# Empirical Equations for Predicting the Vapour Pressure of HFA 134a or HFA 227ea Systems containing Ethanol

##### DDL24 – 2013

The vapour pressure of a Metered Dose Inhaler’s (MDI’s) formulation influences the atomisation process and the resultant size of the emitted droplets within the inhaler’s dose1,2. This study presents the vapour pressure of pure HFA 134a and HFA 227ea formulations as well as formulations containing 100μg of Beclometasone Dipropionate (BDP) per 50μl and 5 – 40%w/w ethanol at 3°C, 20°C and 30°C. Vapour Pressure measurements were performed using a MMD-30E Electronic Diaphragm Gauge readable to 0.05bar.
Equations describing the vapour pressure of MDI formulations are not readily available. Therefore the Antoine equation3 (Eq. 1) has been used to correlate experimental vapour pressures between temperatures of 3-30°C.

P = EXP(A-B/(T+C)) (1)

Where, P = Vapour Pressure (Bar), T = Temperature (°C), and A, B and C are Antoine coefficients that vary from substance to substance.
Utilising regression software, coefficients A, B and C have been determined and empirical equations 2 and 3 were derived for HFA 134a and HFA 227ea systems respectively. Coefficients B and C were determined to be dependent upon ethanol content, E, (% w/w) for each propellant system.

P = EXP(3.28-(86.37+0.91*E)/(T+(37.91+0.35*E))) (2)
P = EXP(2.83-(79.85+1.24*E)/(T+(36.32+0.35*E))) (3)
Where, 3°C ≤ T ≤ 30°

Equations 2 and 3 enable the predicted vapour pressures of pure and binary mixtures from knowledge of MDI ethanol content and temperature. There was an excellent correlation (R2 >0.99) between the experimental and calculated vapour pressure values over the range of formulations (0 – 40%w/w ethanol) and temperatures (3°C – 30°C) evaluated.