The b.p. of a solution of 5g of sulphur in 100g of carbon disulphide is 0.476^(@) above that of pure solvent. Determine the molecular formula of sulphur in this solvent. The b.p. of pure carbon disulphide is 46.30^(@)C and its heat of vaporisation is 84.1 calories per gram.

The b.p. of a solution of 5g of sulphur in 100g of carbon disulphide i

1.	The b.p. of a solution of 5g of sulphur in 100g of carbon disulphide is 0.476^(@) above that of pure solvent. Determine the molecular formula of sulphur in this solvent. The b.p. of pure carbon disulphide is 46.30^(@)C and its heat of vaporisation is 84.1 calories per gram.
Answer» Solution :We have, `K_(b)=(RT^(2))/(1000l_(v))=(2xx(46.30+272)^(2))/(1000xx84.1)=2.425` `:.m=(DeltaT_(b))/(K_(b))=(0.476)/(2.425)` And also `m=("moles of solute")/("wt.of solvent in grams")xx1000` `=(5)/(M)xx(1000)/(100)=(50)/(M)` where M is the mol. wt. of SULPHUR Thus, `(50)/(M)=(0.476)/(2.425)`, `M=255` Since the atomic wt. of sulphur is 32 and its mol.wt. is `255`, therefore, number of sulphur atoms associated to form a SINGLE molecule is `(255)/(32)=7.96` , i.e., 8. Hence the formula is `S_(8)`.