Calculate Molality of 27% H2SO4 Solution

[fishingspree2]

Homework Statement

Find the molality of a sulfuric acid solution which contains 27,0% by mass of H₂SO₄ and a density of 1,198 g/mL

Homework Equations

molality = moles of solvent / mass of H₂SO₄ (kg)

The Attempt at a Solution

If we have 1kg of the solution, then we have 0,270 kg of H₂SO₄
We also have 1 - 0,270 = 0,730 kg of water

If one mole of water weighs 18 grams and we have 730 grams of water, then we have (730/18) moles of water.

molality = moles of solvent / mass of H₂SO₄ (kg)
= (730/18) moles / 0,270 kg of H₂SO₄
= 150,2 moles/kg

This is not the correct answer, the correct answer is 3,78
What to do??
Thank you

 

[hage567]

I'm no chemist, but I think molality is moles of solute per kg of solvent. Look this up in your textbook to make sure you are starting with the right definitions.

 

[jqnsmart]

I see...your problem in the equation for molality. Molality is equal to moles of solute over one kilogram of solvent. I think you flipped your equation

 

[link2110]

my definition of moles is things per amount of liquid (solvent)
so the calculation formula for molarity is M = mol/L
that means Molarity = moles over Volume in liters

 

[link2110]

so your equation would be M = mol/L, but you have it in Kg. This is not a problem because one gram of water is approximately equal to one ml of water. So if you have one L of water, that would mean that 27% of it is H₂SO₄. In one liter of water there are 1000 ml of water, so that means that 27% of 1000 is 270. That means that there are 270 ml of H₄SO_{4 (aq)}. There are 1.198g/ml, so there are 323.46 grams of H₂SO₄. The molar mass of H₂SO₄ is 98 grams per mole, so to get moles of H₂SO₄, you divide the grams by the molar mass. That means that there are 323.46/98 = 3.3 moles of H₂SO₄. Now you do the rest, so i don't tell you the whole thing. =D

 

[Borek]

my definition of moles is things per amount of liquid (solvent)
so the calculation formula for molarity is M = mol/L
that means Molarity = moles over Volume in liters

Question asks for molality, not molarity. Thus both your posts are unfortunately off.

Additionally, it is 27% w/w solution, so 1000 mL of solution doesn't contain 270 mL of sulfuric acid, but 1 kg of solution contains 270 g of sulfuric acid. That is huge difference.

 

[link2110]

oh i thought it was a spelling mistake