Question

An organic compound of molar mass greater than $100$ contains only C, H and N. The percentage of C is 6 times that of H while the sum of percentages of C and H is 1.5 times that of N. What is the least molar mass of the compounds?

• A. $175$ g/mol
• B. $140$ g/mol
• C. $105$ g/mol
• D. $210$ g/mol

Answer 1

The correct option is B $140$ g/mol

Let us assume $\text{percent of}Hasx\%$,
$\therefore \text{Percent of}Cis6x\%$
As per question $\%C+\%H=1.5\left(\%N\right)$
$\therefore \text{Percent of}Nis\frac{14}{3}x\%$
Assuming $100$ g of the total compound,
Mass of $H$ is $x$ g $\Rightarrow$ moles of $H$ is $x$ mol
Mass of $C$ is $6x$ g $\Rightarrow$ moles of $C$ is $\frac{x}{2}$ mol
Mass of $N$ is $\frac{14x}{3}$ g $\Rightarrow$ moles of $N$ is $\frac{x}{3}$ mol
Taking simplest mole ratio of all three i.e. $C:H:N$ comes out to be $\frac{x}{2}:x:\frac{x}{3}$.
On simplifying it comes out to be $3:6:2$
Empirical formula: $C_3{H}_6{N}_2$
Empirical mass = $70g$
Since the molar mass is greater than 100, least mass would have the formula (on multiplying empirical formula by 2)
$C_6{H}_{12}{N}_4$, whose molar mass is 140 g i.e. greater than 100 g.