Question

100ml of ethyl alcohol [d=0.92g/ml] and 900 ml of water [d=1g/ml] are mixed to form 1 lit solution. The Molarity and molality of the resulting solution are
1) 2M and 2m
2) 2M and 2.22m
3) 2.2M and 1.1m
4) 2M and 1m

Answer 1

Hint: The answer lies in the fact that includes basic formulas to calculate molarity and molality according to their definitions which includes substituting density and volume of solution provided in question.

Complete step by step solution:
By the lessons in the chemistry we know that molarity and molality of the solution is given by the formula respectively as,
\[Molarity=\dfrac{no.of moles}{volume}\]
\[Molality=\dfrac{no.of moles}{weight of solvent(kg)}\]
Now, mass of ethyl alcohol present is given by,
\[\begin{align}
& Mass=density\times volume \\
& \Rightarrow Mass=100\times 0.92=92g \\
\end{align}\]
Therefore, number of moles of ethyl alcohol= given mass/ mass of alcohol.
Thus, Moles of ethyl alcohol$=\dfrac{92}{46}=2$moles.
Thus, molarity$=\dfrac{2}{1}$
$\Rightarrow $molarity=2M
Similarly, molality is the ratio of number of moles of solute in 1 kg of solvent and we know that 900g of water have 92g of ethyl alcohol by previous calculation.
Thus, in 1g of water 92/900g of ethyl alcohol is present.
Therefore, in 12000g of water $\dfrac{92}{900}\times 1000$g of ethyl alcohol is present.
\[=102.22g\]
$\Rightarrow moles=\dfrac{102.22}{46}$
Molality of solution=2.22m
Thus, the correct option is B.

Additional information:
There is intermolecular hydrogen bonding in both water and an alcohol. After we mix these two solutions together, the extent of hydrogen bonding decreases in mixture and in turn intermolecular forces decrease which shows positive deviation from Rault’s law. Thus, the volume of mixture will be greater than zero and thus total volume of mixture will be slightly greater than the calculated ones.

Note: There can be a chance of mixing up of formulas of molarity and molality during the calculation which deviates the answer from actual. Care must be taken so that the answers do not go wrong as some options in MCQ’s may be even one of your wrong answers.