[AWK]

volumes (x for ethanol)
x+y = 54.2 [·0.998]
masses
x·0.789+y·0.998 = 49.6 [·(-1)]
gives 0.209·x = 54.0916-49.6 = 4.4916
=> x = 21.491 ml [·0.789] => 16.956 g
16.956/49.6 = 0.342 or 34.2 %

[dshipp17]

Thank you; I got the answer myself; but, I saw the last post too; but, here is how I worked it out:

d(e)V(e) + d(w)V(w) = 49.6
m(e)/d(e) + m(w)/d(w) = 54.2; m(e)/d(e) =54.2-m(w)/d(w); d(e)(54.2 - m(w)/d(w)) + d(w)V(w) =49.6;

d(e)(54.2-m(w)/d(w)) + d(w)(54.2-m(e)/d(e)) = 49.6;
(54.2)(0.789) -(m(w)/0.998)(0.789) + (54.2)(0.998) - (m(e)/0.789)(0.998) = 49.6;
96.8554 - (0.7906)m(w) - (1.2649)m(e) = 49.6;
m(e) = (47.255-0.7906m(w))/1.2649
m(e)/d(e) = 54.2 - m(w)/d(w)
m(e) = d(e)(54.2-m(w)/d(w))
d(e)(54.2-m(w)/d(w)) = (47.255-0.7906m(w))/1.2649
-54.0919 + m(w) = -47.255 + 0.7906m(w)
m(w) = 32.65
m(e) = (47.255 -(0.7906)(32.65))/1.2649 = 16.95g
%m(e) = (16.95g/49.6g)*100% = 34.17%

[AWK]

This is the second equivalent method. I always design a way od calculation with minimal number of
divisions. Usually it gives a simplest way of solution and is more safe from the point of view of numerical stability of solution (problem of numerical stability often happens in the chemical equations).

[Borek]

Sigh, what a stupid mistake I made :/

[sjb]

Sigh, what a stupid mistake I made :/

In the spirit of the forum, care to share your blind alley?

[KungKemi]

I came across this problem and my answer seems to either be slightly off or the textbook might be wrong: A sample of an ethanol–water solution has a volume of 54.2 cm3 and a mass of 49.6 g. What is the percentage of ethanol (by mass) in the solution? (Assume that there is no change in volume when the pure compounds are mixed.) The density of ethanol is 0.789 g/cm3 and that of water is 0.998 g/cm3.

Would you help me with this problem by working it out step by step? This problem shouldn't involve molar masses, although it could require using molar masses (e.g. no examination of the periodic table should be necessary); it should just be a conservation of mass problem.

Also, just for future reference, dshipp17, if the answer you obtain is more than 5% greater or lesser than that of the given textbook answer, then the mistake is almost certainly not a negligence of significant figures.

n.b: Of course, if you're working with figures that are >10000 or <0.0001 then significant figures, of course, can cause such an error to occur.

Just for future reference.
KungKemi

[Borek]

Sigh, what a stupid mistake I made :/

In the spirit of the forum, care to share your blind alley?

Nah, careless math mistake. Got correct volumes but multiplied by a wrong density.

[AWK]

Look for more:
http://www.chemicalforums.com/index.php?board=67.0 - Stoichiometry exercise.

[Enthalpy]

Assume that there is no change in volume when ethanol and water are mixed.

Professor failure once again.

It doesn't prevent answering the question, but keep in mind that this is wrong. More so with ethanol and water, bad luck.

[AWK]

Assume that there is no change in volume when ethanol and water are mixed.

Professor failure once again.

It doesn't prevent answering the question, but keep in mind that this is wrong. More so with ethanol and water, bad luck.

This problem can be found in mamy textbook. The newest one is
Darrell Ebbing, ‎Steven D. Gammon - 2016

[dshipp17]

Assume that there is no change in volume when ethanol and water are mixed.

Professor failure once again.

It doesn't prevent answering the question, but keep in mind that this is wrong. More so with ethanol and water, bad luck.

This problem can be found in mamy textbook. The newest one is
Darrell Ebbing, ‎Steven D. Gammon - 2016

You tracked it down; I'm using one of his older textbooks (Ninth Addition; 2007) and it seems that it's been repeated in successive volumes. I'm a professional chemist (but, actually, not since late 2006), but, I'm going through all of my courses, because I'm contemplating taking the chemistry and physics GREs so that (I can go to graduate school; but, the last time I'm been in a classroom was in 2001 and a chemistry or physics classroom, 1999; trying to sharpen my skills back up; I took a chemistry examine for tutor.com and did awful (but, mostly because of the timing to take the examine; if there was no time limits, I would still have passed, just very rusty; but, that was a poor sign for something like heading into graduate school); just a lot of stuff lost, but, solving these problems and things are coming back, slowly but surely; but, if I ask elementary questions, which this problem proved not to be, it's because I'm trying to sharpen back up. It's very different trying to prepare for examine, if I last had a chemistry class last semester versus 22 years ago (e.g. when I started college). Since I'm just starting chapter 2, maybe you can track down a free addition of the 2016 version?

[AWK]

I just searched GOOGLE using the whole text of your problem.

[KungKemi]

If you might like a little bit more practice, I found the following question in my textbook (it is somewhat similar to this one):

An experiment was performed in which an empty 100-mL graduated cylinder was weighed. It was weighed once again after it had been filled to the 10.0-mL mark with dry sand. A 10-mL pipet was used to transfer 10.00 mL of methanol to the cylinder. The sand-methanol mixture was stirred until bubbles no longer emerged from the mixture and the sand looked uniformly wet. The cylinder was then weighed again. Use the data obtained from this experiment (and displayed at the end of this problem) to find the density of the dry sand, the density of methanol, and the density of sand particles. Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting?

Mass of cylinder plus wet sand    45.2613 g
Mass of cylinder plus dry sand     37.3488 g
Mass of empty cylinder               22.8317 g
Volume of dry sand                    10.0 mL
Volume of sand plus methanol     17.6 mL
Volume of methanol                   10.00 mL

[AWK]

Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting?

Not all air is removed this way, but the result is within the 5% error.

[dshipp17]

If you might like a little bit more practice, I found the following question in my textbook (it is somewhat similar to this one):

An experiment was performed in which an empty 100-mL graduated cylinder was weighed. It was weighed once again after it had been filled to the 10.0-mL mark with dry sand. A 10-mL pipet was used to transfer 10.00 mL of methanol to the cylinder. The sand-methanol mixture was stirred until bubbles no longer emerged from the mixture and the sand looked uniformly wet. The cylinder was then weighed again. Use the data obtained from this experiment (and displayed at the end of this problem) to find the density of the dry sand, the density of methanol, and the density of sand particles. Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting?

Mass of cylinder plus wet sand    45.2613 g
Mass of cylinder plus dry sand     37.3488 g
Mass of empty cylinder               22.8317 g
Volume of dry sand                    10.0 mL
Volume of sand plus methanol     17.6 mL
Volume of methanol                   10.00 mL

What's the title of the chapter for this problem? Is it after chapter 1 of your book, provided it's a general chemistry book? Looks like this is a problem dealing with relative density.