[iheartsludge]

Do gases dissolved in a liquid increase the volume of that liquid?

System:
The system considered in an 11,000 gallon tank. 10,000 gallons are liquid, 1,000 gallons are "headspace". Initially, the system is at neutral pressure. System is sealed and chemical is added (30 gal). System is regulated at 15 psig. Pressure generated is a function of reactions in the liquid phase. Negligible pressure rises due to addition of 30 gal. chemical. This is not a two-phase system. Gas is a NOx/CO2 mixture, liquid is an acidified wastewater sludge (pH = 2.0).

Assumptions:
- Ideal gas law applies
- Isothermal at 80F
- Henry's Law for gases dissolved in water applies without temperature compensation
- The balance component of gas is air (79% N2, 21%O2) - this overestimates the concentration of O2 because O2 reacts with NO.

Henry's law constants being used:

kH, O2   (mol/L) / atm   1.27E-03
kH, N2   (mol/L) / atm   6.30E-04
kH, CO2   (mol/L) / atm   3.46E-02
kH, CO   (mol/L) / atm   2.00E-03
kH, NO   (mol/L) / atm   1.80E-03
kH, NO2   (mol/L) / atm   2.43E-02
kH, N2O   (mol/L) / atm   2.40E-02

Steady state gas phase concentrations:

Conc, CO2   ppmv        50,000
Conc, CO   ppmv        658
Conc, NO   ppmv        20,756
Conc, NO2   ppmv          8,813
Conc, N2O   ppmv          493
Conc, N2   ppmv          726,231
Conc. O2   ppmv          193,049

In running the calculation, I get 246 SCF in gas and 163 SCF in liquid. Considering the pressure of the system, these comes to 123 ACF in gas and 81.5 ACF in liquid, which equates to 610 gal in the liquid phase.

IF the liquid level did rise 610 gal due to liquid phase reactions, then my new volume is 10,610 gal, with 390 gal of headspace. It would take some iteration, but approximately the system is now at 10,610 gal liq and 390 gal gas (the increase in liquid volume increases the volume of gas dissolved in solution, further adding to the liquid volume, but this is neglected).

Questions:
1. How valid is Henry's law assumption here? The liquid phase is not water - but sludge is often modeled as water. But what affect would a pH = 2 have on Henry's law?
2. Is my methodology correct for estimating the volume of gas in this system?

[Enthalpy]

Yes, dissolved gases use to increase the volume of the liquid. The resulting volume resembles vaguely the sum of the solvent's volume and the gas' volume if it were liquified - just like the volume of a mix of liquids often resembles the sum of the volumes. There are exceptions: typically the gases that are extremely soluble and produce much heat, like ammonia in water. Then the resulting volume may be smaller than expected, resembling more the initial solvent volume.