Chem Eng stuff: Equilibrium diagrams from gas component solubility data

- Fractions of a gas component in the mixture and liquid phase, at equilibrium -

$p_t$ $T$ .

$x$ $y$ , for either constant pressure or constant temperature.

$p_t$ $T$ . Let us consider each case in turn but first some explanation of the variables in the solubility data is needed.

How the solubility data is obtained

Go to the top

You need to know how soluble a gas component is in a given liquid. Two parameters will modify the solubility of this gas component: pressure and temperature.

Fig. 01 Idealization of solubility meausurements.

In an experimental setup for this purpose, both pressure and temperature need to be mesarured. A fix coposition of the gas mixture will produce certain pressure and temperature changes and these changes will keep constant once the equilibrium in the system is achieved. This equilibrium is reached when molecules of soluble gas components in the gas mixture and in the liquid do not travel back and forth.

Next, if the composition of the gas mixture is changed, another set of pressure and temperature will be reached at equilibrium, providing in this way data on the solubility of a given gas component. Of course, the composition of the gas mixture is presented as the concentration of the soluble gas component.

One detail is worth to mentioned here. The pressure recorded at the manometer (as shown in the sketch above) corresponds to the total pressure of the gas. However, another pressure contribution needs to be introduced: the partial pressure. Every gas component in the gas mixture (say A, B, C, etc.) will exert a pressure contribution to the total pressure so that,

$p_t=p_A+p_B+p_C+\ldots$ Eq. (01)

$p_A$ $p_B$ $p_C$ $x_A$ $x_B$ $x_C$ , etc. as follows,

$x_A=\dfrac{p_A}{p_t},\,\, x_B=\dfrac{p_B}{p_t},\,\, x_C=\dfrac{p_C}{p_t},\,\, etc.$ Eq. (02)

$p_A$ $p_t$ $p_t$ in the manometer.

What about equilibrium? Well, concentration gradients and rate of diffusion are indicative that the system is out of equilibrium. So, for equilibrium to be reached, all gradients must fall to zero. The equilibrium reached is one called dynamic equilibrium because there is time dependency or in other words: the soluble gas component molecules do not cease to move back and forth between the gas mixture and the liquid. In this dynamic equilibrium, the rate at which soluble gas component molecules enter the liquid are the same at wich some other molecules of this component leaves the liquid to the gas mixture.

Some principles are common to systems like this:

at a fixed set of pressure and temperature conditiions there exist a set of relationships for equilibrium,
in a system in equilibrium, the net diffusion of components across the interface is zero,
if the system is not in equilibrium the diffusion of components across the inteface will bring it to a condition of equilibrium.

Equilibrium diagrams for constant pressure

Go to the top

$A$ .

$x$ $y$ in the liquid phase and gas mixture, respectively, need to be calculated. Since the concentration of the gas component in the liquid phase is given in the solubility data as,

$\dfrac{m_{gc}}{m_{lp}}=\dfrac{mass\, of \, gas\, component}{mass\, of\, liquid\, phase}$ Eq. (03)

$x$ can be calculated by using the following relationship,

$x=\dfrac{m_{gc}/M_{gc}}{m_{gc}/M_{gc}+m_{lp}/M_{lp}}$ Eq. (04)

$M$ $m$ $gc$ $lp$ $y$ in the gas mixture, the relationship of this with the partial pressure can be used. This is,

$p_{gc}=p_t\,y$ Eq. (05)

$p_{gc}$ $p_t$ is the total pressure. You should recall that Eq. (05) makes sense only if the gas mixture behaves as an ideal gas (which is a rough approximation).

$p_t$ $y$ $x$ can be given from the solubility data.

Fig. 02 Equilibrium diagram of

$y$ vs

$x$ for constant pressure.

Equilibrium diagrams for constant temperature

Go to the top

A similar plot to that sketch in Fig. 02 can also be built for constant temperature and varying pressure.

Fig. 03 Equilibrium diagram of

$y$ vs

$x$ for constant temperature.

The most significant change is the effect of increasing temperature and pressure. The process to follow is just the same as in the prevous section and sample solubillity data is presented in the post: Gas absorption: General commments.

This is the end of the post. I hope you find it useful.

Any question? Write in the comments and I shall try to help.

Other stuff of interest

==========
Ildebrando.

Chem Eng stuff

ChemEng stuff followers

Equilibrium diagrams from gas component solubility data

- Fractions of a gas component in the mixture and liquid phase, at equilibrium -

How the solubility data is obtained

Equilibrium diagrams for constant pressure

Equilibrium diagrams for constant temperature

Other stuff of interest

No comments:

Post a Comment

Most popular posts

Get new posts by email:

Total Pageviews

Report Abuse

See our posts topics