Estimating concentration of gases species in solution?

Good Morning,

Is there a means to provide the estimate of the following:

Large tank containing solvent. Small tank on top of large tank with valve. Open valve and contents of small tank (with known vapor pressure, slowly expands into large tank (we want this to happen). The vapor from the small tank will slowly increase in vapor pressure until it reaches its saturation vapor pressure.

There will also be some solubility of the small vapor material into the large tank solvent. Is there a way to calculate what the concentration of the small tank material may end up to be in the large tank?