We are creatures of light and air. Life’s a gas, in every sense. We are oxygen, hydrogen and nitrogen, packed together with the carbon that photosynthesising life has plucked, one molecule at a time, from the atmosphere in the form of carbon dioxide. At cremation, our bodies bake down to a handful of minerals. When Hamlet beseeched his too, too solid flesh to melt, thaw and resolve itself into a dew, he got it about right: the Prince of Denmark would have been about 70% water, which is itself an atmospheric vapour. And he certainly could have been blown away.

Harry Truman – “not that Harry Truman”, as Sam Kean says in this bright and breezy book – was blown away by Mount St Helens. Truman was the defiant man who dismissed the warnings of volcanologists and refused to leave the high slopes of America’s most violent modern volcano before it erupted in May 1980. Kean reconstructs his death because, as a chemist, he knows the temperatures at which water, viscera and bones could vaporise as a black cloud of intense heat, 100 storeys high and 10 miles wide, came roaring down the mountain at 350mph: “Truman’s clothes would have flared and disappeared, and then Truman himself would have sublimed in the scientific sense – transformed from solid to spirit almost instantly. And with a final hiss, he would have risen up into the air.”

As Kean says, there’s a chance that your last breath contained just the tiniest whiff of the late Harry Truman, just as it quite possibly contains a remnant of the air exhaled by Julius Caesar as he cried “Et tu, Brute,” and expired. The atmosphere is vast, but so is the number of atoms and molecules inhaled with each breath: the number of lungfuls in the air and atoms in each lungful run to the billion trillions and more or less match. So each inhalation is also likely to incorporate the last wheeze of a dying tyrannosaurus 70m years ago; and the breath exhaled by Marc Bolan of T Rex as he sang “Life’s a Gas”, or by Joey Ramone of the Ramones (who wrote a different song of the same title).

Our planet is for the moment an ideal home, solar-powered, air-conditioned, fitted with hot and cold running water and underfloor central heating, but it is the atmosphere that provides the currency with which life pays its way. This book starts with a blood-soaked toga and the conceit of Caesar’s last gasp, but it does truly have an epic story to tell, and Kean takes us at a canter right through the entire 4.5bn year saga, from the moment of planetary assembly, mostly from interstellar gas molecules, to the chaotic challenge of planetary weather, the sorry comedy of flying saucers at Roswell and the even more mournful tale of humanoid survivors from spaceship Earth – should there be any – in search of another habitable planet a dozen light years away.

Earth’s first atmosphere during the Hadean period can hardly have been promising: the steamy magmatic exhalations would have been at pressures high enough to crush a human skull, but they cooled to condense into sea. Earth was also hit by another space object big enough to tilt it off its axis, and give it a companion moon: the same collision, says Kean “not only ejected our atmosphere, it may well have boiled our frickin’ oceans”.

Lake Nyos, Cameroon. Photograph: Alamy

Let’s get this bit out of the way: at times, Kean takes his admirable conversational tone in directions not always familiar to those brought up on the measured language of Thomas Henry Huxley, Richard Dawkins or Nigel Calder. So in an aside, the aforementioned Harry Truman “woke up in the snow in his tighty-whities”; the chemist Fritz Haber “developed one helluva crush” on the Kaiser; Humphry Davy tried “chugging a bottle of wine as fast as possible”; Alfred Nobel spilt some “nitro onto a pile of kieselguhr like a klutz” and so on.

More awkwardly, the whole story – serious science all the way – is told in measurements of miles, pounds and Fahrenheit, rather than the metric units now universal in science.

Inevitably, some of it is familiar: who could talk about oxygen without invoking Joseph Priestley, or Lavoisier; nitrogen without mentioning Haber, or nitrous oxide without Davy? The numbers, too, are numbing: we don’t think in septillions but that’s the traffic in oxygen molecules consumed by a human in 24 hours in the course of powering muscle movement. The poisonous gas hydrogen sulphide, for instance, makes up a vanishingly small component of the air, but you gulp 60m molecules every four seconds. You never think about the noble gases, but every four seconds you breathe in – and breathe out – 20 quadrillion molecules of helium and 100 quintillion of argon.

Albert Einstein makes an appearance as a fridge designer

The narrative embraces not just the nature of air but the breathtaking qualities of some of its gases, and their connection with human history, so there are enjoyable detours into the story of guano that – before the Haber-Bosch process – supplied the nitrogen that fuelled 20th-century food supply; and into the grim deaths at Lake Nyos, Cameroon, which in 1986 foamed like soda water, with deadly levels of carbon dioxide that killed 1,746 people. “Survivors remember an eerie stillness for days afterward. There weren’t even flies around to snack on the dead bodies.”

This airy adventure bobs along with the first balloonists; the atmospheric link between the collapse of the Tay Bridge and the fame of William McGonagall, that enduring disaster of a poet; the improbable spontaneous combustion of Mr Krook in Dickens’s Bleak House; the vacuum pumps and steam machinery of Newcomen and Watt and the explosive value of gunpowder, nitroglycerin and dynamite (all of which release gases, very suddenly, and with great force). We meet Joseph Pujol, aka Le Pétomane, the Parisian performer of evocative farts. Albert Einstein makes an appearance as a fridge designer; the nuclear force locked in atomic matter pops up even more forcefully with the atmospheric weapons tests in the Pacific. The overarching story is instructive, told lightly and with pace.

Kean thoughtfully packs even more digressions into his endnotes. My favourite nominates the 832°F temperature at which brimstone (hell has a lake of it, according to the Revelation of St John the Divine 21:8) remains liquid; and then takes the temperature of heaven (Isaiah 30:26 seems to say the sun shines sevenfold as the light of seven days). Temperature increases as the fourth power of sunlight, so with 49 suns heaven would enjoy a temperature of 1,000°F and therefore be hotter than hell. It’s a helluva read. And it’s a gas.

• Caesar’s Last Breath is published by Doubleday. To order a copy for £17 (RRP £20) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.