density question chemistry

[fatedMD]

Q: Concentrated sodium hydroxide is 19.4 M and 50.5% NaOH by mass. What is the density of concentrated NaOH?

can someone give me a full detail about this, this is how i thought about it:

19.4 mols/L
mw for NaOH= 40 g/mols

50.5% of NaOH- I assumed 50.5g of NaOH /100g of solution

so i got the moles of NaOH 50.5% by mass: 50.5g X 1mol/40g = 1.26 mol of NaOH

so 19.4mols/1L = 1.26 mol/X L
I solved x to be 0.0649 L

density= mass/Volume

mass of NaOH= 50.5g as assumed
volume= 0.0649 L

50.5g/0.0649L ~ 778 g/L <---as my final answer, is this correct? if not, why not?

Thanks in advance,

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[bidiboom]

My logic is this:

50.5% of the solution is NaOH
49.5% of the solution is H2O

The contribution of NaOH in the total density is 19.4gr/L x 0.505 = 9.797gr/L
The contribution of H2O in the total density is 1000gr/L x 0.495 = 495gr/L

Average density is (9.797 + 495) / 2 = 252.4 gr/L

 

[Ssina]

Q: Concentrated sodium hydroxide is 19.4 M and 50.5% NaOH by mass. What is the density of concentrated NaOH?

can someone give me a full detail about this, this is how i thought about it:

19.4 mols/L
mw for NaOH= 40 g/mols

50.5% of NaOH- I assumed 50.5g of NaOH /100g of solution

so i got the moles of NaOH 50.5% by mass: 50.5g X 1mol/40g = 1.26 mol of NaOH

so 19.4mols/1L = 1.26 mol/X L
I solved x to be 0.0649 L

density= mass/Volume

mass of NaOH= 50.5g as assumed
volume= 0.0649 L

50.5g/0.0649L ~ 778 g/L <---as my final answer, is this correct? if not, why not?

Thanks in advance,

http://answers.yahoo.com/question/index?qid=20071126093758AAqoxdI

shorter way/"MCAT was of doing it", but I am still confused as to why they multiplied it by 100/50.5 in the end!?

 

[fatedMD]

^ thanks for that, I actually saw it, but I don't undertsand why in the end as well. It's as if they take the mass of water and NaOH/ the volume I got. That's whats a bit confusing. I think the answer is what yahoo answers says it is, but I don't understand why.

 

[fatedMD]

My logic is this:

50.5% of the solution is NaOH
49.5% of the solution is H2O

The contribution of NaOH in the total density is 19.4gr/L x 0.505 = 9.797gr/L
The contribution of H2O in the total density is 1000gr/L x 0.495 = 495gr/L

Average density is (9.797 + 495) / 2 = 252.4 gr/L

Hmmmm but why density of water as well? Isn't it just the density of 50.5% by mass ofNaOH?

 

[bidiboom]

Hmmmm but why density of water as well? Isn't it just the density of 50.5% by mass ofNaOH?

FatedMD, when I see "concentrated NaOH" I take it as a solution in which NaOH exist as a solute in high amount, but not as much as water, the solvent.. and I took the question in a way as it asks the density of this solution as a whole. "Concentrated" means to me a solution quality.

 

[FishyTheFish]

Assume 1 L of solution, this 1L of solution has
19.4 mols of NaOH which is 19.4mols * 40g/mol = 776g of NaOH in 1 L of solution

but if concentrated sodium hydroxide is 50.5% NaOH by mass then the
776g of NaOH that we found is only 50.5% of the mass of the solution. Let x be the total mass of the
solution, then

x*.505 = 776g
x = 1536g.

So this 1L of solution weighs 1536grams and since density = mass/volume

density = 1536g/1L = 1.54g/ml

Hope this helped!

 

[bidiboom]

Assume 1 L of solution, this 1L of solution has
19.4 mols of NaOH which is 19.4mols * 40g/mol = 776g of NaOH in 1 L of solution

but if concentrated sodium hydroxide is 50.5% NaOH by mass then the
776g of NaOH that we found is only 50.5% of the mass of the solution. Let x be the total mass of the
solution, then

x*.505 = 776g
x = 1536g.

So this 1L of solution weighs 1536grams and since density = mass/volume

density = 1536g/1L = 1.54g/ml

Hope this helped!

I thought in a way totally out of chemistry, but yes, of course this must be the answer 😳 thank you, it worked for me too..