11 replies to this topic

[p_stark95]

In gaseous mixtures fugacity measures the deviation from ideality of the gas. In a vapor liquid equilibrium it is stated that the fugacity of a component should be same in both vapor and liquid phase for attainment of equilibrium. How is fugacity described or defined for liquid phase?

Edited by p_stark95, 20 April 2016 - 12:00 AM.

[breizh]

Hi ,

let you try to get a copy of : The properties of gases and liquids by Pauling,Prausnitz and O'connell .

 

Google should help you

 

Good luck

 

Breizh

[MrShorty]

How is fugacity described or defined for liquid phase?

Exactly the same as it is for gases, really. "Ideal gas" is still the "reference" for fugacity of liquids, and we mostly use the same equations of state to describe gases and liquids.

 

In gaseous mixtures fugacity measures the deviation from ideality of the gas.

As a thought question to get you to consider exactly what you are saying here. Usually, the first measure of "deviation from an ideal gas" that one learns is the compressibility factor Z=PV/(nRT). Z=1 for an ideal gas, and Z<>1 for real gases. When you say that "fugacity measures the deviation from ideality of the gas", exactly what do you mean? How is this similar to and different from the concept of "compressibility" that also measures deviation from ideal gas?

[p_stark95]

@MrShorty the definition of fugacity is that it is equal to the pressure of an ideal gas which has the same chemical potential as the real gas. So since the two pressures will be different, it will be a measure of the deviation. But for liquid solutions no such pressure as in vapour/ gaseous form can be stated, how is fugacity coming into play for liquids?

[breizh]

Hi,

 

additional resource to support your work .

 

https://www.e-educat...520/m16_p6.html

 

 

Hope this helps

 

Breizh

[MrShorty]

But for liquid solutions no such pressure as in vapour/ gaseous form can be stated

Why not?

 

For liquids, I can state that at a temperature T and a Pressure P, the density is rho.

From that information, I can compute a "compressibility factor" Z from Z=P*V/(n*R*T), just the same as I do for gases. And this compressibility factor describes how that liquid deviates from an ideal gas in the same way that it does for gases.

In an analogous way, the same equations that describe fugacity for gases also describe fugacity for liquids. And, if we like, it can still mean the same thing (what is the pressure of an ideal gas that has the same chemical potential as the liquid at T and P).

Perhaps what is confusing is that wondering how can a single quantity like fugacity have the same value in both the liquid phase and the vapor phase? We get so used to thinking of gases and liquids as completely different things (maybe even two different "states of matter"?), that we have a difficult time conceptualizing a quantity that can have the same value in both phases (at equilibrium).

[shantanuk100]

Dear P_Stark95,

 

1. The fugacity of a vapor is nothing but a way of modelling a real gas under ideal gas conditions. A lot of our equations are based on ideal gas assumptions, so the fugacity coefficient is used to relate this.

 

2. The fugacity of a real gas R is the effective partial pressure of that real gas R, if it were an ideal gas I having the same chemical potential (partial molar free energy) as that of the real gas R.

 

3. This means that if we have real gas G with a partial pressure of P1, and have the same gas considering it to be ideal, then the partial pressure of that gas to exhibit the same chemical potential as the real case 1, would be much lower.

 

4. This lower partial pressure of the ideal gas, which gives the same chemical potential as the real gas is called fugacity.

 

5. The ratio of the Partial pressure of the gas existing in the ideal case to the partial pressure of the gas existing in the real case is called the fugacity coefficient, and this fugacity coefficient (not fugacity), is always less than 1, because the partial pressure of an ideal fluid will always be lower than the partial pressure it would take a real fluid, when their chemical potentials are equal.

 

6. Now if we take a liquid that is under stable conditions with its vapor phase, we consider it to be in equilibrium. For a liquid at equilibrium, the pressure exerted by the liquid molecules to escape is the same as the partial pressure exerted by its own vapor phase which is in equilibrium with it.

 

7. So, the fugacity of a pure liquid = fugacity of the vapor phase in eqbm. with the liquid

 

 

Regards,

Shantanu

Edited by shantanuk100, 23 April 2016 - 09:11 AM.

[p_stark95]

@shantanuk100 Your 6th point says "For a liquid at equilibrium, the pressure exerted by the liquid is the same as the partial pressure exerted by its own vapor phase which is in equilibrium with it."

Here when you say "pressure exerted by the liquid", does it mean that by Pascal's law? Is it the hydrostatic pressure?

[p_stark95]

@MrShorty when you say compressibility factor can show deviation of the liquid from ideal gas, do you mean deviation from liquid from ideal liquid?

[MrShorty]

@MrShorty when you say compressibility factor can show deviation of the liquid from ideal gas, do you mean deviation from liquid from ideal liquid?

No, I mean deviation of liquid from ideal gas (I don't know how to describe an ideal liquid in this context).

 

For example, water at 297 K and 1E5 Pa has a specific volume of 1.00 mL/g or 1E-6 m3/(1/18) mole. If I put that into my definition of compressibility

z=1E5*1E-6/(1/18)/8.3145/297 = 7.29E-4. [compared to z(ideal gas)=1]. So, obviously, liquid water is very different from an ideal gas.

[shantanuk100]

@shantanuk100 Your 6th point says "For a liquid at equilibrium, the pressure exerted by the liquid is the same as the partial pressure exerted by its own vapor phase which is in equilibrium with it."

Here when you say "pressure exerted by the liquid", does it mean that by Pascal's law? Is it the hydrostatic pressure?

 

 

p_stark95,

 

1. No, by a liquid pressure I mean, that the tendency of liquid molecules inherent in them to escape is equal to the
 

-- sum of the surrounding ambient pressure + the Vapor pressure of the liquid Vapor that is in equilibrium with the liquid. That is the reason the liquid stays a liquid and doesn't freely escape as a gas (In addition to inherent liquid molecule-molecule cohesional attraction if any).

 

2. You could call it hydrostatic pressure at the top of the liquid surface, but not the hydrostatic pressure of the liquid, which acts inside the bulk fluid.

 

Regards,

Shantanu

Edited by shantanuk100, 23 April 2016 - 09:00 AM.

[shantanuk100]

@MrShorty when you say compressibility factor can show deviation of the liquid from ideal gas, do you mean deviation from liquid from ideal liquid?

 

 

1. There is no compressibility factor as per ideal / real gas law for liquids, because the law is applicable to only gases.

 

2. That is why, we judge the deviation of liquids from ideal nature by checking the deviation of the liquid's own vapor on the surface, that is in equilibrium with the liquid. Since they are in equilibrium, we judge the deviation of the liquid's ideality by the deviation of its vapor.

 

3. Ideal nature here is where cohesive and attractive forces between molecules are ideally governed, and no Van der walls forces exist. For ideal gases, this is the reason they have no intermolecular forces and the reason they occupy maximum volume. Ideal liquids have zero viscous forces for similar reasons.

 

4. That is why the fugacity of a pure liquid is equal to the fugacity of the vapor in equilibrium to it. 

 

Regards.

Shantanu

Edited by shantanuk100, 23 April 2016 - 09:08 AM.