Calculating the Volume of a 40% Solution

[barryj]

Homework Statement

What volume of 40% NaNO3 solution contains 0.15 mole of NaNO3 ? Density = 1.32 g/mL = 1320 g/L

Relevant Equations

mwt of NaNO3 = 85 0.15 moles of NaNO3 = 12.5 grams
Soluability of NaNO3 is 900 g/L at 25 C

Since the density is 1320 g/L then for every L of solution there is 320 grams of solute.

320 is 35% of 900 hence the statement it is is a (about) a 40% solution

So the volume that would have 12.5 grams would be 12.5/320 L = .039 L = 39 mL

 

[barryj]

The correct answer is 24.1 mL Where is my logic incorrect??

 

[Steve4Physics]

Homework Statement:: What volume of 40% NaNO3 solution contains 0.15 mole of NaNO3 ? Density = 1.32 g/mL = 1320 g/L
Relevant Equations:: mwt of NaNO3 = 85 0.15 moles of NaNO3 = 12.5 grams
Soluability of NaNO3 is 900 g/L at 25 C

Since the density is 1320 g/L then for every L of solution there is 320 grams of solute.

320 is 35% of 900 hence the statement it is is a (about) a 40% solution

So the volume that would have 12.5 grams would be 12.5/320 L = .039 L = 39 mL

The three problems I can spot are:

1. You haven’t stated if the concentration is 40% w/w or 40% w/v.

2. It is wrong to say “Since the density is 1320 g/L then for every L of solution there is 320 grams of solute.” (Though this may be approximately true).

If you dissolve 320g of a solute in 1 litre (1000g) of water, the total mass will be 1320g - but the volume will not still be 1L. So the density will not be 1320g/L.

3. 0.15 mol of NaNO₃ is not 12.5g

 

[barryj]

1. the stated problem didn't state w/w or w/v
2. I was afraid of this so this will make my solution incorrect
3. mwt of NaNO3 is 85. 0.15 * 85 = 12.75 I stated 12.5 is this the problem?

I did come up with this equation that gave the correct answer but I do not fully know why.

0.40 * V * 1.32 = 12.5
V = 24.1 ml the correct answer.

I do not totally undertand what a 40% solution is. 40% of what?
Maybe you could enlighten me.

 

[mjc123]

40% w/w means that 100 g of solution contains 40 g solute.
40% w/v means that 100 ml of solution contains 40 g solute.
Let's assume that the solution is 40% w/w (that leads to the stated answer).
From the density, you know the mass of 1 L of solution. What mass of NaNO₃ does this contain?
So what volume of solution would contain 12.75 g NaNO₃?

 

[Chestermiller]

A 40% solution of NaNO3 means that the solution is 40% NaNO3 by weight. If the density is 1320 g/L, this means that there are $(0.4)(1320)$ grams of NaNO3 per liter, or 528 grams NaNO3/l .

How many moles NaNO3/liter is that?

How many liters of this do you have to have for you to have 0.15 moles?

 

[barryj]

A 40% solution of NaNO3 means that the solution is 40% NaNO3 by weight. If the density is 1320 g/L, this means that there are $(0.4)(1320)$ grams of NaNO3 per liter, or 528 grams NaNO3/l .

How many moles NaNO3/liter is that?

How many liters of this do you have to have for you to have 0.15 moles?

mwt of NaNO3 is 85. 528 grams would be 528/85 = 6.21 moles/liter
so, 6.21 m/1000mL = 0.15 m/x ml
solving gives x = 24.1 mL and this is correct.

40% w/w means that 100 g of solution contains 40 g solute.
40% w/v means that 100 ml of solution contains 40 g solute.
Let's assume that the solution is 40% w/w (that leads to the stated answer).
From the density, you know the mass of 1 L of solution. What mass of NaNO₃ does this contain?
So what volume of solution would contain 12.75 g NaNO₃?

From the density, you know the mass of 1 L of solution. What mass of NaNO₃ does this contain? I guess I do not know how to find this. I would like to know how.

 

[barryj]

mwt of NaNO3 is 85. 528 grams would be 528/85 = 6.21 moles/liter
so, 6.21 m/1000mL = 0.15 m/x ml
solving gives x = 24.1 mL and this is correct.

From the density, you know the mass of 1 L of solution. What mass of NaNO₃ does this contain? I guess I do not know how to find this. I would like to know how.

40% w/w means that 100 g of solution contains 40 g solute.
40% w/v means that 100 ml of solution contains 40 g solute.
Let's assume that the solution is 40% w/w (that leads to the stated answer).
From the density, you know the mass of 1 L of solution. What mass of NaNO₃ does this contain?
So what volume of solution would contain 12.75 g NaNO₃?

Assuming w/w 1 liter would be 1320 grams. How can you determine what part is water and what part is NaNO3.

 

[Chestermiller]

Assuming w/w 1 liter would be 1320 grams. How can you determine what part is water and what part is NaNO3.

It's 40% by weight of NaNO3 and 60% water.

 

[Steve4Physics]

Assuming w/w 1 liter would be 1320 grams. How can you determine what part is water and what part is NaNO3.

1 litre weighs 1320g because we are told this (the density). It is nothing to do with w/w or w/v is being used for concentration.

But using 40% w/w gives:
40% of 1320g = 528g
So 1 litre of solution contains:
528g of NaNO₃
1320g – 528g = 792g of water

 

[barryj]

The ole brain has figured it out.
Thanks all.