Calculating Volume of Oleic Acid in Mixture Using Dilution Method

[ibysaiyan]

Homework Statement

The question is as following:

5cm3 of oleic acid are mixed with 95 cm3 of methanol. 5 cm3 of this mixture are
then diluted with a further 95cm3 of methanol, achieving an overall dilution of oleic
acid of a factor 400. A method is perfected of creating identical droplets; counting
out 97 such droplets gives a total volume of 1 cm3. What is the volume of oleic acid
contained in one droplet of the mixture?

Homework Equations

The Attempt at a Solution

I have absolutely no idea on how to solve this problem. Usually problems indicate some quantity which we can substitute into an equation.
Any tips will be greatly appreciated.

 

[cepheid]

You know that the amount of oleic acid in the final mixture is 1 part in 400. So all you have to do is figure out the volume of a single droplet, and the volume of oleic acid in that droplet will be 1/400 of that droplet volume.

So, what is the volume of a droplet? Well, 97 droplets have a volume of 1 cm³, so 1 droplet has a volume of ____?

 

[ibysaiyan]

You know that the amount of oleic acid in the final mixture is 1 part in 400. So all you have to do is figure out the volume of a single droplet, and the volume of oleic acid in that droplet will be 1/400 of that droplet volume.

So, what is the volume of a droplet? Well, 97 droplets have a volume of 1 cm³, so 1 droplet has a volume of ____?

Hi, thanks for your reply.
Hm will it be 1/97 cm$^{3}$ , if so then would I multiply this fraction by 400 ?

 

[cepheid]

Hi, thanks for your reply.
Hm will it be 1/97 cm$^{3}$ , if so then would I multiply this fraction by 400 ?

That's right.

 

[ibysaiyan]

That's right.

Thank you very much! The wording of the question brought about confusion to my mind.This question has another parts as well, which I'll try to solve.

 

[SteamKing]

Are you sure multiplication by 400 equals the correct volume of oleic acid?

 

[ibysaiyan]

Are you sure multiplication by 400 equals the correct volume of oleic acid?

Volume of oleic acid in one droplet ?
why is it wrong ?

 

[SteamKing]

Because the oleic acid was being diluted in methanol.

 

[cepheid]

Are you sure multiplication by 400 equals the correct volume of oleic acid?

Yeah, sorry, I missed that. I thought he meant multiply the denominator by 400 (i.e. multiply by 1/400 just the way I told him to).

 

[ibysaiyan]

Because the oleic acid was being diluted in methanol.

Yeah, sorry, I missed that. I thought he meant multiply the denominator by 400 (i.e. multiply by 1/400 just the way I told him to).

Oh I see.. I initially thought of multiplying by 1/400 , i even had that posted as an answer until I changed my mind.Some misunderstanding from both ends. Now it's clear. Thanks.

 

[ibysaiyan]

So here's my final answer for this question: 1/97 x 1/400 ~ 2.6x10^-5 cm3

The questions which follow on are:

The surface of a tank of water is dusted with fine powder. A single drop of the
diluted mixture is allowed to fall on the water surface. The alcohol component mixes
with the water and the oil forms a monolayer film on the water surface, displacing
the dust so it is clearly visible, with a diameter of 9.4 cm. What is the thickness of
the film?

I have answered this: All that was needed to be done was using the Volume = Area x thickness.My final answer is: 3.7x10^-7 cm.

Next question's:
The shape of an oleic acid molecule can be approximated by a cuboid l ´ l ´ 7l .
One end (COOH) loves water (hydrophilic) and the other end hates it (hydrophobic).
Assume that these molecules stick out of the water and form a monolayer close
packed in a square arrangement. What are the dimensions of the molecule?

What does the statement which I have highlighted in bold mean ? do I find out the unit dimension of the molecule? I know lxlx7l denotes volume of the molecule.


Again thanks for your help.

 

[ibysaiyan]

Never mind I have found the answer for this. Thanks everyone for your help!

 

[ibysaiyan]

I need a quick tip on how to solve one of the last bit of this question. The question basically wants me to derive Avogadro's number of oleic acid. So the molecular mass I have got is : 282.
Now I know moles = Mass/ Mr.
To get mass I will have to use density = Mass/ volume.
But once I sub in the numbers.. I get something in the range of 5x10^24! :(

My volume for oleic acid in one droplet was: 2.6x10^-5 (cm3 , do i divide this by 100 to get m3, or is it 1x10^-6 ? )
Density in the question is given to be 890 kg/m3.

Any help will be much appreciated. Thanks!

 

[Jessefisser]

How do I find out the volume of something that is 36w - 16h - 16d. Would it just be 36 * 16 * 16.