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I'm trying to write a story where a gas leak causes an explosion. How much minimum gas would there need to be for a small shed/small room to ignite when a match is lit in there?

The doors and windows are all shut tight, and the gas has sat in a container with no lid for several days, so it's mostly evaporated into the air.

For example, if I have two gallons of gas that have evaporated into a small shed's room (let's say the width and length of 4 cars squished together) and then light a match, would the room ignite?

If not, how many gallons of gasoline would I need to be present in there?

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    $\begingroup$ A "gas leak" typically describes a leak in a natural gas pipe system. An open container of gasoline evaporating in a small space could contribute to an explosion, but it wouldn't be aptly described as a "gas leak". $\endgroup$
    – Nuclear Hoagie
    Jul 22, 2022 at 12:48
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    $\begingroup$ This does not seem to be a question about establishing a face about a fictional world but a question about how physics works in the real world. $\endgroup$
    – sphennings
    Jul 22, 2022 at 12:55
  • $\begingroup$ Can you elaborate on the effect you are after? 'Igniting the room' is a little vague - if there is a combustible mixture of air and gasoline fumes (the fumes being heavier than air this might happen in a smaller region above the gasoline-puddle) the resulting sudden combustion might blow off the roof of the shed, or blow out the doors and windows - filling the whole shed with fumes at the perfect stochiometric ratio would certainly be overkill $\endgroup$
    – bukwyrm
    Jul 22, 2022 at 13:24
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    $\begingroup$ VTC. This isn't about worldbuilding. No rule of your world is being discussed. In fact, you appear to be asking a Real World question for a Real World application. Our help center specific states that the purpose of this Stack is to help you build an imaginary world, not to tell your story. (Emphasis from the Help Center.) (*Continued*) $\endgroup$
    – JBH
    Jul 23, 2022 at 3:36
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    $\begingroup$ There's no such thing as an airtight shed. That's the flaw in your story, not the amount of gas. $\endgroup$
    – Kyle B
    Jul 23, 2022 at 5:17

5 Answers 5

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L.Dutch is correct that you need to look at the Air-Fuel ratio, but you do not necessarily need the ideal air fuel ratio. Gasoline can maintain combustion at ratios anywhere between 6:1 and 20:1. So if you are looking for a bare minimum, you need about a 20:1 ratio.

The average car is 1.77m wide so if we assume a 3m ceiling, you are looking at a volume of 150m^3. The means you need a minimum of 7.5kg or 10.42 liters (2.75 gallons) of vaporized gasoline.

That said, just because you have that much gas does not mean it will all vaporize in the air. Over time some will escape or be absorbed into the wall.

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  • $\begingroup$ 7.5kg of gasoline have 370MJ of energy stored, theoretically enough to lift a three-ton garage-roof to cruising altitude - it might behoove to keep the Boom out of all-caps territory and use the fumes higher specific weight (and thus accumulation on the floor) to craft a more contained experience... $\endgroup$
    – bukwyrm
    Jul 22, 2022 at 13:33
  • $\begingroup$ @bukwyrm you are correct, but lighting a match probably assumes you are using something in the middle layer of air. We don't have have enough details to calculate that exactly, but I believe it should be somewhere near the average particle density for the room. One way or another, lighting a match in a room full of vaporized gasoline like this is going to go up like a thermobaric bomb killing everyone inside or next to the shed, and probably causing significant property damage in the near by area. $\endgroup$
    – Nosajimiki
    Jul 22, 2022 at 13:42
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What you are looking for is called air-fuel ratio

Air–fuel ratio (AFR) is the mass ratio of air to a solid, liquid, or gaseous fuel present in a combustion process. The combustion may take place in a controlled manner such as in an internal combustion engine or industrial furnace, or may result in an explosion

As a first reference you can use the stoichiometric ratio.

The stoichiometric mixture for a gasoline engine is the ideal ratio of air to fuel that burns all fuel with no excess air. For gasoline fuel, the stoichiometric air–fuel mixture is about 14.7:1 i.e. for every one gram of fuel, 14.7 grams of air are required.

Considering that air is about 1 kg per cubic meter while gasoline is is 720 g per liter, if you know the volume of your shed you can quickly determine how much gasoline there need to be for combustion to happen.

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    $\begingroup$ You're not looking for the stoichiometric ratio, you're looking for the lower (and upper) explosive limits. $\endgroup$
    – Mark
    Jul 22, 2022 at 20:55
  • $\begingroup$ I would suggest that he put an upper limit on how much would be necessary. The lower limit would be highly dependent upon the size of the room and how near the flame was. Also, since gasoline vapor is heavier than air, he might also need to factor in the vertical height of the flame above the floor. $\endgroup$
    – Robert Rapplean
    Jul 23, 2022 at 4:46
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Both answers (@L.Dutch and @Nosajimiki) assume a perfect mix between the air and the fuel vapors.

This is not usually the case.

What we usually have is a stratified mixture with more fuel at the bottom.

At the bottom, we have whatever the saturated vapor pressure of the fuel is, given the temperature.

When we go higher, we get less and less fuel and more air in the mixture.

If we use gasoline with its quite low flash point, we can get ignitable concentration at some level with as little as 0.5 or 1 liter of liquid fuel for a small room.

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L.Dutch's discussion of air/fuel ratios correctly explains what's needed to get the gasoline fumes to burn, but that doesn't completely answer your question. Burning the gasoline isn't the same thing as starting a fire, which is what you're looking for.

The answer to your question will largely depend on the contents of the shed: what else is in there, how close is it to the gasoline, and how flammable is it. The composition of the shed itself similarly matters. Gasoline fumes in air burn fairly quickly. You'll get a fireball for a couple of seconds and then it's over. If the heat from that fireball was enough to ignite the shed or something in it, then you'll have the fire you're looking for. If this is a metal storage shed where you store your leftover ceramic tile and stone pavers, then your fireball might blow the windows out but a fire is unlikely. A wooden hay shed with bales of dry straw would very likely catch fire quickly.

While that doesn't give you the numerical answer that you were hoping for, it means that you have a lot of freedom to customize your story to ensure that the desired result happens. For maximum effectiveness, add something near the gasoline that is very flammable and that burns slowly. That will maximize the chances that the fire can start to sustain itself and spread. A decent example would be thin cloth curtains. Natural fibers burn easily, and curtains hold the fire close to the wall and help it spread to the structure.

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To get a match light to explode the room, you'd need to have a concentration of gasoline in the air above the lower flammability limit.

An average car is 14.7 feet (4.5 meters) long. An average car is 5.8 feet (1.7 meters) long. A shed is somewhere between 8-10 feet (2.4 meters) tall, so the shed would be about 2700 cubic feet big (77 cubic meters). We'll assume the shed is eight feet tall and completely empty except for the gas.

At room temperature, a space that big has about 3160 moles of air. The lower flammability limit of gasoline is 1.4%, so we need 44 moles of gasoline to ignite if the room is evenly mixed -- you can handwave this a little bit if you're arguing that the match is next to the gas, but probably not more than a factor of two unless the match is really close to the gas. The molecular weight of gasoline is about 93 or so depending on the season and blend, so that's 9 lbs (4 kg), or, with a density of 0.72 g/cm^3, the volume of gas you'd need to evaporate (and keep in the shed) is 1.5 gallons (5.7 Liters).

You probably want to have more on the floor if you want it to keep burning, though, or to have soaked something wood.

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