TBR Gen Chem: P7 #41

[ilovemcat]

41: Adding water to an aqueous solution of known concentration always decreases all of the following EXCEPT:

A. density
B. molarity
C. molality
D. mass percent of solute

I want to compare this to #39: Addition of water to an aqueous salt solution would do all of the following EXCEPT:
A. lower the molality
B. lower the molarity
C. increase the density
D. increase the mass percent of solvent





The answer for question 41 is A, while the answer for question 39 is C.

41: "If the density of the solution is less than the density of water, then the addition of water to the solution may actually increase the density of the solution."
39: "The salt solution is denser than the pure water, so the addition of water (a less dense solution) to the salt solution decreases the density of the solution."

I'm having a difficult time understanding how density is changing in both of these situations. In question 41, if you mix an aqueous solution less than water to a solution of pure water, how is it that the density of the combined solution would increase. From my understanding, density = mass solutes / volume solution. Combing the aqueous solution wouldn't change the mass of the solutes, but the volume those solutes are in would increase (the solvent). How is it that the density could even increase? If someone could clarify this, it'd be a huge help.

ps - passage 7 of TBR Gen Chem, Ch. 1 - just made my head explode -sigh-

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[Catburr]

I might be off base here, but I have an idea that might be useful...

In #41, it just says aqueous solution. This might be a salt solution, or a solution of say water and methanol, maybe. Putting more water in the methanol/water mix would increase the total density, because water is the heavier component there.

In #39, they're specific about it being a salt solution. Here's where I may be wrong, but I can't think of a salt molecule that is lighter than a water molecule. So all salt solutions are more dense than pure water.

If someone posts a lighter than water salt in like 5 minutes, then facepalm for me I guess. : )

 

[Rabolisk]

Density of a solution is mass of solution / volume of solution. I suppose you might be able to argue that B could be an answer for 41, although I don't know of an aqueous solution (water being the solvent) that adding water reduces volume. Typically it is the solute that has the negative partial molar volume. Likewise, B could be an answer for 39, but I don't know of any example. A, and C are the best answers for 41, and 39, respectively.

 

[ilovemcat]

I might be off base here, but I have an idea that might be useful...

In #41, it just says aqueous solution. This might be a salt solution, or a solution of say water and methanol, maybe. Putting more water in the methanol/water mix would increase the total density, because water is the heavier component there.

In #39, they're specific about it being a salt solution. Here's where I may be wrong, but I can't think of a salt molecule that is lighter than a water molecule. So all salt solutions are more dense than pure water.

If someone posts a lighter than water salt in like 5 minutes, then facepalm for me I guess. : )

Thanks for the response. That sounds about right.
I spent a while thinking about this (talking to myself, lol) and I think I understand it now. Please correct me if this is wrong.

Let's say you had:
- 100 mL solution of water (1g/mL)
- 100 mL solution of an unknown aqeous salt (0.5g/mL)

The mass of the water solution: (100mL)(1g/mL) = 100g
The mass of the aqueous solution: (100mL)(0.5g/mL) = 50g

Combining both solutions would yield a new total mass of: 150g
The combined total volume = 200mL

Combined New Density = mass solution / volume solution
Combined New Density = 150g / 200 mL = 0.75g/mL

The density of the aqueous solution is higher than before. (0.5g/mL ==> 0.75g/mL).
The density of the pure water solution is lower than it was originally (1g/mL ==> 0.75g/mL).

For 39, a salt solution is always more dense than water (like you said). So adding water would only decrease the total density of the original salt solution.

For 40, they're not specifically limiting the solution to being just a "salt solution." So I'm guessing if you had an "aqueous" solution of oil with a tiny bit of water (less dense than water) and you mixed that with a solution of pure water, the density would increase. On the other hand, if you had a solution more dense than water (ie. a salt solution like in #39), it would decrease.

The word aqueous kind of threw me off though because I've never heard of an oil solution being termed aqueous. I thought the only things that were aqueous were things that could dissolve in water ..and oil being less dense and polar can't... but I guess when you're considering only density of an oil + water solution, that doesn't really matter anyways.

 

[ilovemcat]

Density of a solution is mass of solution / volume of solution. I suppose you might be able to argue that B could be an answer for 41, although I don't know of an aqueous solution (water being the solvent) that adding water reduces volume. Typically it is the solute that has the negative partial molar volume. Likewise, B could be an answer for 39, but I don't know of any example. A, and C are the best answers for 41, and 39, respectively.

Yeah, I caught that while re-reading the passage. I realize now that the total mass includes the mass of the solute + solvent, which makes sense.

 

[ilovemcat]

Does that sound about right by the way? ...the way I calculated the combined density? If I did something wrong, please let me know Muchas gracias.

 

[Rabolisk]

It's more or less correct. While mass is strictly additive by conservation of mass, volume is not. You can't guarantee that adding a 100 mL solution of pure water to a 100 mL aqueous salt solution would result in a 200 mL solution. But it'll be close, and your reasoning is correct. An "oil solution" would not be a solution since oil is not soluble in water. However, there is a polar liquid that is completely miscible with water. It is extremely important to human culture, has been known to man since the dawn of time, currently consumed widely in most of the world, and is less dense than water.

 

[Catburr]

Let's say you had:
- 100 mL solution of water (1g/mL)
- 100 mL solution of an unknown aqeous salt (0.5g/mL)

The mass of the water solution: (100mL)(1g/mL) = 100g
The mass of the salt solution: (100mL)(0.5g/mL) = 50g

Combining both solutions would yield a new total mass of: 150g
The combined total volume = 200mL

Combined New Density = mass solution / volume solution
Combined New Density = 150g / 200 mL = 0.75g/mL

The density of the salt solution is higher than before. (0.5g/mL ==> 0.75g/mL).
The density of the pure water solution is lower than it was originally (1g/mL ==> 0.75g/mL).

I do all my best thinking while talking to myself. Or so I like to think.

It sounds like you have a good grasp on it quantitatively, because the math part above is an example of where adding the water to the aqueous solution increases the solution's density. I wouldn't use a salt solution of 0.5mg/mL density as an example because I'm not sure that exists, at least if it's just a salt in water. Same goes for an oil in water solution, that doesn't exist without the help of some kind of detergent as far as I know. I used the methanol example because I actually use methanol/water solutions all the time, and that's definitely an example of a solution less dense than pure water. Something like vodka is another aqueous solution that's less dense than water too.

But like I said, your math is totally right, I believe, which is probably the important part anyway!

EDIT: Rabo there beat me to it with a nice summary. I was distracted by hockey, sorry. :/

 

[ilovemcat]

I do all my best thinking while talking to myself. Or so I like to think.

It sounds like you have a good grasp on it quantitatively, because the math part above is an example of where adding the water to the aqueous solution increases the solution's density. I wouldn't use a salt solution of 0.5mg/mL density as an example because I'm not sure that exists, at least if it's just a salt in water. Same goes for an oil in water solution, that doesn't exist without the help of some kind of detergent as far as I know. I used the methanol example because I actually use methanol/water solutions all the time, and that's definitely an example of a solution less dense than pure water. Something like vodka is another aqueous solution that's less dense than water too.

But like I said, your math is totally right, I believe, which is probably the important part anyway!

EDIT: Rabo there beat me to it with a nice summary. I was distracted by hockey, sorry. :/

Yeah haha. I realized that afterwards so I changed it to aqueous. Anyways, thanks both of you for your insight. You guys were really helpful

 

[BerkReviewTeach]

Let's say you had:
- 100 mL solution of water (1g/mL)
- 100 mL solution of an unknown aqeous salt (0.5g/mL)

I think the problem lies in your assumption for the density of a salt water solution. How would it be possible to add salt to water and have the density of the solution drop to a value such as 0.5 g/mL? Adding salt to water will increase the density of the solution to a value greater than 1.00 g/mL.

Even if you want to make a spacial case where you take water at 0 degrees C and add one tiny spec of salt while heating it to 100 degrees C, the density of the solution will still be very close to 1.

 

[ilovemcat]

I think the problem lies in your assumption for the density of a salt water solution. How would it be possible to add salt to water and have the density of the solution drop to a value such as 0.5 g/mL? Adding salt to water will increase the density of the solution to a value greater than 1.00 g/mL.

Even if you want to make a spacial case where you take water at 0 degrees C and add one tiny spec of salt while heating it to 100 degrees C, the density of the solution will still be very close to 1.

I thought I edited that. I meant to say aqueous solution, not salt. I don't think I've ever encountered a question where I had to consider how the density of a solution would change when adding two solutions of different densities. That's what really confused me. But after reading the explanations in the back, I think it all makes sense now. Basically what I gained from those questions is that if you mixed 2 different solutions of different densities, the new combined density would basically be an average of the two densities. The change in density (increase/decrease) is all relative to the original density of the solution your considering. It seems kind of obvious now, but when I read those questions, I was like "...whaaat?" haha