Find molarity, seemingly simple but I can't do it.

[bublik13]

Homework Statement

Lauryl alcohol, C12H25OH, is prepared from coconut oil; it is used to make sodium lauryl sulfate, a synthetic detergent. What is the molarity of lauryl alcohol in a solution of 17.1g lauryl alcohol dissolved in 148g ethanol, C2H5OH?

a) 0.310m b) 0.620m c) 0.842m d) 1.41m e) 2.52m

Note: I'm not sure, but I think that the internet is allowed for this problem, in the sense that we can look up the densities of both the lauryl alcohol and the ethanol, because I see no way to solve this problem otherwise. (I can't solve it with the densities anyway)

Homework Equations

n=m/M
d=m/v

The Attempt at a Solution

1) There is 17.1g of C12H25OH
molar mass of C12H25OH is 186.18g/mol
number of moles of C12H25OH is 0.09185mol

2) There is 148g of C2H5OH
molar mass of C2H5OH is 46.08g/mol
number of moles of C2H5OH is 3.2118mol

3) The density, or (m/v) of C12H25OH is 0.8309g/mL (I used the internet for this step and the following)

4) The density, or (m/v) of C2H5OH is 0.789g/mL

5) This is where I start to feel unsure.
17.1g/v=0.8309g/mL
v(C12H25OH)= 0.0206L

6) 148g/v=0.789g/mL
v(C2H5OH)=0.1876L

7) total volume = 0.0206L + 0.1876L = 0.2082L

8) 0.09185mol/0.2082L = 0.4412m, which does not correspond with any of the answers.

 

[Borek]

I don't see how to solve the problem more precisely, unless someone will find a table of densities of lauryl alcohol in ethanol solutions (don't waste your time trying too hard).

The only thing that is wrong is that you assumed final volume to be sum of both volumes - it will be not, as volumes are not additive*, BUT - for a given data, that's the best reasonable guess of what the final volume is. Check if ignoring volume of lauryl alcohol (that is, assuming final volume is that of ethanol - 187.6 mL) won't result in one of the given answers. If it does - that's what you were expected to do, sadly, that's not the correct approach. Alternatively, you can check if you will not get one of the answers given assuming total mass of 17.1+148 and density of pure ethanol - again, that won't give a correct answer in general, but it is one of the approximations used in such cases.

* If you combine two volumes of identical solution, volumes are additive - say, 50 mL of 1 M NaCl and 50 mL of 1 M NaCl gives 100 mL of 1 M NaCl. But when you mix different solutions or different substances, it won't work this way - 50 mL of water and 50 mL of ethanol yield 96.4 mL of a mixture. Differences are rarely large, but they do exist.

What you can be always sure about is that the final mass is the sum of both masses.

 

[bublik13]

Borek - I appreciate your attempt to help, but I however made a mistake in reading the question.

Turns out "molality" was not a typo for "molarity" and the two mean different things.

My bad.

 

[Borek]

If it is about molality it is just plug and chug.