Question

22.22 gram of urea was dissolved in 300 grams of water. Calculate the number of moles of urea and molality of urea solution. [Given Molar mass of urea = $60\; grams\;mol^{-1}$]

Answer 1

Hint: Molality is defined as the number moles of a solute contained in a kilogram of a solvent. The SI unit of molality is mol/kg.

Formula used: \[\begin{align}
& Molality=\dfrac{Mass\,of\,salute}{Mass\,of\,solvent\,in\,kg} \\
\end{align}\]

Complete answer:
Given,
Mass of urea = 22.22g
Mass of water = 300gm
Molar mass of urea = 60g/mole
Now, we have to find the moles of urea,
Number of moles of urea
\[\begin{align}

&=\dfrac{Mass\,of\,urea}{Molar\,mass\,of\,urea} \\

&=\dfrac{22.22}{60} \\

&=0.370 mol \\
\end{align}\]
Therefore, the number of moles of urea = 0.370 mol
We have calculated the moles of urea and mass of solvent is given as,
Mass of solvent = 300 grams
Applying the formula of Molality,
\[\begin{align}
& Molality(m)=\dfrac{Moles\,of\,urea}{Mass\,of\,water\,(in\,kg)} \\

& Molality(m)=\dfrac{0.370\times 1000}{300} \\
& Molality(m)=1.23 mol/kg \\
\end{align}\]
Thus Molality of urea solution = 1.23 mol/kg

Note: Molality and Molarity both are different so don’t confuse between them.
Molarity is the number of moles of a substance per litre of a solution. A capital M signifies solutions labelled with molar concentration. A 1.0M solution contains 1mole of solute per litre of solution. Molality is the number of solvent moles per kilogram.