# Saturation Temperature of Binary Mixture

I have a binary mixture of water and methane. The system is at 2000kPa and I am trying to find the saturation temperature of the water in the mixture.

I know Tsat is a function of partial pressure, but cant find a formula. I do not know the ratio of water to methane in the system.

I do know that the system is currently at 100C. If I assumed that 100C is the Tsat for the water, is there a way to calculate the ratio of water to methane?

• From Fundamentals of Classical Thermodynamics, I have the saturation temperature for water at 2,000 kPa as 212$^{\circ}$C. That could make a difference from your assumption of 100$^{\circ}$C. – Carlton Oct 21 '15 at 16:07
• So would I be right in saying that the partial pressure of water in the system woud be 100kPa. Therefore the system would be 5% water? – quanticks Oct 21 '15 at 19:15
• You really need to know the relative amounts of each component to calculate partial pressure. – Carlton Oct 21 '15 at 19:29

## 2 Answers

For the ratio of methane and water use henry's law: From NIST site: constant for methane 0.0014 mol/kg bar at 298K. At 2000 kpa = 20 bar, Concentration in water is 0.028 mol/kg at 298 K. At your temp of 373K, you should use the temperature correction equation to get the correct constant. This equation is on the same NIST page for methane.

For the question of the influence on boiling point: It sounds like you are thinking of the Clausius-Clapeyron equation to estimate boiling point from vapor pressure and heat of vaporization.

My opinion is that a better thermodynamic answer would be to say that there would simply be less dissolved methane at the boiling point of water at 2 mPa and 485 K. So, like the other comments said, the saturation point is assumed as 212 degC with less dissolved gas than at 100 degC.

Water is a compressed liquid at 2000 kPa and 100C, and the methane is well above it's critical temperature, so it's essentially all gas. From this, I would think that the liquid phase is almost entirely water, and the gas phase is almost entirely methane. So, the presence of methane probably has very little effect on the saturation temperature of the water. Tsat for the water is probably close to what it would be for pure water, 212C at 2000 kPa.

My source for water saturation temperature is TLV, and source for methane properties is Engineering Toolbox.

• Could you explain why the methane would have very little impact on theTsat of water? – quanticks Oct 22 '15 at 16:32
• The reason is that there's not much mixing between the water and methane. The properties of a mixture are dependent on the various species in the mixture, but in your case it looks like you have a liquid phase that's all water and a gas phase that's all methane. So, there's not much of a mixture, it's just two separate species. – Carlton Oct 22 '15 at 20:45