Question

In an organic compound of molar mass greater than 100 containing only carbon hydrogen and nitrogen the percentage of carbon and hydrogen is 1.5 times the percentage of nitrogen what is the least molar mass? ​

Answer 1

answer : option (b) 140

explanation : your question is incomplete. A complete question is ----> In an organic compound of molar mass greater than 100 containing containing only carbon hydrogen and nitrogen the percentage of carbon 6 times the percentage of hydrogen while the sum of percentage of carbon and hydrogen is 1.5 times the percentage of nitrogen what is the least molar mass?

solution : Let the percentage of hydrogen = x %

then, percentage of carbon = 6x % [ a/c to question]

And then, percentage of nitrogen = (100 - x - 6x) %

1.5 × percentage of nitrogen = percentage of carbon + percentage of hydrogen

or, 1.5 × (100 - x - 6x) % = x% + 6x%

or, 3(100 - 7x) = 7x × 2

or, 300 - 21x = 14x

or, 35x = 300

x = 300/35 = 60/7 %

6x = 360/7 %

and (100 - x - 6x) = 100 - 7x = 100 - 420/7

= 280/7 %

hence, percentage of hydrogen = 60/7 %

percentage of carbon = 360/7 %

and percentage of nitrogen = 280/7 %

percentage mass ratio

H = (60/7)/1 = 60/7

C = (360/7)/12 = 30/7

N = (280/7)/14 = 20/7

now simple ratio of percentage mass ratio :

H : C : N = 60/7 : 30/7 : 20/7 = 6 : 3 : 2

so, empirical formula is C3H6N2

mass of empirical formula = 12 × 3 + 6 × 1 + 14 × 2 = 36 + 6 + 28 = 70 < 100

but we know, molecular formula is integral multiple of empirical formula.

so, molecular formula = n × C3H6N2

to get least value of molar mass but greater than 100, n must be 2

so, chemical formula is C6H12N4

then, molar mass = 2 × 70 = 140g/mol