Question

A certain organic substance used as a solvent in many reactions contains carbon, hydrogen, oxygen and
sulphur Weight % of hydrogen in the compound is 7.7. The weight ratio C:O:S= 3.2: 4. What is the
least possible molar mass of the compound ?
(A) 86
(B) 63
(C) 94
(D) 78​

Answer 1

Answer:

The correct answer is option D.

Explanation:

Suppose in 100 gram of organic compound, 7.7 % is hydrogen.

And Carbon , oxygen and sulfur are ratio of 3:2:4.

Mass of hydrogen in organic compound = $\frac{7.7}{100}\times 100=7.7 g$

Let the mass of carbon, oxygen and sulfur be 3x,2x and 4x respectively.

7.7 g+3x+2x+4x=100 g

x = 10.25 g

Mass of carbon = 3x = 3 × 10.25 g =30.75 g

Moles of carbon =$\frac{30.75 g}{12 g/mol}=2.5625 mol$

Mass of oxygen = 2x = 2 × 10.25 g =20.5 g

Moles of oxygen =$\frac{20.5 g}{16 g/mol}=1.28125 mol$

Mass of sulfur = 4x = 4 × 10.25 g =41 g

Moles of sulfur =$\frac{41 g}{32 g/mol}=1.28125 mol$

Moles of hydrogen =$\frac{7.7 g}{1 g/mol}=7.7 mol$

Least possible molecular formula will be equivalent to the empirical formula of this organic substance.

Empirical formula of the compound can be determined by individually dividing the moles of all element with smallest number of moles.

Carbon =$\frac{2.5625 mol}{1.28125 mol}=2$

Hydrogen =$\frac{7.7 mol}{1.28125 mol}=6$

Oxygen =$\frac{1.28125 mol}{1.28125 mol}=1$

sulfur=$\frac{1.28125 mol}{1.28125 mol}=1$

The empirical formula or molecular formula the compound is :

$C_2H_6OS$

Molar mass of the molecular formula is:

2 × 12 + 6 × 1+ 1 × 16 + 1 × 32 = 78 g/mol