How to convert from molality to molarity?


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I am having difficulty converting molality to molarity.  The problem involves an aqueous solution of ammonium sulfate (NH4)2SO4 with a molality of 3.11.  The density of the solution is 1.23 g/mL.  The Molar mass of ammonium sulfate is 132g/mol.  Given these numbers how would I find the molarity?

Any input will be greatly appreciated.  Thank you.

The problem of converting molality to molarity (and vice versa) arises because molarity is the ratio of moles of solute to LITERS of SOLUTION, whereas molality is the ratio of moles of solute to KILOGRAMS OF SOLVENT.  In general chemistry, molarity is much more useful, but molality is useful when dealing with the colligative properties such as boiling point elevation and freezing point depression.

Molality is defined as moles of solute per kilogram of solvent.  In the problem you're given that the molality of the solution is 3.11 moles of (NH4)2SO4 per kilogram of water.

To find the molarity we need to find the number of moles of solute per Liter of solution (Molarity=moles solute/Liter solution)

The good news is that you already know the moles of solute (3.11 moles)

What you are left with is having to find the volume that the solute is dissolved in.  To do that, you must remember that the solution is the total of the solute and the solvent.  If you find the total mass of the solution (which will equal the mass of the solute and the mass of the solvent (1 kg)),  you can then use the density to find the volume.

So, first calculate the mass of the solute:  mass of (NH4)2SO4 = moles  x Molar mass
Find the total mass of the solution:    mass of (NH4)2SO4 + 1000 g of water

Rearrange the density formula to solve for volume:  volume =  mass of solution / density

Convert the volume of the solution into liters

Plug your volume into the molarity formula:  Molarity = moles of solute / volume of the solution