Increasing Water Density

[clw]

I am working on a project that shows that even though lots of clear plastic water bottles filled almost to the top with a clear liquid may look the same, the liquid in each bottle can actually have a different density, which will affect how the individual bottles float in a large container of tap water and I need quidance on how to create my salt (sugar) water solution.

Each water bottle holds 16 ounces. I want to add salt in increments of 5 grams to the bottles. I have done some experimenting so far, and I definitely see a difference in my control and the bottles with 10g, 30g and 50g of salt regarding how much buoyancy they have. However, I want to make sure that I am doing my calculations correct.

My first thought was that I need to keep the volume the same in all the bottles (16 ounces), but if I add salt to those 16 ounces, doesn't that increase the volume? (I realize that I can add a small amount of salt to water before the volume increases, but what if I want to add a whole bunch?)

Then I thought that maybe I should add the salt to the bottle first and then add the necessary amount of water to equal 16 ounces, but then it seems like I have two variables (amount of salt and amount of water) instead of just one - salt.

My third thought was to mix 16 ounces of water with the appropriate amount of salt in a separate container, until all of the salt is dissolved, and then pour that solution into the water bottle, up to the 16 ounce mark; but since I might not be able to put all of the solution into a bottle that may not work.

I want to make sure that when I do my Density calculations, I am using the correct volume and mass numbers for all my calculations. I did two sets of experiments and the difference in density between 0g and 10g, and 10g to 30g wasn't that significant, but the difference between 30g and 50g was, which leads me to believe that how I created the solution has something to do with it. (All the water I used was room temperature.)

Please help me understand the correct formula for creating this solution.

Any guidance you can give will be greatly appreciated.

[staryl13]

Hi!
It is extremely important, as you said, to keep some variables constant, in this case, the volume. For the salt and water, you can have different amounts of salt mixed with water to equal 16 oz. It is easy to think of these solutions as, for example, a 1%, 2%, or a 5% saline solution. It might be easier to do this in a separate container and mix the salt and water until most of the salt has dissolved. This way, even if the entire solution is more than 16 oz., there will be less error becaue the solution is basically spread out evenly. As long as there are equal volumes, it should be fine. Hope this helps!

[geoffbruton]

Hi clw,

This sounds like a very interesting way to demonstrate the increasing densities of solutions! The information posted by staryl13 should definitely help, and I would echo the comment made about thinking about your solutions as a percentage of the material in solution.

How much information have you been able to find out in your background reading regarding the solubility of sodium chloride and sucrose in aqueous solutions and at different temperatures? One thing that you must definitely be sure of is that the contents of the bottles are truly a solution - and does not contain any undissolved material. Probably the easiest way to do this would be to take a measured amount of salt or sugar (in grams), and dissolve this in the minimum amount of distilled water. This concentrated solution can then be diluted to 100 milliliters with distilled water. The mass of the dissolved material can then be expressed as a percentage. When you begin to approach a saturated solution (where no more material will dissolve in the solvent at a given temperature), the temperature of your solution is a very important factor - 'room temperature' is fine, but make sure to record what this value truly is.

Naturally, if you want to make more of the solution, you can simply increase the amount of material (the solute) and proportionally increase the amount of water (the solvent). For example, if you want to make a 5 % sodium chloride solution, simply dissolve 5 g of sodium chloride in water and dilute the concentrated solution to 100 ml. To make 200 ml of a 5 % sodium chloride solution, this would require 10 g of sodium chloride to be dissolved in water, and diluted to 200 ml. Does that make sense? Just make sure that you use the same volume of differing concentrations in all of your water bottles - that is, 16 oz of 0 % NaCl solution (i.e. pure water), 5 % NaCl solution, 10 % NaCl solution, and so on, in your comparisons.

You will find that you eventually reach a point where you simply cannot dissolve any more material in your solvent at a particular temperature - and depending upon what information you have already found, this may well be less than the 50 g of sodium chloride you mentioned earlier (also depending upon the volume of solvent used, of course). As long as you structure your experiment in such a way that all the variables are kept constant - except the percentage solution used - you should be able to demonstrate the differences very effectively.

Best of luck, and please let us know if you have any more questions.
Geoff.

[clw]

Thanks for the tips, we used them to get us started but we have run into a bit of a roadblock. We have 10 bottles, labled 1-10, we weight each bottle empty, record the value and then add salt by weight to the bottle. Bottle 1 has 0 g of salt. Bottle 2 gets 5g of salt, bottle 3 gets 10g and so on until bottle 10 which gets 45g of salt. We then add enough water to each bottle to bring up the volume to 500mL. Actually we use a graduated cylnder and transfer the contents to the bottle once we reach 500mL. Afterwards we record the weight of each bottle and solution and were surprised by the results. Rather than a nice linear line, we have bumps, plateaus and even a valley. Is there some magical combination of water and salt that we are not aware of or is there a problem with our procedures or instrumentation?

[ChrisG]

Hi CLW,
It sounds like you may be seeing the effects of some unidentified experimental error. How big are the bumps, valleys, and plateaus? Did you measure the exact volume of liquid added to each bottle? One possibility is that the bottles have slightly different volumes and weights of their own. Of course there are many other possibilities too which we can explore.
Chris

[clw]

Below are the results he has as of his third trial. He's done the steps three times because he keeps getting Solution Mass numbers that seem to be within 1 or 2 grams of each other for a few bottles, and then the next one jumps by five or six grams. Although is he doing the measurements, I watched while he weighed the salt each time, and each one was within .02g of the amount listed. (Sometimes, it was just too difficult for him to get the .00 exactly. He remembered to tare the bowl weight each time.) When he added the salt to the glass container, I watched everytime he added the necessary amount of water to first, dissolve the salt, and then to bring the volume up to the 500 mL line on the container. Granted, his amounts might be off by a small amount, but not by very much. The water temperture was the same for all the bottles, so it's not like he was weighing hot and cold water and expecting the same results.

His actual project is about Water Density, but he hasn't gotten that far because we need to make sure what he has so far is correct.

So, after going through the necessary steps, it looks like some of the Solution Mass amounts are increasing by about half of the Salt Mass added, at least for the bottles with 15g, 20g, 25g and 40g. If that's what it should do (which I don't know), then I do not know why Solution Mass for 5g only increased .96g, 10g only increased 2.84g, 15g jumped over 5g, 30g only increased .88g, 35g jumped almost 7 grams, 45g only increased less than 1g.

Bottle....Salt....Solution....% of Salt.....Empty.....Filled.....Solution
Label.....Mass..Volume.....in Solution...Bottle.....Bottle.....Mass
1----------0g-----500mL------0.0%---------16.00g----515g------499.00g
2----------5g-----500mL------1.0%---------16.04g----516g------499.96g
3---------10g-----500mL-----2.0%----------16.16g----518g------501.84g
4---------15g-----500mL-----3.0%----------16.00g----523g------507.00g
5---------20g-----500mL-----4.0%----------16.06g----527g------510.94g
6---------25g-----500mL-----5.0%----------15.98g----528g------512.02g
7---------30g-----500mL-----6.0%----------16.10g----529g------512.90g
8---------35g-----500mL-----7.0%----------16.02g----536g------519.98g
9---------40g-----500mL-----8.0%----------16.14g----538g------520.86g
10-------45g-----500mL------9.0%----------16.16g----538g------521,84g

Since I have no clue, do these numbers make since? My initial thought is that there should be some consistency, but I sure don't see it. And I really don't understand how he can add 10g to a bottle, and yet the Solution Mass only increases by 2.90g (20g bottle to 30g bottle.) The same goes for the 0g bottle to the 10g bottle.

Please let me know if you have any ideas on how I can lend my son some guidance.

Thanks

[ChrisG]

Hi,
Those are very interesting results. Maybe they are not the sort of "interesting" that you were hoping for, but they do raise some questions.

how he can add 10g to a bottle, and yet the Solution Mass only increases by 2.90g

If I understand your procedure correctly, the mass increase for each solution is not the same as the increase in salt mass added because the salt displaces some of the water. As you add more salt, you are adding less water to reach the 500 mL mark.

I do not know why Solution Mass for 5g only increased .96g, 10g only increased 2.84g, 15g jumped over 5g, 30g only increased .88g, 35g jumped almost 7 grams, 45g only increased less than 1g.

I believe the concern here is that there is a lot of "noise" in the data. Noise is always an issue, and it is good to see that at least the overall trend makes sense - as you add more salt, the mass (and density) of the solution increases. However, if your noise is so large that it interferes with interpretation of the data trends, then we will need to figure out the source of the noise and try to fix it.

From your description, the errors in the weighed mass of salt (+/-0.03 g) are small relative to the noise in your solution masses (+/- several grams). I suspect that most the noise comes from errors in the measurements of water volumes. I don't know what sort of bottles you are using, but suppose they are cylinders with a 5 cm diameter. In this case, the 500mL mark would be at 25.5 cm height. If you need 1 gram (approximately equal to 1 mL water) accuracy, then your meniscus would have to be within 1/500th of the total height of water, or within 1/2 a millimeter. That is a very small margin for error, and even the sharpest eyes and steadiest hands would have trouble avoiding errors of +/- several grams.

Also, it sounds as though you are using different bottles for each volume measurement. This introduces additional error, because there will be some slight differences in the actual volume that fills each bottle to its 500mL mark. Even if the % difference between bottles is very small, it could create the amount of noise that you are seeing.

If the volume measurements really are the problem, there are a few possible ways to reduce the % error: (1) Use a more accurate method of volume measurement. (2) use larger increases in the mass of salt (for example, 0, 50, 100, 150 g... you should be able to dissolve up to 150-180 g of salt per 500mL of water) (3) Complete multiple trials so that you can average the results and improve your accuracy (sounds like you have already done three trials). Alternatively, once you are content that you understand the source of error, you may decide that you can still proceed and interpret the data set as a whole, even with the existing noise. Understanding and working with noise in data is a very important part of the scientific process.

I hope that is helpful.

Chris

[geoffbruton]

Hi clw,

Just to add some thoughts to Chris' excellent response:

My initial thought was that the salt was not fully dissolved, but I re-read your post and saw that is not the case. The salt *is* being dissolved, and then diluted up to the necessary volume.

So, I then thought a bit more about the processes involved. As Chris mentioned, you are not using the same *mass* of water in each case, even though the final volume is the same. This is because the salt is taking up space! Consequently, as you add the water to this mass of salt, there is progressively less water available than in the 0 % salt solution. Does that make sense?

It has been a while since I took some chemistry classes, but I did some looking around: A search for the density of sodium chloride comes up as approx. 2.16 g / cm^3 (and, interestingly, a solubility in water of approx. 35.9 g / 100 mL at 25 degrees Centigrade, so we know that you should be able to fully dissolve all of the salt in this experiment). Liquid water, on the other hand, has a density of 1.00 g / cm^3 - approximately half of that of sodium chloride. Take a look at the results you posted for, say, the 20 g NaCl addition, and compare that to the 0 g NaCl solution. The result is approx. 11 g difference (or about half of the 20 grams added). Similarly, the 40 g NaCl addition is approx. 20 grams heavier than the 0 % salt solution, and so on.

It would therefore appear that the volume occupied by the sodium chloride is displacing the water. Indeed, although when this data is plotted there does not appear to be a great deal of linearity, I think that this may be to do with your potential errors (as already discussed by Chris). A scatter plot may be useful in showing the trend...

Now as I said, it has been a while since I took some chemistry classes, but hopefully some of the chemists on this forum may take a look at this and see if this might be on the right track.

Sorry I can't be of more help, and good luck!
Geoff.