Finding Percent of Water & Oil in a Mixture from Surface Tension

In summary: In short, you would calculate ##G_{mix}^{ideal} = g_ax_a + g_bx_b## and then use the ideal gas law to calculate ##\frac{P}{T}## and ##\frac{V}{n}##.
  • #1
sagigever
25
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I was looking for on the internet for a while without a success.
If I know that the surface tension of pure oil is ##\gamma_o=A## and I know that the surface tension of pure water is ##\gamma_w=B##
so if I have a mixture of water and oil with surface tension ##\gamma_m=C## am I able to know the percent of water and oil in the mixture? if yes how? where the derivation is come from?
 
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  • #2
Water and oil don't mix at standard temperature and pressure so you don't have a mixture of water and oil, but the oil simply sits on top of the water. Are you asking about the surface tension between oil and water?
 
  • #3
You might find The surface tension of binary liquid mixtures an interesting read. However, what you are dealing with is an emulsion, not a mixture. "Pure Oil" is a mixture (of hydrocarbons) already...and the surface tension (of an emulsion with water) will strongly depend on the chemical composition of the oil and, even in case this should be relatively constant, the physical properties (droplet size, temperature) of the emulsion.
Still, the answer to your question is "Yes". In practice you would measure the surface tension of emulsions with known oil content within the concentration range you are interested in - and use these as "standards" to measure your unknown emulsion against.
 
  • #5
I think I wasn't clear enough with my question, I will give a numeric example:
Lets assume I am doing an experiment of measuring surface tension, I have some
alcohol liquid and I measure ##\gamma_m = 37 \frac{dyne}{cm}## but I know that the surface tension of pure alchohol is ##\gamma_a = 22 \frac{dyne}{cm}## and on the other hand surface tension of pure water is ##\gamma_w = 72 \frac{dyne}{cm}## so it easy to conclude that I have mixture of water and alchohol, now I am asking how can I know the percent of alchohol and water in the mixture
 
  • #6
Well I think it depends whether you are dealing with an ideal solution or not. In an ideal solution the interactions between molecules of specie A and molecules of specie B are the same (i.e. the energy of those interactions is ##E_{AA} = E_{BB} = E_{AB}##). In that simple case thermodynamic quantities should be a simple a weighted sum of the ones referred to ##A## and ##B##. For example, ##G_{mix}^{ideal} = g_ax_a + g_bx_b## (##G## is the gibss free energy). Now ##\gamma = \frac {\partial G}{\partial A}_{T, P}##. On the other hand, if the solution is not ideal, then the interactions between A and B are generally different from each other, so you have to take that into account. In that case ##\gamma = \frac {\partial G}{\partial A}_{T, P}## still holds, but there is not a simple way to calculate ##G## of the mixture.

Unfortunately I don't think ethanol-water could be approximated as an ideal mixture, but I might be wrong. I think the only way is to measure it or find some sort of empirical correlation between ##\gamma## and the molar fraction of ethanol in water.

PS: To be very clear, when I wrote ##G_{mix}^{ideal} = g_ax_a + g_bx_b## for an ideal mixture, it is important to stress that ## g_a## and ## g_b## are defined as ##g_i = g^{pure}_i(T, P) + RT \log(x_i)##. https://en.wikipedia.org/wiki/Ideal_solution
 
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  • #7
We didn't learned those equation u mentioned so I guess there is another and simplier way for the problem I mentioned
 

FAQ: Finding Percent of Water & Oil in a Mixture from Surface Tension

1. How do you determine the percent of water and oil in a mixture using surface tension?

To determine the percent of water and oil in a mixture using surface tension, you will need to perform a test called the drop count method. This involves dropping a known volume of the mixture onto the surface of water and counting the number of drops it takes for the mixture to spread out to a certain diameter. The number of drops will correspond to the percent of water in the mixture.

2. What is the relationship between surface tension and the percent of water and oil in a mixture?

The surface tension of a liquid is directly related to its composition, specifically the presence of water and oil. Water has a higher surface tension than oil, so a mixture with a higher percent of water will have a higher surface tension than a mixture with a higher percent of oil.

3. Can surface tension be used to determine the exact percent of water and oil in a mixture?

No, surface tension can only be used to determine the approximate percent of water and oil in a mixture. Other factors such as temperature, impurities, and surfactants can also affect surface tension, so it is not a precise method for determining composition.

4. Are there any limitations to using surface tension for determining the percent of water and oil in a mixture?

Yes, there are some limitations to using surface tension. As mentioned before, other factors can affect the surface tension, so the results may not be completely accurate. Additionally, this method is only suitable for mixtures with water and oil as the main components, and may not work for more complex mixtures.

5. How can the results of the drop count method be used to calculate the percent of water and oil in a mixture?

The number of drops it takes for the mixture to spread out to a certain diameter can be used to calculate the percent of water in the mixture. This is done by using a conversion factor, which takes into account the volume of the drops and the diameter they spread out to. The percent of oil can then be calculated by subtracting the percent of water from 100.

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