Question

If the density of methanol is ${\text{0}}{\text{.8kg}}{{\text{L}}^{{\text{ - 1}}}}$ , what is the volume needed for making $2.5{\text{L}}$ of $0.4{\text{M}}$ solution?
A.${\text{0}}{\text{.4L}}$
B.${\text{4}}{\text{.0L}}$
C.${\text{0}}{\text{.04L}}$
D.${\text{40L}}$

Answer 1

Hint: The term ‘molarity of a solution’ is used to refer to the number of moles of the solute dissolved per litre or ${\text{d}}{{\text{m}}^{\text{3}}}$ of the solution. It is designated by the letter M. From the molarity, the number of moles of the solute can be evaluated. This can be used to determine the mass of the solute which in turn can be used to calculate the volume as density equals mass per unit volume.

Complete step by step answer:
Mathematically, molarity of a solution ‘M’ can be expressed to be equal to the number of moles of solute divided by the volume of the solution in litres.
If ‘n’ is the number of moles of a solute present in V litres of the solution, then,
Molarity $ = \dfrac{{\text{n}}}{{\text{V}}}$
According to the given question, the molarity of the methanol solution is equal to $0.4{\text{M}}$ and the volume of the solution in litres is $2.5{\text{L}}$ . In other words, V is equal to $2.5{\text{L}}$ . Therefore, the number of moles of methanol ‘n’ will be:
$
  0.4 = \dfrac{{\text{n}}}{{2.4}} \\
   \Rightarrow {\text{n}} = 0.4 \times 2.4 \\
   \Rightarrow {\text{n}} = 0.96{\text{moles}} \\
 $
Now, molecular mass of methanol (${\text{C}}{{\text{H}}_{\text{3}}}{\text{OH}}$ ) is
$
   = 12 + 3 \times 1 + 16 + 1 \\
   = 32{\text{g/mol}} \\
 $
We know that the number of moles of a substance is equal to its given weight in grams divided by its molecular mass. Therefore, the weight in grams will be equal to the product of the number of moles and the molecular mass.
Hence, the mass of methanol needed will be
$
   = 0.96{\text{mol}} \times 32{\text{g/mol}} \\
  {\text{ = 30}}{\text{.72g}} \\
 $
Density of methanol is given to be ${\text{0}}{\text{.8kg}}{{\text{L}}^{{\text{ - 1}}}}$ which is equal to $0.8 \times {10^3}{\text{g}}{{\text{L}}^{{\text{ - 1}}}} = 800{\text{g}}{{\text{L}}^{{\text{ - 1}}}}$ .
We know that density is equal to mass by volume and so, volume is equal to mass by density.
Hence, the volume of methanol required
$
   = \dfrac{{30.72{\text{g}}}}{{800{\text{g}}{{\text{L}}^{{\text{ - 1}}}}}} \\
   = 0.0384{\text{L}} \\
   = 0.04{\text{L}} \\
 $

Hence, the correct option is C.

Note:
The term ‘normality of a solution’ is used to refer to the number of gram equivalents of the solute dissolved per litre of the solution. It is designated by the letter N. If the normality was given instead of molarity, then the molarity can be determined from the normality and molarity relation.
Normality $ = $ Molarity $ \times $ Valence factor