Question

How many grams of ${\text{C}}{{\text{H}}_{\text{3}}}{\text{OH}}$ is needed to make a 0.244 m solution in 400 g of water?
A.3.1240 g
B.0.313 g
C.1639 g
D.97.6 g
E.32 g

Answer 1

Hint: We know that molality is a way of expressing concentration of a solution. Molality is defined as the moles of solute present in 1 kg of solvent. Here, we have to calculate the mass of solute $\left( {{\text{C}}{{\text{H}}_{\text{3}}}{\text{OH}}} \right)$ needed to make 0.244 m solution in 400 g of water.

Complete step by step answer:
The molality (m) of the solution is given as 0.244 m. The mass of solvent is 400 g.
We know the formula of molality, that is,
Molality=$\dfrac{{{\text{Moles}}\,{\text{of}}\,{\text{solute}}}}
{{{\text{Mass}}\,{\text{of}}\,{\text{solvent}}}}$ …… (1)
We know that the moles of solute is,
Moles of solute=$\dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{solute}}}}
{{{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{solute}}}}$
So, equation (1) becomes,
Molality=$\dfrac{{\dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{solute}}}}
{{{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{solute}}}}}}
{{{\text{Mass}}\,{\text{of}}\,{\text{solvent}}}}$
Molar mass of ${\text{C}}{{\text{H}}_{\text{3}}}{\text{OH}}$
=$12 + 4 + 16 = 32\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}$
Mass of solvent=400=$\dfrac{{400}}
{{1000}}\,{\text{kg}}$
Molality=0.244 m
Now, we have to substitute the above values in the formula of molality.
$0.244\, = \dfrac{{\dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{solute}}}}
{{32}}}}
{{\dfrac{{400}}
{{1000}}\,}}$
$ \Rightarrow 0.244\,{\text{mol}}\,\,{\text{k}}{{\text{g}}^{ - 1}} = \dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{solute}}}}
{{32\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}}} \times \dfrac{{1000}}
{{400}}{\text{kg}}$
$ \Rightarrow {\text{Mass}}\,{\text{of}}\,{\text{solute}} = \dfrac{{0.244 \times 32 \times 400}}
{{1000}} = 3.12\,{\text{g}}$
Therefore, the mass of ${\text{C}}{{\text{H}}_{\text{3}}}{\text{OH}}$ required to is to make a 0.244 m solution in 400 g of water is 3.12 g.

So, the correct answer is Option A.

Additional Information:
It is to be noted that molality and molarity are not the same. Molarity is also a way of expressing concentration of a solution. It is defined as the number of moles of solute present in 1 litre of solution. But molality is measured considering the mass of solvent. Molarity changes with the change in temperature but molality value does not change with the temperature.

Note: Always remember that molality is regarded better than molarity for expressing the concentration of a solution because its value does not change. But there is one disadvantage also since molality can be determined only if the density of the solution is known.