I heard someone tell me a formula to convert molarity to molality: M= m(density of solution - 0.001 x M x Mb) where M-molarity, m-molality, Mb-molecular weight of solute. Could you please tell me if the formula is right, stating an example too? Thanks
Yes, that formula is correct.
On the other hand, a solution's molality is defined as moles of solute per kilograms of solvent.
So, let's try to determine how you can use one to get to the other. Let's say that you're dealing with a solution of known density and volume in which you dissolve a known mass of solute,
The solution's molarity will be
The solution's molality will be
You multiply the mass of the solvent by 0.001 to go from grams to kilograms, which is what the equation for molality needs.
Notice that both equations feature the number of moles of solute,
The mass of the solvent can be written as the mass of the solution minus the mass of the solute
The mass of the solution can be written using the solution's volume and density
This means that you have
The mass of the solute can be expressed using its number of moles and molar mass
Divide both sides of the equation by
Now, in order to get the units to match, you actually need to have the density expressed in grams per liter, as opposed to grams per mL.
Do get around this problem, multiply the density by 1000 to get
which is equivalent to
Do a quick unit's test to see if the result makes sense
Here's a quick example. Let's say that you have a 1-L solution of glucose (
According to the formula, you'd have
This is the same result you'd get using the classic approach.