Vapor/air mixtures are flammable only over a limited range of vapor concentrations. This range is defined by the **lower** and **upper** flammability limits. Mixtures outside this range are described as, respectively, too "lean" or too "rich" for ignition. The flammability limits are best explained by an example; we chose the common hydrocarbon acetone here. At standard temperature and pressure (STP), the lower and upper limits are 2.6% and 12.8% by volume [Britton, 1997]. A **stoichiometric** mix of vapor and air contains just enough oxygen to burn all the vapor, with nothing left over. The stoichiometric ratio for acetone at STP is 5.0%. Note that this value is about twice the lower flammability limit and about one-half the upper limit.

The chemical formula for acetone is: C_{2}H_{3}COH_{3} and the balanced oxidation reaction for complete (stoichiometric) combustion is:

C_{2}H_{3}COH_{3} + 4O_{2} --> 3CO_{2} + 3H_{2}OThis 4:1 ratio of oxygen molecules to acetone molecules is readily shown to be consistent with the stoichiometric amount of 5% by volume as stated above.

We wish to determine the correct amount of liquid acetone required to obtain a stoichiometric vapor/mixture occupying one cubic meter at STP. First, the constituents of pure air are 78% N_{2}, 21% O_{2}, and ~1% Ar (plus other gases), and the density of air at STP is ~1.2 kg/m^{3}. The molecular weights of the four constituents are:

- N
_{2}: 28 gr/mole - O
_{2}: 32 gr/mole - Ar: ~40 gr/mole
- acetone: 58 gr/mole

Using these values, the mass percent of O_{2} in air may be calculated as follows:

(0.21)(32)/[(0.78)(28)+(0.21)(32)+(0.01)(40)] = 0.232 (or 23.2%)From this result, it is straightforward to determine the mass of acetone required to achieve a stoichiometric mix in one cubic meter.

(0.232)(1.2)(0.95)Ä(1)(58)/(4)(32) = 0.12 kg acetone per cubic meter of vapor/air mixtureThe density of liquid acetone is 791 kg/m^{3} at 23 degrees C, so the required volume of liquid is 0.000152 m^{3}, or 152 milliliters. The stoichiometric mix is achieved by evaporating this volume of liquid into a one cubic meter volume of air.

#### Library references

Britton, L.G., unpublished collection of MIE and conductivity data for insulating materials, 1997.

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Last modified: Wednesday, 21-Feb-2007 20:40:08 EST