Question

Given,$5mL$ of a gaseous hydrocarbon was exposed to 30mL of ${O_2}$. The resultant gas, on cooling, is found to measure $25mL$ of which $10mL$are absorbed by $NaOH$ and the remainder by pyrogallol. Determine molecular formula of hydrocarbon. All measurements are made at constant pressure and temperature.

Answer 1

Hint: We have to write the general formula of hydrocarbon first. Then, we have to write the combustion reaction of hydrocarbons. Then, find the volume of carbon dioxide produced and the volume of oxygen that is being used. From these data, we can get the formula of hydrocarbons.

Complete answer:
We are provided with the following data,
Volume of gaseous hydrocarbon is $5mL$.
Volume of oxygen is $30mL$.
Volume of gas upon cooling is $25mL$.
Volume absorbed by sodium hydroxide is $10mL$.
So, let us keep the formula of hydrocarbon as ${C_x}{H_y}$.
We can write the combustion equation for hydrocarbons as,
${C_x}{H_y}\left( g \right) + \left( {x + \dfrac{y}{4}} \right){O_2}\left( g \right)\xrightarrow{{}}xC{O_2}\left( g \right) + \dfrac{y}{2}{H_2}O\left( l \right)$
We can say that 1 volume of ${C_x}{H_y}$ reacts with $\left( {x + \dfrac{y}{4}} \right)$ vol of oxygen to form x vol of carbon dioxide.
Five volumes of ${C_x}{H_y}$ reacts with $5\left( {x + \dfrac{y}{4}} \right)$ volumes of oxygen to form 5x volumes of carbon dioxide.
From the data, let us calculate the contraction of volume on adding sodium hydroxide$\left( {25 - 10} \right)mL = 10mL$.
So, we have calculated the contraction of volume on adding sodium hydroxide as $10mL$. From this, we can now calculate the volume of carbon dioxide that is formed.
The volume of carbon dioxide produced is calculated as,
$5x = 10$
$x = 2mL$
We have calculated the volume of carbon dioxide produced as $2mL$.
The volume of oxygen that is left is $15mL$.
We can calculate the volume of oxygen used as,
${\text{Volume of oxygen used}} = 30 - 15 = 15mL$
So, we have calculated the amount of oxygen as $15mL$.
Let us determine the formula of hydrocarbon.
$5\left( {x + \dfrac{y}{4}} \right) = 15$
(or)
$4x + y = 3 \times 4$
The value of y is calculated as,
$y = 12 - 4x = 4$
We have calculated the value of y as $4$.
From the value of y, let us now calculate the value of x.
$4x + y = 3 \times 4$
On substitute the y value we get,
$4\left( x \right) + 4 = 12$
On simplification we get,
$x = 2$
We have calculated the value of x as $8$.
So, the formula of hydrocarbon is determined as ${C_2}{H_4}$.

Note:
We have to know that audiometric method is a method for obtaining the molecular formula of gaseous hydrocarbon without percent composition (or) molecular mass. When using this method to obtain the molecular formula, we have to first determine the volume of gaseous hydrogen which is taken and then determine the volume of oxygen that is used and finally determine the amount (in volume) of carbon dioxide that is produced.