Question

# Molality of the 18 M ${{H}_{2}}S{{O}_{4}}$ (density = $1.8\text{ gm }{{\text{L}}^{-1}}$ ) is: -(a)- 36 mol/kg(b)- 200 mol/kg(c)- 500 mol/kg(d)- 18 mol/kg

Hint: Mass of the solution can be calculated by multiplying the density into the volume of the solution. The molality of the solution is calculated by dividing the moles of the solute to the mass of the solvent in kg.

Molality: The molality of a solution is defined as the number of moles of the solute dissolved in 1kg (1000 g) of the solvent. It is represented by the symbol, ‘m’.
$Molality=\dfrac{\text{Moles of the solute}}{\text{Mass of the solvent in kg}}$
Molarity: The molarity of the solution is defined as the number of moles of the solute present per liter. It is represented by the symbol, M.
$Molarity=\dfrac{\text{Moles of the solute}}{\text{Volume of the solution}}$
Moles of the solute is calculated by dividing the given mass of the solute to the molecular mass of the solute.
$Moles=\dfrac{\text{mass of the solute}}{\text{molar mass of the solute}}$
So, the question says 18 M of ${{H}_{2}}S{{O}_{4}}$ (sulfuric acid)
It means that $1\text{ }L$ of the solution contains $18\text{ }moles$ of ${{H}_{2}}S{{O}_{4}}$ (sulfuric acid)
So, the volume of the solution is $1\text{ }L$ and the mole of the ${{H}_{2}}S{{O}_{4}}$ (sulfuric acid) is$18$ .
The density of the solution is given $1.8\text{ gm }{{\text{L}}^{-1}}$, the mass of the solution can be calculated.

The mass of the solution can be calculated by multiplying the density with the volume of the solution.
Mass of the solution = $1\text{ x }1.8\text{ }=\text{ }1.8\text{ }Kg$
So, the 1 L ${{H}_{2}}S{{O}_{4}}$ is equal to 1.8 kg or 1800 g of solution.
So, in the solution the mass of ${{H}_{2}}S{{O}_{4}}$ is:
Molarity x molar mass of ${{H}_{2}}S{{O}_{4}}$= $18\text{ x }98\text{ }=\text{ }1.764\text{ }kg.$

So, the mass of the solution is 1.8 kg and the mass of ${{H}_{2}}S{{O}_{4}}$ is 1.764 kg, so the mass of the solvent is:
$=1.8-1.764=0.036\text{ kg}$
So, the molality of the solution is:
$Molality=\dfrac{\text{Moles of the solute}}{\text{Mass of the solvent in kg}}=\dfrac{18}{0.036}=500\text{ m}$
Hence the molality of the solution is$500\text{ }m$ .
So, the correct answer is “Option C”.

Note: You should always take care that when molality is calculated the mass of the solvent is taken, not the mass of the solution. Don’t get confused that the molarity and molality of the solution are the same.