Question

A Gaseous Alkane is exploded with Oxygen. The volume of $\sf O_{2}$ for complete combustion of alkane to $\sf CO_{2}$ formed is in the ratio 7 : 4. Find the molecular formula of alkane.

Answer 1

Answer:

C2H6 ethane the explanation is in the image

Answer 2

Given :-

A Gaseous Alkane is exploded with Oxygen. The volume of $\sf O_{2}$ for complete combustion of alkane to $\sf CO_{2}$ formed is in the ratio 7 : 4

To Find :-

The molecular formula of alkane

Solution :-

At First , Write the general Equation for the combustion of Alkanes i.e ;

${ \bigstar { \underline { \boxed { \red { \bf { C_{n}H_{2n+2} + { \bigg ( \dfrac{3n+1}{2} } \bigg )O_{2} \longrightarrow n CO_{2} + ( n + 1 ) H_{2}O + ∆ }}}}}{\bigstar}}$

Here , ∆ Represents Energy

Now , As here complete combustion is taking place . So ;

• Volume of ${ \sf { O_{2} = \dfrac{3n + 1}{2} }}$

• Volume of $\sf CO_{2} = n$

Also Given that , ratio of volume of $\sf O_{2} \:\: to \: \: CO_{2}$ = 7 : 4 . Which Implies ;

$\quad \qquad { : \longmapsto { \tt { \dfrac{\dfrac{3n+1}{2}}{n} = \dfrac{7}{4} }}}$

$\quad \qquad { : \longmapsto { \tt \dfrac{3n + 1}{2} × \dfrac{1}{n} = \dfrac{7}{4} }}$

$\quad \qquad { : \longmapsto { \tt \dfrac{3n+1}{n} = \dfrac{7}{4} × 2 }}$

Now , Seperate LCM of LHS ;

$\quad \qquad { : \longmapsto { \tt \dfrac{3n}{n} + \dfrac{1}{n} = \dfrac{7}{2} }}$

$\quad \qquad { : \longmapsto { \tt 3 + \dfrac{1}{n} = \dfrac{7}{2} }}$

Transpose 3 to RHS ;

$\quad \qquad { : \longmapsto { \tt \dfrac{1}{n} = \dfrac{7}{2} - 3 }}$

$\quad \qquad { : \longmapsto { \tt \dfrac{1}{n} = \dfrac{7 - 6}{2} }}$

$\quad \qquad { : \longmapsto { \tt \dfrac{1}{n} = \dfrac{1}{2} }}$

Now , Reciprocal both sides ;

$\quad \qquad { \bigstar { \underline { \boxed { \red { { \bf \therefore n = 2 }}}}}{\bigstar}}$

Now , Put value of " n " in the general formula of alkane we have ;

$\quad \qquad { \sf { C_{n} H_{2n+2} }}$

$\quad \qquad { \sf : \longmapsto { C_{2} H_{2 × 2 + 2} }}$

$\quad \qquad { \sf : \longmapsto { C_{2} H_{4+2} = \:\: C_{2} H_{6} }}$

${ \bigstar { \underline { \boxed { \red { \bf { \therefore Required \:\: Compound \:\: = C_{2} H_{6} = \: Ethane }}}}}}{\bigstar}$