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Question: If relative decrease in vapour pressure is 0.4 for a solution containing 1 mole NaCl in 3 moles of \...

If relative decrease in vapour pressure is 0.4 for a solution containing 1 mole NaCl in 3 moles of H2O{H_2}O, then %\% ionization of NaCl is
A. 60%60\%
B. 80%80\%
C. 40%40\%
D. 100%100\%

Explanation

Solution

Since the relative decrease in the vapour pressure is given in the question and we also know the relative decrease in the vapour pressure equals p0−psp0\dfrac{{{p^0} - {p^s}}}{{{p^0}}}. We will find the value of Van’t hoff factor ‘i’. Now as NaCl will be dissociated into Na+N{a^ + } and Cl−C{l^ - }, so n will be equals 2. Now that we know ‘i’ and ‘n’, we will find the degree of dissociation/ionisation, α\alpha .

Complete step by step answer:
Relative decrease in the vapour pressure is given by =p0−psp0=0.4 = \dfrac{{{p^0} - {p^s}}}{{{p^0}}} = 0.4
Since, p0−psp0=insoluteinsolute+insolvant\dfrac{{{p^0} - {p^s}}}{{{p^0}}} = \dfrac{{i{n_{solute}}}}{{i{n_{solute}} + i{n_{solvant}}}}
Where, i = Van’t hoff factor
Because NaCl will be dissociated into Na+N{a^ + } and Cl−C{l^ - }
NaCl→Na++Cl−NaCl \to N{a^ + } + C{l^ - }
p0−psp0=insoluteinsolute+insolvant\dfrac{{{p^0} - {p^s}}}{{{p^0}}} = \dfrac{{i{n_{solute}}}}{{i{n_{solute}} + i{n_{solvant}}}}
⇒0.4=i(1)i(1)+3i\Rightarrow 0.4 = \dfrac{{i(1)}}{{i(1) + 3i}}
⇒0.4i+1.2i=i\Rightarrow 0.4i + 1.2i = i
⇒1.6i=i\Rightarrow 1.6i = i
⇒0.6i=1\Rightarrow 0.6i = 1
⇒i=1.6\Rightarrow i = 1.6
Since, n=2n = 2 (n = number of dissociated or associated particles). In this case it will be dissociated particles.
We know, α=i−1n−1 \alpha = \dfrac{{i - 1}}{{n - 1}} (for dissociation)
α=1−i1−1n\alpha = \dfrac{{1 - i}}{{1 - \dfrac{1}{n}}} (for association)
⇒α=1.6−11.1\Rightarrow \alpha = \dfrac{{1.6 - 1}}{{1.1}}
⇒α=0.6\Rightarrow \alpha = 0.6
⇒α%=60%\Rightarrow \alpha \% = 60\%
So, the %\% ionization of NaCl is 60%60\%

Therefore, the correct answer is option (A).

Note: The degree of dissociation is the phenomenon of generating current that carries free ions, which get dissociated from the fraction of solute at a given concentration. It is represented by the symbol. The ratio of the actual concentration of the particles produced (solute + solvent) when the substance is dissolved and the concentration of a substance (solute) as calculated from its mass is the van 't hoff factor.