Miller Research Group - Partial Molar Volumes

Partial Molar Volumes And Density

What is the partial molar volume? Why do we care? How can we estimate the partial molar volume using ONLY skills from General Chemistry?

A binary solution is a solution made up of two different types of molecules. Ethanol and water form a binary solution. Water and NaCl form a binary solution.

When 50.00 mL of ethanol (CH3CH2OH) is mixed with 50.0 mL of water (H2O), the total volume of the solution is NOT 100.00 mL. It is 96.40 mL. Broadly, this can be attributed to interactions such as hydrogen bonding between the ethanol molecules and the water molecules that allows the mixture to pack the molecules into a smaller volume than the separate pure liquids. It is actually much more complicated than this, but the idea is correct.

If the volume were exactly 100.00 mL, then the solution would be an ideal solution. For ideal solutions, the volumes that you add together perfectly: 50.00 mL + 50.00 mL = 100.00 mL.

For nonideal solutions, the volumes do not add together perfectly. Ethanol/water solutions are nonideal. 2-propanol/water solutions are also nonideal. It is solutions of 2-propanol/water that we will be working with in our experients, but for now let’s talk about ethanol/water solutions.

The molar volume is the volume of one mole of something. Gases, liquids, solids, and solutions all have molar volumes.

A pure substance has a molar volume. For example, pure water has a molar volume of 18 mL/mol. The molar volume of ethanol is 58.4 mL/mol. A solution has a molar volume that can be determined by taking the total volume and dividing it by the total number of moles of solution. If you plot the molar volume (Vm) of an ethanol/water solution versus the mole fraction of ethanol (xEtOH), the graph will look something like this,

with Vm,H2O being the molar volume of the pure water, and Vm,EtOH being the molar volume of the pure ethanol. At every mole fraction of the solution, the molar volume is lower than the ideal molar volume (a straight line between the two end points). As we’ve mentioned before, the ethanol/water system is nonideal.

The partial molar volume of water, m,H2O, is the molar volume of water in the solution. It is a function of the mole fraction of ethanol (or water) in the solution. It can be found (I’m not proving this right now – I’m just telling you that it works. We can talk more about this later if you’d like.) from the following graph by drawing a tangent to the curve at a particular xEtOH and extending that tangent to the axes. Notice that since the partial molar volumes of the water and the ethanol are lower than the molar volumes of the pure water and the pure ethanol.

The partial molar volume of water, m,EtOH, is the molar volume of the ethanol in the mixture and can be found the same way.

If the ethanol/water solutions have a smaller volume, then they have a higher density. Smaller molar volume = higher density.

Please watch the following videos about these subjects. For these videos, we will be working with a different but similar system: 2-propanol/water.

1. 1. An Introductory Video for Partial Molar Volumes:
    
    https://www.youtube.com/watch?v=lRvi3AHTHE8

This video goes into more depth than we need, but it does show how partial molar volumes fits into the bigger picture of chemistry, specifically Physical Chemistry, a junior level undergraduate course.

1. 1. How to take data for the mass of 2-propanol and water in a 25.00 mL volumetric flask and turn it into mol fraction of 2-porpanol and solution density:

https://youtu.be/q2T7MQmaxVQ