Question

Calculate the $$ degree of dissociation of electrolyte $X{{Y}_{2}}$ (Normal mol mass$=164$) in water if the observed molar mass by measuring elevation in boiling point is $65.6$?
A.25
B.65
C.45
D.75

Answer 1

Before talking about the answer, you should know how to calculate total number of moles, and the conversion of degree of dissociation into percentage of degree of dissociation. You should have an idea about the degree of dissociation which is calculated from dissociated moles per initial moles.
Formula Used:
$i=\dfrac{N.M}{O.M}$
Where, $i$ is the van't hoff factor
$N.M$ is the normal molar mass
$O.M$ is the observed molar mass

Complete step by step answer:
$\underset{1}{\mathop{X{{Y}_{2}}}}\,\rightleftharpoons \underset{0}{\mathop{{{X}^{2+}}}}\,+\underset{0}{\mathop{2{{Y}^{-}}}}\,$(with initial number of moles)
At equilibrium,
$1-\alpha$ $\alpha$ $2\alpha$
where, $\alpha$ is the degree of dissociation.
Therefore, total number of moles is,
$1-\alpha +\alpha +2\alpha \\\ \Rightarrow 1+2\alpha \\\$
$i=\dfrac{Normal{ }M.M}{Observed{ }M.M}=\dfrac{1+2\alpha }{1}=\dfrac{164}{65.6}$
Here, $i$ is the total number of moles.
$\alpha =0.75$
Percentage of degree of dissociation, $(\%\alpha )=75$ .
Hence, the correct option is D. $75$.

Additional information:
-The degree of dissociation is defined as a phenomenon of generating current carrying free ions, that are dissociated from the fraction of solute at a given concentration. It is denoted with a Greek symbol, that is, $\alpha$ .
-Degree of dissociation is also calculated from dissociated moles per initial moles.
$\alpha =\dfrac{x}{a}$
where, $x$ is the dissociated number of moles and $a$ is the initial number of moles.
Important points to remember:
-Degree of dissociation is only used in the decomposition reaction.
-If initial moles are not given, then take initial moles $(a)$ equal to $1$ .
-When degree of dissociation $(\alpha )\le 0.05$ or $5$ , then consider $1-\alpha$ nearly equal to $1$
-Decomposition reaction is defined as a reaction where a compound breaks down into two or more simpler substances. Let us see an example,
$AB\to A+B$
-Moles are defined as the unit of measurement for atoms, ions, and molecules. Hence, one mole is equal to $6.022\times {{10}^{23}}$ , which is Avogadro's number.
-Initially, some number of moles is present in reactants, not products. But as a chemical reaction proceeds, reactants start forming the products.

Note: Here, $i$ is the van't hoff factor.
-The van't hoff is slightly less than its calculated value. If the concentration is high then the ionization value is low because two opposing are colliding.
-Van't hoff factor is used to measure the effect of solute on colligative properties.
-At equilibrium, we will take $2\alpha$ , not only one $\alpha$ because stoichiometry of $4$ is $2$ . -Therefore, it will be $2\alpha$. Stoichiometry plays a very important role in a chemical reaction and also in the formation of products and reactants.