Benzene is carcinogen, The short term exposure limit for airborne benzene is 5 ppm for 15 minutes see https://en.wikipedia.org/wiki/Benzene#Benzene_exposure_limits
I would like to know which volume of air could contain toxic benzene if an benzene ship with 2000 ton benzene should vaporise vaporization to the air. Benzene is heavier than air so it would be closed to the ground. How close is not a chemical subject but a physical phenomenon which is out of the scope of this question. In this calculation I use a lot of assumptions, just because the lack of info. But at least it gives a idea what might happen. Hopefully, on a later moment, some assumptions could be replace by facts, making the calculation more accurate. For now it is meant to get an idea what would happen in the worst case scenario. Assumption only 1% of the benzene vaporise. The question how much benzene could vaporise is out of the scope of this question. Calculation adjusted with info of @maurice : Benzene is not a ideal gas. The vapor pressure of benzene is about 0.04 bar at 0°C.
Mol mass benzene: 78,11184 g/mol
Mol / kg: ~12,8 mol benzene (1000 g / 78,11184 g/mol)
0.022413969545014... m3/mol at 0 °C, see https://en.wikipedia.org/wiki/Molar_volume using Avogadro's law
The vapor pressure of benzene is at 0°C: 0.04 bar
1 kg benzene liquid: 0,01148 m³ benzene gas at 1 bar (~12,8 mol benzene * 0.022413969545014... m3/mol * 0,04bar / 1 bar)
Benzene to vaporize: 1 %
Mass vaporized benzene: 20.000 kg ( 2000.000 kg * 1%)
Total 100% benzene gas: 230 m³ ( 20.000 kg liquid benzene * 0,01148 m³/kg)
Assumption height benzene cloud from the ground:
- 1 meter high: Surface: 230 m²
- 3 meter high: Surface: 77 m² (230 m² / 3m)
Assumption gas will spread as a circle:
Radius with height of 3 meter: 8,5 m (230 m³ = 3,14 * r²)
Diameter cloud of 3 m high: 17 m
Which can move with the speed of wind which can be 0 m/s (0 Beaufort) up to 28 m/s (10 Beaufort) Benzene will probably mix with air. But airborne benzene stay toxic up to 5 pmm.
So the maximum size of the toxic cloud would be:
- The short term exposure limit for airborne benzene is 5 ppm
- Maximum amount of gas which could be carcinogen: ~46 * 10⁶m³ (230 m³ / 5* 10-⁶ ppm)
- Assumption height benzene cloud from the ground:
- 1 meter high: Surface: 46 * 10⁶m²
- 3 meter high: Surface: 9,2 * 10⁸m² ( 46 * 10⁶m³ / 3m)
- Assumption gas will spread as a circle:
- Radius with height of 3 meter: 3,8 km (46 * 10⁶m² = 3,14 * r²)
- Diameter cloud of 3 m high: 7,6 km
If the cloud gets larger it would be less than 5 pmm and is not toxic anymore. This will be a matter of windspeed and time, which both are beyond the scope of this question.
The key question for me is: Is the calculation for a vessel loaded with 2000 ton benzene where 1% leaks generate a cloud with carcinogen air between about 230 m³ and 46 * 10⁶m³ correct? Or do I miss important issues.