# Water vapor pressure in oxygen bubble

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?

• 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. – David White Jan 1 '19 at 5:46
• the young-laplace equation will furnish the mechanical pressure present inside the bubble due to surface tension effects. – niels nielsen Jan 1 '19 at 6:03
• @DavidWhite so you think the vapor pressure of water will be independent of the oxygen pressure that builds up? – Guiste Jan 3 '19 at 4:40
• @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? – Guiste Jan 3 '19 at 4:48
• 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. – niels nielsen Jan 3 '19 at 5:54