Calculating the Volume of a 40% Solution

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In summary: 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.In summary,The statement "Since the density is 1320 g/L then for every L of solution there is 320 grams of solute" is approximate.The correct answer is 24.1 mL.
  • #1
barryj
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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
 
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  • #2
The correct answer is 24.1 mL Where is my logic incorrect??
 
  • #3
barryj said:
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
 
  • #4
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.
 
  • #5
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?
 
  • #6
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?
 
  • #7
Chestermiller said:
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.
mjc123 said:
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.
 
  • #8
barryj said:
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.
mjc123 said:
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.
 
  • #9
barryj said:
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.
 
  • #10
barryj said:
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
 
  • #11
The ole brain has figured it out.
Thanks all.
 

Related to Calculating the Volume of a 40% Solution

1. How do you calculate the volume of a 40% solution?

To calculate the volume of a 40% solution, you need to know the concentration of the solution and the total volume of the solution. Then, you can use the formula: Volume of Solution = (Concentration / 100) * Total Volume.

2. What is the concentration of a 40% solution?

The concentration of a 40% solution means that it contains 40 grams of solute per 100 milliliters of solution. This is known as the solute-to-solvent ratio and is often represented as a percentage.

3. Can you give an example of calculating the volume of a 40% solution?

Sure, let's say you have a 40% solution of saltwater and you want to know the volume of the solution. If you have 100 mL of this solution, then the volume of salt in the solution would be (40 / 100) * 100 = 40 mL. This means that the volume of water in the solution would be 100 - 40 = 60 mL.

4. How is the volume of a 40% solution different from the concentration?

The volume of a solution refers to the amount of space it occupies, while the concentration refers to the amount of solute in a given amount of solution. So, the volume of a 40% solution may vary depending on the total volume of the solution, while the concentration will always be 40% regardless of the volume.

5. Can the volume of a 40% solution change?

Yes, the volume of a 40% solution can change depending on the amount of solute and solvent added or removed from the solution. However, the concentration of the solution will remain constant at 40% as long as the solute-to-solvent ratio remains the same.

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