# Total pressure in a chamber calculation

I have a chamber containing two different gases and a liquid which needs to be heated at a certain temperature to bring it to vapor state. I have worked out that we can calculate the total pressure of a mixture of gas using Dalton's law using partial pressure of each gas. To calculate total vapor pressure we have Raoult's law. If I have both gases and vapors in the medium can we calculate the total pressure by adding them both, as in a "collecting gases over water experiment"?

• Okay, let me put it this way. If I know the partial pressure of 2 gases and vapor pressure of liquid turned vapor, can I directly add them to get total pressure in the chamber? – NidhiS Sep 9 '15 at 10:53
• This not my homework question. I am an electronics engineer working on an interdisciplinary project wherein I need some information on mixture of gases. I have worked out that we can calculate the total pressure of a mixture of gas using Dalton's law using partial pressure of each gas. To calculate total vapor pressure we have Raoult's law. If I have both gases and vapors in the medium I think we can calculate the total pressure by adding the both like 'collecting gases over water experiment'. I read these things long ago so I wanted to confirm it. – NidhiS Sep 9 '15 at 11:15
• Thank you for the clarification, could you please add this detail to the question – user15489 Sep 9 '15 at 11:17

Dalton's Law is only true for ideal compounds, which theoretically have no intermolecular forces between their molecules. Those forces become more and more significant when increasing the concentration of any compound, because all molecules become packed up closer.

This will lower the pressure, because if any molecule is about to hit the container wall, it gets pulled backwards $-$ and thus slowed $-$ due to the attraction of the other molecules behind it. But for high temperature this effect is negligible, because they can't be slowed down so easily.

Now lets come to the calculation using Kay's rule:

Since you only have one liquid component, you don't need Roult's Law to calculate the vapor pressure for a mixture of liquids.

1.) You need to find the values for the critical temperatures and critical pressures for your components (gases and water vapor).

2.) You need to know the relative amounts of each substance: $$y_i = \frac{n_i}{n_m}$$

$n_i$... amount of a specific component [mol]

$n_m$... total amount of substance of the mixture [mol]

3.) Calculate the pseudo-critical temperature and pressure: $$T_c' = y_1 \times T_{c1} + y_2 \times T_{c2} + y_3 \times T_{c3}$$

$$P_c' = y_1\times P_{c1} +y_2\times P_{c2} +y_3\times P_{c3}$$

$T_c$... critical temperature of a specific component [K]

$P_c$... critical pressure of a specific component [Pa]

4.) calculate the pseudo-reduced values for T and the volume: $$T_r = T / T_c'$$ $$v_r' = V / (R \times T_c' / P_c')$$

$T$... temperature in the container

$V$... volume of the gas phase [m$^3$]

$R$... universal gas constant = 8.314 J/(K mol)

5.) Now you need to look up $v_r$ and $T_r$ in a compressibility chart to get the value for a specific $Z$ factor, where their lines intersect.

6.) And finally calculate the pressure: $$P = ZRT / V$$

This will be more accurate than if you would use the standard way for ideal gases, especially for low temperatures

References: real gases

calculation

compressibility chart examples