The Relationship between Saturated Hydrogen Peroxide, Water Vapour and Temperature

Hydrogen peroxide (H₂O₂), in the form of a vapour, has become the compound of choice for gaseous biodecontaminations in the pharmaceutical industry and some sectors of health care. The vapour is generated by evaporating an aqueous solution of H₂O₂, which not only raises the H₂O₂ gas concentration, but also the water content of the carrier gas. As some processes operate at vapour concentrations below the dew point, to avoid condensation, and some at concentrations that cause the formation of dew, it is important to understand the relationship between the vapours and to have a method of establishing the dew point.

The relationship between water and H₂O₂, and the point at which saturated vapours occur and hence when condensation may be expected has been investigated. An analysis of the equations governing equilibrium vapour pressures of these gas mixtures has been done and a method of calculating the dew point has been derived. Somewhat surprisingly, results have shown that the dew point will frequently be reached during a hydrogen peroxide biodecontamination when the relative humidity is only 40%. This is important because it has implications for the understanding of the fundamental mechanisms of H₂O₂ biodecontamination. There has, for some time, been a debate regarding whether gaseous H₂O₂ is a wet or dry process, and the purpose of preparing this paper is to give those who are interested in the process a tool to allow them to know at what vapour concentrations and temperature saturated vapour will be reached.

Condensation will occur when vapour mixtures become saturated. This may happen at conditions when there is a high water content and a low H₂O₂ content, or vice versa, or indeed at a range of intermediate values. Raising the temperature of the gas mixture will also raise the saturated vapour pressures.

Regardless of how the vapours are generated, once the saturated vapour pressures have been reached, condensation will occur (depending only on the temperature and the vapour concentrations). If water and H₂O₂ vapour are injected in sufficient quantities into a closed space, the dew point will be reached and condensation will form. The condensation formed will be at a concentration that ensures that the liquid condensate and vapour are in equilibrium.

The fundamental equations

Saturated water vapour pressure may be calculated using the following equation by Keyes

¹

and is expressed in a log

₁₀

format (Equation 1):

Scatchard et al.2 developed a similar equation for H2O2 (Equation 2):

Equation 2, for the saturated vapour pressure of H₂O₂, was reviewed and published by Schumb.³ Using Raoult's Law it is possible to calculate the equilibrium vapour pressure of a perfect multicomponent liquid. Unfortunately, because of the bond formed between H₂O₂ and water molecules, Raoult's Law has to be modified by the addition of an activity coefficient (which is always less than unity), and is then expressed as follows (Equation 3):

The activity coefficients for water and H₂O₂ were calculated by Scatchard et al.² and then later reviewed and published by Scumb (Equations 4 and 5).³ From Raoult's Law, it is clear that the saturated vapour pressure of water above a solution of H₂O₂ will always be less than that of pure water at the same temperature. In any liquid system, the sum of the mol fractions of the components must be unity; thus, for an aqueous solution of H₂O₂ we have Equation 6.

The vapour concentration at dew point

Unlike pure water, or pure H

₂

O

₂

, it is not possible to directly calculate the vapour pressures or gas concentration at which dew will form in a mixture of H

₂

O

₂

and water vapour. Not only will this be temperature dependent, but some vapour mixtures will condense at high water content and others at high H

₂

O

₂

content. It is the interaction of the two vapours, at any specified temperature, that will determine if the mixture of vapours is saturated and will therefore condense.

Definitions

Condensation will occur when the vapour and liquid are in equilibrium. Consider a closed vessel into which a mixture of water and H₂O₂ vapour is put. If the concentration of the vapours is increased then, at some point, condensation will form and the condensate and vapour will be in equilibrium. To find the point of condensation we must find the equilibrium point (that is, a concentration of condensate that has the same vapour pressures as the vapours that have been built up in the closed vessel).

Equation 3 may be rewritten for both water and hydrogen peroxide using the subscripts _H and _W (Equation 7). Substitution for x_W and x_H in Equation 6 gives Equation 8.

Equation 8 may be rearranged as follows (Equation 9).

Equation 9 is the equilibrium relationship between water and hydrogen peroxide vapour above an aqueous solution. We can use this equation to find the relative humidity at which condensation will form - given the temperature and hydrogen peroxide gas concentration.

It is, unfortunately, necessary to calculate this relationship iteratively. An estimation must first be made of the mol fraction of the water x_WE in the condensate. Using the above equations, the known temperature and the estimated mol fraction it is possible to calculate p_WE, g_WE, g_HE, P^O_W and P^O_H. The subscript E has been used to indicate that these values result from the estimation of the mol fraction. Insertion of these values into Equation 10 (derived from Equation 9), together with the measured value of the gas concentration, allows a value for p_W to be calculated.

The resulting calculated value of p_W should be compared with that from the estimated mol fraction p_WE. If they do not agree, further estimations must be made until the value from Equation 10 and the estimated mol fraction are equal. Equality is achieved when the equation is in balance and hence gives the saturated water vapour pressure at the known temperature and H₂O₂ gas concentration. The relative humidity (RH%) is found using Equation 11.

Figure 1: Dew point of hydrogen peroxide and water vapour.

Set out in Table I is a method of performing the calculations using an Excel spreadsheet. Copy the descriptions from Column 2 into the spreadsheet. The only values that must be entered are in Rows 1, 3 and 5. All other values are calculated as shown in Column 3. If 28, 1000 and 0.444 are entered respectively in Rows 1, 3 and 5 then the calculations should produce the check values shown in Column 5.

To find the saturated values of RH% and H₂O₂ gas concentration at any temperature, simply enter the temperature in Line 1 and the gas concentration in Line 3. This will generate an error in Line 18 which can be reduced by adjusting the value of the mol fraction in Line 5. Increasing the value in Line 5 will increase the size of the error; for example, if the error is negative increase the value in Line 5 to make it positive and vice versa. Once the error in Line 18 is zero or almost zero then the RH% is correct.

The calculated values of RH and hydrogen peroxide concentration will be those at which condensation will form. Saturated water and hydrogen peroxide concentrations at a range of temperatures are shown in Figure 1.

Table I: Performing the calculations on an Excel spreadsheet.

Conclusion

This method for calculating the dew point of H

₂

O

₂

and water vapour mixtures may be used to establish operating conditions required to reach dew point. Cycle development is assisted by calculating the required amount of hydrogen peroxide.

References

1. F.G. Keyes, "Thermodynamic Properties of H

₂

O Substance, 0 to 150 °C,"

J. Chem. Phys.

15, 602–612 (1947).

2. G. Scatchard et al. "Vapour–Liquid Equilibrium VIII Hydrogen Peroxide–Water Mixtures," J. Am. Chem. Soc. 74, 3715–3720 (1952).

3. W.C. Scumb et al., "Hydrogen Peroxide," Amer. Chem. Soc. Monograph (1955).