Suppose we have a source of O$_2$ bubble formation in water at specific nucleation sites, how can we estimate the water vapor pressure inside the O$_2$ bubbles?

I know that:

(1): $p_\mathrm{O_2}+p_\mathrm{H_2O} = p_\mathrm{tot}$

(2): $c_\mathrm{O_2} = K_\mathrm{O_2}\cdot p_\mathrm{O_2}$ (Henry's law)

where $c_\mathrm{O_2}$ is the concentration of $O_2$ in the liquid phase, and $p_x$ are partial pressures. How can I get $p_\mathrm{H_2O}$ probably as a function of $O_2$ gas pressure?

  • $\begingroup$ The partial pressure of the water inside the oxygen bubble will be the vapor pressure of water at its temperature. See the Antoine equation on Wikipedia for more details. $\endgroup$ – David White Jan 1 '19 at 5:46
  • $\begingroup$ the young-laplace equation will furnish the mechanical pressure present inside the bubble due to surface tension effects. $\endgroup$ – niels nielsen Jan 1 '19 at 6:03
  • $\begingroup$ @DavidWhite so you think the vapor pressure of water will be independent of the oxygen pressure that builds up? $\endgroup$ – Guiste Jan 3 '19 at 4:40
  • $\begingroup$ @nielsnielsen indeed the surface tension will play a role here. can we get the oxygen partial pressure as a function of surface tension and O2 partial pressure? $\endgroup$ – Guiste Jan 3 '19 at 4:48
  • $\begingroup$ for a static bubble the young-laplace equation will furnish the interior pressure. equate this to the sum of the partial pressures. Include water vapor pressure and assume saturated conditions. $\endgroup$ – niels nielsen Jan 3 '19 at 5:54

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