Question

Given,100ml of ethyl alcohol is made up to a litre with distilled water. If the density of ${{C}_{2}}{{H}_{5}}OH$ is $0.46\,gr/mL$. Then its molality is:
A. 0.55 m
B. 1.11 m
C. 2.22 m
D. 3.33 m

Answer 1

Hint: In order to use the formula of molality, the weight of the solvent, in this case, water is required. Obtain the weight of the solvent by finding the volume of the water in the solution and density.

Complete answer:
Let us learn about a method by which concentrations are expressed in chemistry, called molality. In molality, the number of moles of the solute are measured with respect to the mass of the solvent. It is the number of moles present per 1kg or 1000 grams of the solvent. In our case, ethyl alcohol is the solute, as it is present in low concentration and distilled water is the solvent. Molality is represented by the unit “m”. The formula of molality is represented by:
$molality=\dfrac{given\,mass}{molar\,mass}\times \dfrac{1000}{mass\,of\,solvent(gm)\,}$……………( i )
Let us find out the moles of ethanol, for which we need the mass of ethanol. Now as volume and density are given, we can find out the mass as
$mass=volume\times density$
So,
$mass=100mL\times 0.46g/mL=46g$
So, the mass of ethanol is 46g, with which we will find out the moles:
$moles=\dfrac{given\,mass}{molar\,mass}=\dfrac{46g}{46g/mol}=1mol$
Again, from the mass-volume-density relation, we get the mass of water as
$mas{{s}_{{{H}_{2}}O}}=vol\times density=900mL\times 1g/mL=900g=0.9kg$
So, the final molality of the ethanol can be obtained from relation ( i ). By substituting the values in the desired equation, we get the value of molality as:
$\begin{align}
  & molality=\dfrac{moles\,of\,ethanol}{mass\,of\,{{H}_{2}}O(kg)}=\dfrac{1\,mol}{0.9kg}=\dfrac{10}{9}m=1.11m \\
 & \\
\end{align}$

So, we get the value of molality as 1.11 m, which gives us option B as our correct answer.

Note:
Molality is a better term to express concentration than molality. It is so because when temperature changes, the volume also changes but molality does not change as it temperature can’t change mass, which molality depends upon.