Various Pressures in mass transfer

[Rahulx084]

I'm confused between partial pressure, total pressure, boiling point , vapour pressure , saturation pressure and saturation temperature.These things haunt me in my subject mass transfer. I get really confused when this words come in a liquid - vapour system, I cannot identify what these pressure stands for in a liquid -vapour system. Like liq-vapour equilibrium and sometimes saturated vapour and liquid as well . Please someone help me with these terminology.

 

[Chestermiller]

First you. Please tell us your understanding of these terms so that we can better help you.

 

[Rahulx084]

First you. Please tell us your understanding of these terms so that we can better help you.

Okay sir
These are my understandings
Partial pressure : It is the pressure of a single component in a mixture of components in gas phase .
Vapour pressure : pressure applied by single component in a mixture of gas on its condensate .
Boiling point : when vapour pressure = atmospheric pressure.
I have no understanding of saturation pressure,temperature and concentration.
And I'm more confused when these terms are in a mixture and in liquor -vapour phase .

 

[Chestermiller]

Okay sir
These are my understandings
Partial pressure : It is the pressure of a single component in a mixture of components in gas phase .
Vapour pressure : pressure applied by single component in a mixture of gas on its condensate .

In a single component system, the equilibrium vapor pressure is the pressure of the pure vapor in equilibrium with the pure liquid at the same temperature. This is sometimes referred to simply as the vapor pressure or the saturation vapor pressure. In the case of a gas mixture involving a non-condensible component such as air, at equilibrium, the partial pressure of the condensible component is equal to its equilibrium vapor pressure at the system temperature. The pressure in the condensate is equal to the partial pressure of non-condensible component plus condensible vapor. The total pressure in the vapor phase is equal to the equilibrium vapor pressure of the condensible component plus the partial pressure of the non-condensible component. So the total pressure is the same for both the gas phase and the liquid phase.

Boiling point : when vapour pressure = atmospheric pressure.
I have no understanding of saturation pressure,temperature and concentration.

Saturation pressure is the same as equilibrium vapor pressure at the temperature of the system. Saturation temperature is the temperature at which the partial pressure of the vapor in the gas phase (for a mixture) would be equal to the equilibrium vapor pressure. This is also called the dew point, and would represent the temperature at which liquid would start condensing out of the gas phase.

Until I can get some more feedback from you, these are the answers I would give.

 

[Rahulx084]

In a single component system, the equilibrium vapor pressure is the pressure of the pure vapor in equilibrium with the pure liquid at the same temperature. This is sometimes referred to simply as the vapor pressure or the saturation vapor pressure. In the case of a gas mixture involving a non-condensible component such as air, at equilibrium, the partial pressure of the condensible component is equal to its equilibrium vapor pressure at the system temperature. The pressure in the condensate is equal to the partial pressure of non-condensible component plus condensible vapor. The total pressure in the vapor phase is equal to the equilibrium vapor pressure of the condensible component plus the partial pressure of the non-condensible component. So the total pressure is the same for both the gas phase and the liquid phase.

Saturation pressure is the same as equilibrium vapor pressure at the temperature of the system. Saturation temperature is the temperature at which the partial pressure of the vapor in the gas phase (for a mixture) would be equal to the equilibrium vapor pressure. This is also called the dew point, and would represent the temperature at which liquid would start condensing out of the gas phase.

Until I can get some more feedback from you, these are the answers I would give.

Here you told sir that there would be a condensate and one component like air which is not condensible . Sir how would we define these terms when there is partial vaporisation such as an ethanol-water system In which we will have these both components in gas as well as liquid phase.

 

[Chestermiller]

Are you familiar with Raolt's law for ideal liquid solutions?

 

[Rahulx084]

Are you familiar with Raolt's law for ideal liquid solutions?

Yes sir , its says that the vapour pressure = partial pressure time mole fraction
Sir but how would the things will be defined in this system, like saturation pressure ,vapour pressure and all that you made me understand few texts back .

 

[Chestermiller]

Yes sir , its says that the vapour pressure = partial pressure time mole fraction

Not only is this not Raolt's law, it is not even correct as it stands. Now, please look up Raoult's law for a liquid solution, and state it properly. If you are going to understand vapor-liquid equilibrium of multi-component systems, you need to first understand Raolt's law.

 

[Rahulx084]

Not only is this not Raolt's law, it is not even correct as it stands. Now, please look up Raoult's law for a liquid solution, and state it properly. If you are going to understand vapor-liquid equilibrium of multi-component systems, you need to first understand Raolt's law.

Firstly sir thank you so much for putting efforts to make me understand these things , I'm really really very much thankful to you and this community to help students like me . Now sir , According to my knowledge Till yet
Roults law states that the equilibrium partial pressure of species i in the gas phase is directly proportional to the mole fraction of that species in the liquid phase . And the proportional constant is the vapour pressure of the pure component of that species i at the same temperature.

 

[Rahulx084]

Sir what to do next after knowing the roults law?

 

[Chestermiller]

If you have a liquid and vapor phase in equilibrium, and two components, please write out all the relationships you know of that describe such a system (for an ideal gas and an ideal liquid solution).

 

[Rahulx084]

If you have a liquid and vapor phase in equilibrium, and two components, please write out all the relationships you know of that describe such a system (for an ideal gas and an ideal liquid solution).

 

[Rahulx084]

 

[Chestermiller]

OK. Here's my take on this. Please let me know if you agree.

$$x_A+x_B=1$$
$$y_A+y_B=1$$
$$p_A=P^*_A(T)x_A$$
$$p_B=P^*_B(T)x_B$$
$$p_A=p_{total}y_A$$
$$p_B=p_{total}y_B$$
$$p_A+p_B=p_{total}(y_A+y_B)=p_{total}=P^*_A(T)x_A+P^*_B(T)x_B$$
$$p_{total}y_A=P^*_A(T)x_A$$
$$p_{total}y_B=P^*_B(T)x_B$$

 

[Rahulx084]

OK. Here's my take on this. Please let me know if you agree.

$$x_A+x_B=1$$
$$y_A+y_B=1$$
$$p_A=P^*_A(T)x_A$$
$$p_B=P^*_B(T)x_B$$
$$p_A=p_{total}y_A$$
$$p_B=p_{total}y_B$$
$$p_A+p_B=p_{total}(y_A+y_B)=p_{total}=P^*_A(T)x_A+P^*_B(T)x_B$$
$$p_{total}y_A=P^*_A(T)x_A$$
$$p_{total}y_B=P^*_B(T)x_B$$

What does small p ans capital P represents?

 

[Chestermiller]

P• represents equilibrium vapor pressure of the pure component at temperature T and p represents partial pressure.

 

[Rahulx084]

OK. Here's my take on this. Please let me know if you agree.

$$x_A+x_B=1$$
$$y_A+y_B=1$$
$$p_A=P^*_A(T)x_A$$
$$p_B=P^*_B(T)x_B$$
$$p_A=p_{total}y_A$$
$$p_B=p_{total}y_B$$
$$p_A+p_B=p_{total}(y_A+y_B)=p_{total}=P^*_A(T)x_A+P^*_B(T)x_B$$
$$p_{total}y_A=P^*_A(T)x_A$$
$$p_{total}y_B=P^*_B(T)x_B$$

Got it now sir thank you .
One last thing , vapour pressure = saturation pressure right?

 

[Chestermiller]

Got it now sir thank you .
One last thing , vapour pressure = saturation pressure right?

Only if you have both liquid and vapor present at equilibrium.

Here is a problem to test your understanding. Suppose you have a gas phase at a total pressure of $p_{total}$, and with component mole fractions of $y_A$ and $y_B$. There is no liquid present, and the temperature is higher than that necessary for a liquid phase to form. To what temperature $T_c$ would you have to cool this gas phase (at the same total pressure) for liquid to begin condensing out.? What would be the mole fractions of the two species in the first liquid that forms?

 

[Rahulx084]

Only if you have both liquid and vapor present at equilibrium.

Here is a problem to test your understanding. Suppose you have a gas phase at a total pressure of $p_{total}$, and with component mole fractions of $y_A$ and $y_B$. There is no liquid present, and the temperature is higher than that necessary for a liquid phase to form. To what temperature $T_c$ would you have to cool this gas phase (at the same total pressure) for liquid to begin condensing out.? What would be the mole fractions of the two species in the first liquid that forms?

The temp at which the vapour pressure of the gas will be equal to its saturation pressure ,the liquid will start condensing .The composition will be same in liquid condensate as in the gas phase

 

[Chestermiller]

The temp at which the vapour pressure of the gas will be equal to its saturation pressure ,the liquid will start condensing .The composition will be same in liquid condensate as in the gas phase

This is not correct. The composition will not be the same. More of one species will begin condensing out than the other. Using the equations I listed in post #14, derive an equation for determining the temperature at which condensation begins.

 

[Chestermiller]

At the temperature where the first drop of liquid forms, the mole fractions of the two species in the drop are: $$x_A=\frac{p_{total}y_A}{P^*_A(T)}$$and $$x_B=\frac{p_{total}y_B}{P^*_B(T)}$$. If you guess the wrong temperature T, the sum of the mole fractions in the liquid won't add up to 1.0. So, to find the temperature at which the gas mixture starts condensing (and to find the mole fractions in the liquid at that temperature), you need to solve the following equation for T:$$\frac{p_{total}y_A}{P^*_A(T)}+\frac{p_{total}y_B}{P^*_B(T)}=1$$

 

[Rahulx084]

[QUO

At the temperature where the first drop of liquid forms, the mole fractions of the two species in the drop are: $$x_A=\frac{p_{total}y_A}{P^*_A(T)}$$and $$x_B=\frac{p_{total}y_B}{P^*_B(T)}$$. If you guess the wrong temperature T, the sum of the mole fractions in the liquid won't add up to 1.0. So, to find the temperature at which the gas mixture starts condensing (and to find the mole fractions in the liquid at that temperature), you need to solve the following equation for T:$$\frac{p_{total}y_A}{P^*_A(T)}+\frac{p_{total}y_B}{P^*_B(T)}=1$$

Woah sir , I didn't thought this way . Sir one more query, where we can use the ideal gas equation? Can we apply it on the vapour phase that's is in the equilibrium with the condensate? And can we apply ideal gas equation in a gas mixture like this?
Lets say we have a gas mixture A and B , partial pressure of A is $p_a$ and partial pressure of B is $p_b$ , can we write it like this
$$p_a V=n_a RT$$ and similar for B .
Sir these 2 are last one for this concept.
Thank you soo much sir

 

[Chestermiller]

[QUO

Woah sir , I didn't thought this way . Sir one more query, where we can use the ideal gas equation? Can we apply it on the vapour phase that's is in the equilibrium with the condensate? And can we apply ideal gas equation in a gas mixture like this?
Lets say we have a gas mixture A and B , partial pressure of A is $p_a$ and partial pressure of B is $p_b$ , can we write it like this
$$p_a V=n_a RT$$ and similar for B .
Sir these 2 are last one for this concept.
Thank you soo much sir

Raoult's Law is based on an ideal gas mixture and an ideal liquid solution. We know it's an ideal gas mixture because we are using partial pressures to describe the equilibrium.