Answer to Question #159194 in General Chemistry for dale

Question

A given aqueous solution has a density of x g/mL and y% solute by mass. Derive the mathematical equation relating the molarity of the solution, M, to the molality of the solution,m

Answer 1

Molarity= moles of solute/litres of solution

Molarity= moles of solute/1000ml of solution

Now, recall that

Mole= mass/molar mass

Molarity= mass/molar mass ÷ 1000ml

Molarity = Mass/molar mass x1/1000ml

Molarity= mass/1000ml × 1/molar mass

Making mass the subject of the formula

Mass= molarity x molar mass x 1000ml---------------(eq1)

Also,

Molality= mass of solute/1000g solvent

Making mass the subject of the formula

Mass= molality x 1000g------(eq2)

Replace eq1 in eq2

Molarity x molar mass 1000ml= molality x 1000g

Molarity= molality/molar mass x 1000g/1000ml

molarity= molality/molar mass x mass of solvent (g)/volume of solution(ml)