The density of a $3 ext{ M}$ sodium thiosulphate ($ ext{Na}_2 ext{S}_2 ext{O}_3$) solution is $

Question

The density of a $3 	ext{ M}$ sodium thiosulphate ($	ext{Na}_2	ext{S}_2	ext{O}_3$) solution is $1.25 	ext{ g/mL}$. Which of the following statements is/are CORRECT? (Molar mass of $	ext{Na}_2	ext{S}_2	ext{O}_3 = 158 	ext{ g/mol}$)

Professor PC Thomas Classes · Answer

Consider $1 	ext{ L}$ ($1000 	ext{ mL}$) of the solution. 
Mass of solution $= 1000 	imes 1.25 = 1250 	ext{ g}$. 
Moles of solute $= 3 	ext{ mol}$. Mass of solute $= 3 	imes 158 = 474 	ext{ g}$. 
Mass of solvent (water) $= 1250 - 474 = 776 	ext{ g} = 0.776 	ext{ kg}$. 
Mass $\% = (474 / 1250) 	imes 100 = 37.92\%$ (A is correct). 
Molality of $	ext{Na}_2	ext{S}_2	ext{O}_3 = 3 / 0.776 = 3.865 	ext{ m}$. 
Molality of $	ext{Na}^+ = 2 	imes 3.865 = 7.73 	ext{ m}$ (C is correct). 
Molality of $	ext{S}_2	ext{O}_3^{2-} = 3.865 	ext{ m}$ (D is correct). 
Moles of water $= 776 / 18 = 43.11 	ext{ mol}$. 
Mole fraction of $	ext{Na}_2	ext{S}_2	ext{O}_3 = 3 / (3 + 43.11) = 3 / 46.11 \approx 0.065$ (B is correct).