Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: dshipp17 on March 02, 2017, 02:03:53 PM
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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.
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This is quite simple problem. two different volumes gives you a known volume. Each volume has its own mass. Sum of masses is also known.
Compare your result with table of densities for mixture ethanol-water. You can find that this assumpion (Assume that there is no change in volume when the pure compounds are mixed.) is rather not valid.
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That's precisely what I did; would you work out the calculation and give the answer? You'll either get my answer or the textbook answer; perhaps you would get the density for this mixture from a table of densities?
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According to Forum Rules (http://www.chemicalforums.com/index.php?topic=65859.0) you should show us your calculations.
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Sorry about that; my mistake; I took V (total) = 54.2 and m (total) = 49.6; m (ethanol) = (0.789)(54.2) = 42.76 g; m (water) = (0.998)(54.2) = 54.09 g; m (solution) = 42.76 + 54.09 =96.85 g; %m (ethanol) = (42.76/96.85)*100%; %m (ethanol) = 44.15%; if I went wrong somewhere, please explain how I went wrong with my calculation; it seems slightly off from the textbook answer; not talking about something like possible significant figures causing a minor difference.
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If the V total is 54.2 mL, why do you use it for calculations as if it was just a volume of pure water?
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I'm not sure that I fully understand your question; could you elaborate? Please work the problem out and see where we may differ. I thought I accounted for both ethanol and water.
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Borek pointed out that this is wrong
(ethanol) = (0.789)(54.2)
And all further calculations are also wrong.
You should set a system of 2 equation with 2 variables as I told previously.
The real concentration of your alcohol solution is 49.4 % of ethanol (on the basis of density of solution).
Your assumption (approximation) should give you a result about ± 5% different (my guess).
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Sorry, no, that's not the textbook answer and neither one of you solved the equation, as requested; how did you perform your calculation, was the question? The answer in the back of the textbook is 34%. And volume times density gives the mass; the ethanol density is 0.789g/mL and the total volume of the solution is 54.2 mL.
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m (ethanol) = (0.789)(54.2) = 42.76 g;
m (water) = (0.998)(54.2) = 54.09 g;
m (solution) = 42.76 + 54.09 =96.85 g;
Do you see that you have calculated the same solution to have three different masses at the same time? Don't you think it is impossible?
The answer in the back of the textbook is 34%.
With density tables I got 49.8% of ethanol. A bit different from what AWK got (chances are we used density tables for different temperature), but looks like the book answer is way off from the correct one.
Without density tables (assuming volumes are additive) I got 43% - not even close to the book answer either (unless it has digits switched).
how did you perform your calculation, was the question?
We try to guide you so that you will find how to solve the problem on your own, that's how the forum works. AWK gave you several hints about how to approach it.
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Well, the numbers are used that way, because the problem gave does conditions (e.g. the densities, volumes, and masses); I assumed that these conditions were given, because they're needed in the calculation; isn't this how problems are usually solved (e.g. the question states the conditions and you take those to solve the problem)? If I looked for something other than what's given in the problem, than either I'm going on a tangent or the person creating the problem is creating a bate and switch; but, yes, as I suspected, the answer in the back of the book must be wrong.
If you used a density table, how did you know which temperature to assume for a specific density? You could pick every temperature there. Why do we have to work out the problem but you not? Although not required, it would aid greatly if you extended the courtesy to show how you're deriving the answer. Also, if my calculations are off, I'll need you to be more specific and telling me. But, my answer took each of the masses, got the total mass, than calculated the mass percent of one of the variables. But, each of our answers are close to each others while the textbook answer is way off; if you used a density at a different temperature, than the density would be different from the one stated in the textbook and would explain the differences in our answers (e.g. we all used different densities).
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Instead of defending what you did try to think why it is nonsensical - can the same solution have three different masses at the same time? No, so your approach is clearly wrong. What can I add to that?
Solution has one mass, and it is given. Solution is a mixture of two substances - so the sum of their masses must be the mass of the solution. To solve the problem without density tables you have to assume volumes are additive - that is, the total volume is a sum of their volumes (that's not true, which is why the solution without density tables is only approximate). Express these thing with math and two variables, solve and you are done. You are told that for the second time.
When solving typical problems usually we assume temperatures around 20°C. Yes, it means sometimes we are a bit off, but it is still much better assumption that the one about volume additivity.
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I got 34.2 mass percent of ethanol.
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Well, I didn't calculate three separate masses; the masses were calculated based on the total volume of the solution; from there, the volumes were added; the calculation was based on the partial masses; without knowing how you would do you're calculations, you could basically say anything that gives an answer other than mine; so, I'm still not sure I can follow. Additionally, the problem says that the volume did not change but it didn't say anything about that mass. And, I'm more stating what the problem conditions were, not defending my answer while asking you to point out where I could be wrong; but, the answer has to be derivative of the conditions specified in the problem. But, I think I'm sensing what you're saying, but, there would be two unknown variables; this problem wasn't meant to require matrix algebra to solve, but, maybe it did; it's only in chapter 1 of a general chemistry book.
How did you you 34.2%? Please give some idea of your calculations.
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there would be two unknown variables; this problem wasn't meant to require matrix algebra to solve
Come on, solving system of equations with two unknowns doesn't require matrix algebra. Solve first equation for one unknown, put it into the second equation, solve for the remaining variable.
Well, I didn't calculate three separate masses
Sure you did - you got 42.76 g, 54.09 g and 96.85 g.
How did you you 34.2%? Please give some idea of your calculations.
Actually I am interested in seeing where this number comes from as well, I got 43 following the logic described in this thread.
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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 %
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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%
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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).
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Sigh, what a stupid mistake I made :/
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Sigh, what a stupid mistake I made :/
In the spirit of the forum, care to share your blind alley?
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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
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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.
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Look for more:
http://www.chemicalforums.com/index.php?board=67.0 - Stoichiometry exercise.
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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.
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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
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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?
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I just searched GOOGLE using the whole text of your problem.
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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
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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.
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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.
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I made a mistake in referencing relative density; I was trying to solve a problem in my text book; that problem turned out to be about Archimedes's Principle and fluid displacement, and I solved it; that comes from putting a problem in a chapter that was not covered.
But, still need to know the title of that chapter.
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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.
It's Chapter 1 of my personal textbook - Zumdahl "Chemistry" 9th Edition. You shouldn't need prior knowledge of relative densities as the question asks you to find these.