# Flammability Limits of Vapor/Air Mixtures

#### Thomas B. Jones Professor of Electrical Engineering University of Rochester

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: C2H3COH3 and the balanced oxidation reaction for complete (stoichiometric) combustion is:

C2H3COH3 + 4O2 --> 3CO2 + 3H2O

This 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% N2, 21% O2, and ~1% Ar (plus other gases), and the density of air at STP is ~1.2 kg/m3. The molecular weights of the four constituents are:

• N2: 28 gr/mole
• O2: 32 gr/mole
• Ar: ~40 gr/mole
• acetone: 58 gr/mole

Using these values, the mass percent of O2 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 mixture

The density of liquid acetone is 791 kg/m3 at 23 degrees C, so the required volume of liquid is 0.000152 m3, 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Britton, L.G., unpublished collection of MIE and conductivity data for insulating materials, 1997.