Pale in Ice, Dark in Heat

Three Matching Tubes

Three glass tubes hold the same amount of the same gas, each sealed shut. The page’s tubes are 25 mm across, at 0.3 bar inside at 25 °C.

One goes into ice water, one stays in water at 20 °C, one goes into water at 80 °C. The one in ice turns pale yellow; the one in hot water turns deep red-⁠brown. Taken out, each drifts back to the brownish yellow of the room.

The colour comes only from nitrogen dioxide, NO₂: its molecule has one unpaired electron and absorbs violet and blue light. Two NO₂ molecules can pair into one dinitrogen tetroxide, N₂O₄, which absorbs almost no visible light and is colourless. How deep a tube’s colour looks counts the NO₂ molecules along the light’s path. Where the NO₂ comes from: Copper in Nitric Acid.

2NO₂ ⇌ N₂O₄ · NO₂ brown, N₂O₄ colourless · the page’s tube: 25 mm across, 0.3 bar at 25 °C · ice water 0 °C · 20 °C · hot water 80 °C

Balanced, Never Still

In the tube, NO₂ molecules keep pairing and N₂O₄ molecules keep splitting. When more pair than split, the NO₂ falls; when more split, it rises. When both run equally fast, the number of NO₂ stops changing, and so does the colour: chemical equilibrium. The reactions have not stopped; they run at the same rate both ways.

They are far too quick to see. From measured rate constants, at 20 °C an N₂O₄ molecule in the page’s tube lasts only 22⁠–⁠50 µs on average before it splits, and each NO₂ pairs about 50,⁠000 to 110,⁠000 times a second. An ultrasonic measurement of 1962 gives about 24 µs for this tube (at 25 °C), in the same range.

So a disturbed equilibrium settles again within microseconds. A tube put into hot water takes a while to darken because the glass and the gas take a while to warm; the reaction keeps up all the way.

2NO₂ ⇌ N₂O₄ · at 20 °C: an N₂O₄ lasts 22⁠–⁠50 µs on average · an NO₂ pairs about 50,⁠000⁠–⁠110,⁠000 times a second · back in balance about 4⁠–⁠8 µs after a disturbance (computed)

Heat Splits, Cold Pairs

When two NO₂ molecules pair into N₂O₄, heat comes out, about 57 kJ per mole; splitting N₂O₄ takes the same heat back in.

Warm it, and the equilibrium leans to the side that takes in heat: more splits, NO₂ rises, the colour deepens. Cool it, and it leans to the side that gives heat out: more pairs, the colour fades. By the page’s computation, about 14% of the nitrogen in the ice-⁠water tube is in NO₂, 28% at 20 °C, 85% at 80 °C.

The tube in ice is not colourless: the NO₂ left still takes about four-⁠fifths of the blue light at 450 nm through its middle, so it looks pale yellow. Nor does the hot one darken only because the gas is hot: the same tube of gas holds about six times as many NO₂ molecules in hot water as in ice.

2NO₂ → N₂O₄ gives out about 57 kJ/mol · nitrogen in NO₂: 0 °C 14% · 20 °C 28% · 80 °C 85% (the page’s tube, computed)

A Number Only Heat Moves

At equilibrium, the partial pressure of N₂O₄ divided by the square of the partial pressure of NO₂ is a fixed number, the equilibrium constant K. From the thermodynamic tables it is about 6.7 per bar at 25 °C.

Fill a tube with more gas or less and the share of NO₂ changes, but K does not: at 25 °C, a tube at 0.1 bar has 52% of its nitrogen in NO₂, one at 1 bar only 19%, and both give the same K. Squeezing the gas or adding NO₂ only shares the mixture out again; K stays.

Only temperature changes K: 55.6 per bar at 0 °C, 0.19 per bar at 80 °C, about 36 times smaller from 25 °C to 80 °C. Le Chatelier’s principle says which way the mixture shifts; how far comes from K.

K = p(N₂O₄) / p(NO₂)² · 0 °C 55.6 · 25 °C 6.74 · 80 °C 0.188, per bar (NIST-⁠JANAF, computed)

Push the Plunger

The glass syringe holds the same gas, 0.5 bar at 25 °C, its nozzle capped. Push the plunger in to half the volume and the same molecules crowd into half the space: seen from the side, the NO₂ is at once twice as dense and the colour darkens.

Two NO₂ molecules pairing into one N₂O₄ leave one molecule fewer, taking less room, so after the squeeze the equilibrium leans towards N₂O₄. By the page’s computation, once the gas is back at 25 °C its NO₂ is about 1.5 times as dense as before: paler than just after the push, still darker than before it. Seen along the barrel, the path is half as long, and it ends up paler than at the start.

Many textbooks say the colour fades over a few seconds because the reaction is catching up. In fact the reaction catches up within microseconds. A quick push heats the gas by about 13 °C, which itself makes a little more NO₂; the fading over the next seconds is the gas giving its heat to the glass and cooling.

Half the volume: NO₂ density × 2 → × 2.2 while hot → × 1.5 back at 25 °C · along the barrel × 0.74 · 0.5 bar → 0.95 bar (computed)

Water and Chloride Compete for Cobalt

In water, a cobalt ion Co²⁺ from cobalt chloride is surrounded by six water molecules: pink [Co(H₂O)₆]²⁺. With plenty of chloride, four chloride ions take the place of the six waters: blue [CoCl₄]²⁻. Chloride ions are larger than water molecules, and six do not fit.

This is an equilibrium too. Add concentrated hydrochloric acid and the extra chloride shifts it to the blue side: the solution turns deep blue. Add water and it goes back to pink, only paler. Salt turns it bluer as well, but salt dissolves slowly.

The violet of the middle tubes in the rack is both kinds together, with forms in between that hold one or two chloride ions. The pink one absorbs green light near 525 nm; the blue one absorbs red near 680 nm.

[Co(H₂O)₆]²⁺ + 4Cl⁻ ⇌ [CoCl₄]²⁻ + 6H₂O · pink: six waters, octahedral · blue: four chlorides, tetrahedral · add chloride → blue · add water → pink

Heat Turns It Blue

Going from pink to blue takes in heat. So a violet solution turns blue in water above 90 °C and pink in ice water; swap the two tubes and the colours swap too. Measured at high temperature, the step takes in about 62 kJ per mole.

The solid changes colour the same way: anhydrous cobalt chloride is blue, and with water taken up as the hexahydrate, CoCl₂·6H₂O, it turns pink. Blue cobalt chloride paper turns pink in water, and indicating silica gel uses it to show damp.

Cobalt dichloride is classified in the EU as possibly causing cancer when breathed in, so indicating gel that holds it must be labelled and disposed of as hazardous. It has not been banned, but many humidity indicator cards now use indicators without cobalt dichloride.

Pink → blue takes in heat, about +62 kJ/mol measured at high temperature · above 90 °C blue, in ice water pink · anhydrous CoCl₂ blue, CoCl₂·6H₂O pink

Faster, Not Further

A catalyst speeds up both directions, and by the same factor. The equilibrium comes sooner, but it sits in the same place, and K is unchanged.

Ammonia’s makers set their conditions by the same reasoning: the reaction gives out heat and leaves fewer gas molecules, so ammonia is favoured by cold and high pressure; but in the cold it is far too slow, so a catalyst is used, at 400⁠–⁠500 °C and about 150⁠–⁠250 atmospheres, as a compromise. The industrial side: Nitrogen from the Air.

A catalyst speeds both ways alike, K unchanged · ammonia: N₂ + 3H₂ ⇌ 2NH₃ at 400⁠–⁠500 °C, about 150⁠–⁠250 atm

One Sentence from 1884

In 1884 van 't Hoff wrote down the rule for temperature: on cooling, an equilibrium shifts to the side whose forming gives out heat. In the same year Le Chatelier extended it to pressure and concentration: a system in stable equilibrium, changed from outside, can only undergo inner changes that would oppose that change. Today it is often put in one line: push a balance and it shifts to push back.

It gives a direction, not a cause, and no amount. Put the NO₂ tube in ice water and the equilibrium shifts to the pairing that gives out heat, yet the gas in the tube still cools to the temperature of the ice water.

It has exceptions, too. Add a little nitrogen to the ammonia equilibrium at constant temperature and pressure when nitrogen is already more than half the mixture, and, for ideal gases, the equilibrium shifts towards splitting ammonia. To know which way and how far, the reliable way is to compute with the equilibrium constant.

Le Chatelier, Comptes rendus 99 (1884) · van 't Hoff, Études de dynamique chimique (1884) · the principle for direction, K for amount

Nine Things on the Bench

Three glass tubes sealed with NO₂ and their water: ice water, water at 20 °C and water at 80 °C on a cork mat, each beaker with a red-⁠spirit thermometer; a stainless rack of five tubes of cobalt chloride solution, pink to blue; and at the right end, a 50 mL glass syringe upright in a small stand, also sealed with NO₂.

Three sealed tubes · three beakers of water · three thermometers · rack · cobalt chloride · glass syringe