with enough energy (at least the activation energy) and in a suitable orientation. The rate of a reaction depends on how many such effective collisions happen each second. At the start of a reversible reaction there are many reactant particles and no product particles, so the forward rate is high and the reverse rate is nil. As reactants are used up, collisions between them become less frequent and the forward rate drops; as products accumulate, collisions between product particles become more frequent and the reverse rate rises. Equilibrium is reached at the point where the rates are equal.

Any change to conditions that speeds up one direction more than the other shifts the balance until new equal rates are reached, and this is the starting point for explaining the effects of concentration, pressure and temperature on an equilibrium.

Systems that are not at equilibrium

Some processes are so favoured that the reverse reaction is negligible, and they go effectively to completion. Whether a reaction is favoured depends on two things, the change in enthalpy and the change in entropy. Enthalpy is the heat content of a system, and a reaction that releases heat to the surroundings (a negative $\Delta H$) is favoured. Entropy measures the disorder, or the number of ways energy and particles can be arranged, and a reaction that increases disorder (a positive $\Delta S$) is favoured as well.

Combustion reactions, such as $\ce{CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)}$, are strongly exothermic and usually increase entropy because the products are often more numerous or more dispersed than the reactants. Both factors point the same way, so the reverse reaction has no realistic chance and the reaction is written with a single arrow. The reaction is also open in practice, since the gases disperse.

Photosynthesis is a different example of a system that is far from equilibrium. $\ce{6CO2(g) + 6H2O(l) -> C6H12O6(aq) + 6O2(g)}$ is endothermic and decreases entropy as a few large molecules form from many small ones, so it does not happen on its own: it runs only while a plant takes in light energy and is held away from equilibrium by an input from the surroundings and a continual flow of matter through the plant. The reverse reaction, respiration or combustion of glucose, is the favoured direction.