This simulation models the behavior of a sealed, 1-L autoclave that initially contains mostly water plus a small volume of air, all at 25 °C and 1.0 bar pressure. Change the initial volume of water with a slider and the temperature resets to 25 °C. As the temperature increases by moving the slider, liquid water expands and its saturation pressure increases. At the same time, the gas-phase volume decreases, so gas-phase \(O_2\) and \(N_2\) partial pressures increase (ideal gas law). The amounts of \(O_2\) and \(N_2\) dissolved in the water increase with pressure, but decrease with temperature. The amounts dissolved are shown in the bar chart (green = gas phase, purple = dissolved). Even at moderate temperatures, the pressure inside the sealed container can be quite high.

The final liquid volume \(V_f^L\) of water is given by:

$$V_f^L = (A T^3 + B T^2 + C T + D) V_i^L,$$

where \(V_i^L\) is the initial liquid volume (L) at 25 °C, \(T\) is temperature (°C), and \(A\), \(B\), \(C\) and \(D\) are constants.

The total pressure $P$ in the container is equal to the saturation pressure of water $P_w^{sat}$ plus the partial pressures of oxygen $P_O$ and nitrogen $P_N$:

$$P = P_w^{sat} + P_O + P_N.$$

The saturation pressure of water is calculated using the Antoine equation:

$$P_w^{sat} = 10^{(A_w - \frac{B_w}{T + C_w})},$$

where $A_w$, $B_w$ and $C_w$ are Antoine constants.

The partial pressures of oxygen and nitrogen are calculated using the ideal gas law:

$$P_j = z_j n_j^V R (T + 273) / V^V,$$

where $z_j$ is the fraction of oxygen or nitrogen in air where $z_O = 0.21$ and $z_N = 0.79$, $n_j^V$ is the moles of $j$ in the gas phase, $R$ is the ideal gas constant ([L bar]/[mol K]) and $V^V = 1 - V^L$ is the vapor volume (L).

The total moles of oxygen $n_O$ and nitrogen $n_N$ in the container are calculated at 25 °C and 1 bar pressure, the moles in the gas phase are calculated using the ideal gas law, and the moles dissolved in water are calculated using Henry's law:

$$n_O = \frac{P_O V_i^V}{R (T + 273)} + H_O P_O V_i^L,$$ $$n_N = \frac{P_N V_i^V}{R (T + 273)} + H_N P_N V_i^L,$$

where $H_O$ and $H_N$ are Henry's law constants (mol/[L bar]):

$$H_O = 4.342 \times 10^{-6} e^{1700 / (T + 273)},$$ $$H_N = 7.863 \times 10^{-6} e^{1300 / (T + 273)}.$$

For all $T$ and $P$, the moles in the gas phase and dissolved must equal the total moles at 25 °C and 1 bar:

$$n_O = \frac{P_O V_f^V}{R (T + 273)} + H_O P_O V_f^L,$$ $$n_N = \frac{P_N V_f^V}{R (T + 273)} + H_N P_N V_f^L.$$

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by Drew Smith under the direction of Professor John L. Falconer and Michelle Medlin. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.