Density Question Bugging the crap out of me

[integralx2]

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An organic compound with density that is less then 1.0g/mL is added to organic liquid also with density that is less then 1.0g/mL. What can be said about the concentration of the solution ?

The answer is :

The molality of the solution is greater then the molarity.

Can someone explain why ? My thought process is since, were adding 1mL of volume of two compounds its gonna be 2mL of total volume, so then the volume increases, so molarity is gonna decrease. Now for molality since we are adding 1g of each to it, then 2g total we will have. Since in molality m is proportional to moles of solute then molality will increase and be greater then molarity ? Is this correct ?

My other question is when you mix something that does dissolve into something, what happens to it if the solute is less denser then the solvent ? Does the molarity and molality both increase ?

 

[shffl]

I'm sure there are better answers but I think of it in term of masses.

In molality, it's solute/solvent mass wise. However in molarity when you think of it in term of masses, its solute/(solute+solvent). The number in molality in this case will be larger and hence molality is greater than molarity.

 

[Rabolisk]

Molarity = moles of solute / volume of solution
Molality = moles of solute / mass of solvent

You are not to assume that you are adding 1 mL of solute to 1 mL of solvent. The question doesn't say that. Neither are you to assume that you are adding 1 g of solute to 1 g of solvent. You don't know what the ratio of solute to solvent is, but what you can prove is that regardless of the ratio, molality is always greater than molarity.

The way I would approach this is to set the moles of solute equal to each other and then compare the denominators. So you have x moles of solute and y moles of solvent. For molarity, the volume of the solution is the volume of the solute + the volume of the solvent. For molality, you only need to consider the mass of the solvent. Given such a situation, the volume of the solution (in L) has to be greater than the mass of the solvent (in kg), regardless of how much of solute and solvent you have (i.e. independent of mole fraction). This is because the density of the solvent is < 1 g/mL or 1 kg/L. So if the mass of the solvent is 1 kg, the volume of the solvent is > 1L. Add to that the volume of the solute, and the final volume of the solution has to be greater than the mass of the solvent. But even if there was negligible amount of solute, molality > molarity because of the density of the solvent.

This assumes that the volume of solution increases as you add a substance to a solvent, which is not always true. That is, the volume of solution isn't simply the volume of the solvent + the volume of the solute. It is possible for the volume of the solution to decrease when you add solutes to the solvent, in which case molarity could be larger than molality. Stated another way, the density of the solution could be larger than 1 g/mL even if the individual densities of the solute and the solvent could both be less than 1 g/mL. However, this is obviously being very nitpicky and I wouldn't worry too much about it.

I don't quite understand your second question.

 

[integralx2]

This assumes that the volume of solution increases as you add a substance to a solvent, which is not always true. That is, the volume of solution isn't simply the volume of the solvent + the volume of the solute. It is possible for the volume of the solution to decrease when you add solutes to the solvent, in which case molarity could be larger than molality. Stated another way, the density of the solution could be larger than 1 g/mL even if the individual densities of the solute and the solvent could both be less than 1 g/mL. However, this is obviously being very nitpicky and I wouldn't worry too much about it.



.

This is what I am confused on . How come when you have a denser substance ( >1g/mL) and you dissolve it in something less dense how is it the final product more dense or less. Whats the relationship ?

I do get if two substances mix, and concentration of that final substance decreased ( relative to the other two ? ), that means the volume decreased theoretically speaking. What happens to molality ? Does it change ?

 

[Rabolisk]

This is what I am confused on . How come when you have a denser substance ( >1g/mL) and you dissolve it in something less dense how is it the final product more dense or less. Whats the relationship ?

I do get if two substances mix, and concentration of that final substance decreased ( relative to the other two ? ), that means the volume decreased theoretically speaking. What happens to molality ? Does it change ?

More or less dense than what? Than the solute or the solvent? Typically density will be something in between, reflecting the fact that volume is generally additive, but not always.

I don't understand your second question. What do you mean concentration decreased?