# Raoult’s Law

##### Getting started with the ABIH practice questions.

The American Board of Industrial Hygiene (ABIH) provides a set of practice questions to give examinees an idea of what to expect for questions in the Certified Industrial Hygienist (CIH) exam.  In fact, the first practice question may prove difficult since it requires determining the concentration of benzene in air for a given mixture of liquids. Raoult’s Law can be used by industrial hygienists to help estimate a potential ‘worst case scenario’ for a spilled liquid or a contained mixture of liquids with the caveat that many mixtures will not demonstrate ‘ideal’ properties.

### Raoult’s Law

Raoult’s Law is given by the following equation, which is also provided under the heading of General Sciences, Statistics and Standards on the ABIH Equation Sheet: X refers to the molar fraction of the compound of interest and P refers to the vapour pressure of that compound.

Want to run through an example to make sure you understand how to work with the values? Let’s check out the ABIH practice question, shown below:

Question 1: A mixture contains:

50 mL benzene (m.w.=78) v.p. = 75 mm, Hg sp. gr. = 0.879.
25 mL carbon tetrachloride (m.w. = 154), v.p. = 91 mm, Hg sp. gr. = 1.595
25 mL trichloroethylene (m.w. = 131.5), v.p. = 58 mm, Hg sp. gr. = 1.455.

Assuming Raoult’s Law is obeyed, what will be the concentration of benzene in air at 760 mm Hg saturated with vapor of the above mixture?

a. 3.5%
b. 4.5%
c. 5.1%
d. 9.9%

### Solution

In this case, since the question asks you to determine the concentration of benzene in air, we’ll need to calculate the partial pressure of benzene for the mixture with the following equation:

Pv = Xbenzene×Pbenzene

where Xbenzene= # moles benzene/total #moles of solution and Pbenzene = 75 mm Hg

• # moles benzene = volume × specific gravity / molecular weight = (50 mL)(0.879)/(78) = 0.563 moles
• Repeat the same step to calculate the number of moles for carbon tetrachloride (0.259 moles) and for trichloroethylene (0.277 moles). Sum them together to get the total number of moles for the solution (1.099 moles).
• The value of Xbenzene is then given by (0.563)/(1.099) = 0.512 (i.e. the molar fraction of benzene for the given solution).
• Multiplying the molar fraction of benzene by the vapour pressure of benzene gives the vapour pressure for benzene given this mixture: Pv = (0.512)(75) = 38.4 mm Hg.

You can then calculate the concentration of benzene with the formula shown on the ABIH equation sheet as

ppm = (Pv)/(Patm) × 106 or in this case % = (Pv)/(Patm) × 100

% = (38.4)/(760) x 100 = 5.1%

### Further Understanding

Need to see some more examples to solidify your grasp of the concepts? Check out this page on the UCDavis chemwiki which provides more explanation of the Raoult’s Law concepts.  The books below will also prove to be excellent resources to help your understanding and to stand as references should you need to refer back in the future.

July 18, 2015

### 1 Responses on Raoult's Law"

1. Albert Condello says:

Excellent job of explaining, thank you Ben.

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