Question

The density of 3M solution of sodium thiosulphate ($N{a}_2{S}_2{O}_3$) is 1.56g/mL. Calculate
(A).amount of $N{a}_2{S}_2{O}_{3}in\mathrm{\%}{\displaystyle \frac{w}{w}}$
(B).mole fraction of $N{a}_2{S}_2{O}_3$
(C).Molality of $N{a}^{+}$and $S_2{O_3}^{-2}$ions

Answer 1

Hint: Molality is defined as the number of moles in one kilogram of a solvent. Mole fraction of a component in a solution is the number of moles of that constituent divided by total moles in solution.

Complete step by step answer:
For our convenience, let the volume of the solution be 1L = 1000mL.
Therefore,
Molarity of a constituent = ${\displaystyle \frac{No.ofmolesofthesameconstituent}{Volumeofsolution(inL)}}$
     3 = ${\displaystyle \frac{No.ofmolesofN{a}_2{S}_2{O}_3}{1}}$
     No. of moles of $N{a}_2{S}_2{O}_3$ = 3
Now,
     Mass of $N{a}_2{S}_2{O}_3$= 3158g = 474g

And,
     Density of solution = 1.56g/mL
Density of solution = ${\displaystyle \frac{Massofsolution}{Volumeofsolution}}$
1.56 = ${\displaystyle \frac{Massofsolution(ingms)}{1000}}$
Mass of solution = 1560g

Therefore,
Amount of $N{a}_2{S}_2{O}_3$ in $$

Now,
Mass of solute = (1560-474) g
          = 1086 g

Molecular weight of solute (water) = 18 g/mole

So, the moles of solute = ${\displaystyle \frac{1086}{18}}$
               = 60.83 moles
Hence, mole fraction of $N{a}_2{S}_2{O}_3$ = ${\displaystyle \frac{3}{3+60.83}}$
                    = 0.046
And, Molality of solution = ${\displaystyle \frac{Molesofsolution}{Weightofsolvent(inkg)}}$
 Molality of solution = ${\displaystyle \frac{3}{1.086}}$
 Molality of solution = 2.76m

Now,
$N{a}_2{S}_2{O}_3\to 2N{a}^{+}+S_2{O_3}^{-2}$
Hence, the molality of $N{a}^{+}$= 2 Molality of $N{a}_2{S}_2{O}_3$
And the molality of $S_2{O_3}^{-2}$= Molality of $N{a}_2{S}_2{O}_3$

Therefore,
the molality of $N{a}^{+}$= 2 2.76m
          = 5.52m
And
     the molality of $S_2{O_3}^{-2}$= 2.76m

Hence, concluding
amount of $N{a}_2{S}_2{O}_3$ in % ${\displaystyle \frac{w}{w}}$= 30.38\%
mole fraction of $N{a}_2{S}_2{O}_3$ = 0.046
Molality of $N{a}^{+}$and $S_2{O_3}^{-2}$ ions = 2.76m

Note: A student can confuse between molality and molarity of a solution. Both are concentration terms. Molarity is measured in ${\displaystyle \frac{mol}{L}}$while molality is measured in ${\displaystyle \frac{mol}{kg}}$.