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.

 

[DeeNos]

First of all, it is perfectly normal to feel unsure or struggle with a problem in science. It is a complex and ever-evolving field, and it is okay to not have all the answers right away. As a scientist, it is important to keep trying and learning from your mistakes.

Now, let's take a look at the problem at hand. Finding molarity can be a bit tricky, but it is a very useful tool in chemistry. Molarity is defined as moles of solute per liter of solution. In this case, the solute is lauryl alcohol (C12H25OH) and the solvent is ethanol (C2H5OH).

To find the molarity, we need to first calculate the number of moles of lauryl alcohol and ethanol. From your attempt, we can see that you have correctly calculated the number of moles for each substance. So, we have 0.09185 moles of lauryl alcohol and 3.2118 moles of ethanol.

Next, we need to calculate the total volume of the solution. This is where the densities of the substances come into play. We can use the formula d=m/v to find the volume of each substance. For lauryl alcohol, we have 17.1g and a density of 0.8309 g/mL. So, the volume of lauryl alcohol is 17.1g / 0.8309 g/mL = 20.6 mL. Similarly, for ethanol, we have 148g and a density of 0.789 g/mL. So, the volume of ethanol is 148g / 0.789 g/mL = 187.6 mL.

Now, we need to convert the volumes to liters, since molarity is in moles per liter. This can be done by dividing the volumes by 1000. So, the volume of lauryl alcohol is 0.0206 L and the volume of ethanol is 0.1876 L.

Finally, we can calculate the molarity by dividing the number of moles by the total volume. So, the molarity of lauryl alcohol is 0.09185 moles / 0.2082 L = 0.441 m. This corresponds to answer a) 0.310m, so it seems like there was a mistake in your final calculation.

In conclusion, finding molarity involves calculating the