Chemistry · Chemical reactions · Grade 8

Reversible reactions and equilibrium

Why does an NO₂ ampoule go pale in ice, and why does an ammonia column work at high pressure?

The situation

In the ammonia plant of Navoiyazot a mixture of nitrogen and hydrogen passes over an iron catalyst — but it never turns completely into ammonia: the reaction goes in both directions. Engineers keep it at high pressure (over 100 atm) and at 400–500 °C. The same thing happens in the chemistry room: if you put an ampoule filled with brown NO₂ into iced water, it turns almost colourless, and in hot water it darkens. How do reversible reactions come to equilibrium, and how can that equilibrium be shifted?

Topic

Reversible reactions and chemical equilibrium. Ammonia column at Navoiyazot: N₂ + 3H₂ ⇌ 2NH₃ — higher pressure shifts the equilibrium to the right, higher temperature to the left; an ampoule of brown NO₂ loses its colour in the cold

Key ideas

Dynamic equilibrium
Le Chatelier's principle
Equilibrium constant

Formulas

N_{2} + 3 H_{2} \overset{}{⇌} 2 NH_{3} Δ H = - 92 kJ

Ammonia synthesis: to the right 4 mol of gas → 2 mol of gas, and heat is released.

2 NO_{2} \overset{}{⇌} N_{2} O_{4} Δ H = - 57 kJ

Dimerisation of brown NO₂ into colourless N₂O₄ (laboratory ampoule).

v_{\to} = v_{\leftarrow}

Dynamic equilibrium: the rates of the forward and reverse reactions are equal, and the concentrations do not change.

K_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}

The equilibrium constant for $a A + b B ⇌ c C + d D$ ; it depends only on temperature.

K_{c} = \frac{{[HI]}^{2}}{[H_{2}] [I_{2}]} = 50.5 (448^{\circ} C)

$H_{2} + I_{2} \overset{}{⇌} 2 HI$ : for the problems in the “Equilibrium constant” mode.

Theory

Reversible reactions and dynamic equilibrium

Irreversible reactions go to completion: combustion, the formation of a precipitate or the escape of a gas. Reversible reactions go in two directions at once ( $⇌$ ): the products turn back into the starting substances. At the start the forward reaction is fast and the reverse one slow; as the product accumulates, $v_{\to}$ falls and $v_{\leftarrow}$ rises until they become equal — chemical equilibrium is established. Equilibrium is dynamic: the reactions do not stop, but each second as much N₂O₄ is formed as breaks down, so the concentrations do not change. Equilibrium can be approached from both sides — from pure NO₂ or from pure N₂O₄ — and the result is the same.

Equilibrium constant

For $a A + b B ⇌ c C + d D$ , $K_{c} = {[C]}^{c} {[D]}^{d} / ({[A]}^{a} {[B]}^{b})$ — with equilibrium concentrations (mol/L); solids and the solvent water do not appear in the expression. $K$ depends only on temperature. The same fraction at any moment is the reaction quotient Q: if $Q < K$ the reaction goes to the right, if $Q > K$ to the left, and $Q = K$ means equilibrium. Solving a problem (ICE table): Initial, Change, Equilibrium. For example, in a 1 L vessel with 0.5 mol H₂ and 0.5 mol I₂ (448 °C, $K_{c}$ = 50.5): if $x$ mol of H₂ is used up, ${(2 x)}^{2} / {(0.5 - x)}^{2} = 50.5$ → $2 x / (0.5 - x) = 7.11$ → $x$ = 0.39 mol, HI = 0.78 mol. In $H_{2} + I_{2} \overset{}{⇌} 2 HI$ the number of moles of gas does not change, so $K_{c}$ has no units and does not depend on volume.

Le Chatelier's principle

If a system at equilibrium is disturbed from outside, the equilibrium shifts in the direction that reduces the disturbance (H. Le Chatelier, 1884). Concentration: if a starting substance is added or a product removed — to the right. Pressure: if it rises — towards the side with fewer moles of gas: in $N_{2} + 3 H_{2} \overset{}{⇌} 2 NH_{3}$ (4 → 2 mol) to the right, in $2 NO_{2} \overset{}{⇌} N_{2} O_{4}$ also to the right; in $H_{2} + I_{2} \overset{}{⇌} 2 HI$ (2 → 2) it has no effect. Temperature: if it rises — in the endothermic direction. Ammonia synthesis ( $Δ H$ = −92 kJ) and the dimerisation of NO₂ ( $Δ H$ = −57 kJ) are exothermic, so on heating the equilibrium shifts to the left: the ampoule darkens in hot water and pales in ice. A catalyst does not shift the equilibrium — it speeds up the forward and reverse reactions equally and merely brings the system to equilibrium sooner.

In industry: ammonia synthesis

The Haber–Bosch process: nitrogen is taken from the air and hydrogen from natural gas; the mixture (N₂ : H₂ = 1 : 3) is passed at 400–500 °C and 100–300 atm over an iron catalyst (promoted with K₂O and Al₂O₃). At low temperature the equilibrium yield is high, but the reaction is very slow; 450 °C is a compromise: the rate is sufficient, and the yield is raised by pressure (model: at 450 °C, 100 atm — 16 %, 300 atm — 31 % NH₃). In one pass ≈ 15 % of the mixture turns into ammonia; the NH₃ is separated by cooling and liquefying (the equilibrium shifts to the right), and the remaining gas is returned to the column — the overall yield is ≈ 97 %. In Uzbekistan ammonia is produced by Navoiyazot, Ferganaazot and Maxam-Chirchiq; the new ammonia–urea complex at Navoiyazot (2020) is designed for ≈ 660 000 t of ammonia a year.

Laboratory experiment

1. Iron(III) thiocyanate: $FeCl_{3} + 3 KSCN \overset{}{⇌} Fe (SCN)_{3} + 3 KCl$ — a blood-red colour. A pale solution is divided between four test tubes: tube 1 is for comparison; if FeCl₃ is added to tube 2 or KSCN to tube 3, the colour deepens (more starting substance, equilibrium shifts to the right); if crystals of KCl are added to tube 4, the colour fades. In fact the equilibrium $Fe^{3 +} + SCN^{-} \overset{}{⇌} [Fe (SCN)]^{2 +}$ is established in the solution ( $K$ ≈ 140), and K⁺ and Cl⁻ do not take part in the reaction: the colour fades because Cl⁻ ties up some of the Fe³⁺ as FeCl²⁺ and because the ionic strength rises. 2. NO₂ ampoules: identical ampoules are placed in ice water, at room temperature and in hot water; if their places are swapped, the colours swap too — the process is reversible. Safety: NO₂ is poisonous — work only with a sealed ampoule; be careful with hot water; do not taste the reagents, and wear goggles.

About the model

The gases are taken to be ideal. For ammonia, $K_{p}$ is taken from the formula of Gillespie and Beattie (1930), and the yield is calculated with ideal-gas mole fractions — above 200 atm the real yield is a few per cent higher. For NO₂ ⇌ N₂O₄, $Δ H$ = −57.2 kJ and $Δ S$ = −175.8 J/K (NIST-JANAF); real dimerisation takes place in microseconds — in the simulation time is greatly slowed down. The rate of approach to equilibrium in the ammonia column and the rate constant of the H₂ + I₂ reaction are schematic. Colour is calculated for three colour channels with the Beer–Lambert law. The formation constant of FeCl²⁺ (≈ 5) is approximate. The window of molecules is schematic: the number of events is taken from the rate equation.

Did you know?

The French chemist Henri Louis Le Chatelier published the principle of the shift of equilibrium in 1884; in 1887 the German physicist Karl Braun generalised it, which is why it is sometimes called the Le Chatelier–Braun principle.
Fritz Haber received the Nobel Prize in 1918 for synthesising ammonia from nitrogen and hydrogen, and Carl Bosch in 1931 for developing high-pressure chemical processes.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.