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Question

Answers

(a)- 36 mol/kg

(b)- 200 mol/kg

(c)- 500 mol/kg

(d)- 18 mol/kg

Answer
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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\[500\text{ }m\] .