Question

40 ml of a hydrocarbon undergoes combustion in 260 ml of oxygen and gives 160 ml of carbon dioxide. If all gases are measured under similar conditions of temperature and pressure, the formula of hydrocarbon is:
A. \[{C_3}{H_8}\]
B. \[{C_4}{H_8}\]
C. \[{C_6}{H_{14}}\]
D. \[{C_4}{H_{10}}\]

Answer 1

Hint: Volume and moles are proportional at steady-state conditions (STP), i.e., Constant volume and pressure. Firstly, find the required reaction and then solve accordingly to find the required solution.

Complete Step by Step Solution:
The combustion reaction is given by:
\[\;{C_X}{H_Y} + (x + \dfrac{y}{4}){O_2} \to xC{O_2} + \dfrac{y}{2}{H_2}O.\]

Volume and moles are proportional at steady-state conditions (STP), i.e., Constant volume and pressure
6.5 moles of oxygen will be needed to burn one mole of hydrocarbon.
This will produce 4 moles of carbon dioxide.
Thus, there are four carbon atoms in the molecular formula.
\[x + \dfrac{y}{4} = 6.5\]
\[\therefore y = 10\]
Thus, the molecular formula consists of 10 Hydrogen atoms.

4 moles of the 6.5 moles of oxygen will react with the carbon in the air to create 4 moles of carbon dioxide.
The remaining 2.5 moles of oxygen will mix with 10 moles of hydrogen atoms (from the hydrocarbon) to generate 5 moles of water.
The hydrocarbon is \[{C_4}{H_{10}}\]​ and the combustion reaction is
\[{C_4}{H_{10}} + 6.5{O_2} \to 4C{O_2} + 5{H_2}0\]
Hence, the correct answer is option D.

Additional information: The majority of crude oil, refined petroleum hydrocarbons (such as gasoline, diesel, kerosene, fuel oil, and lubricating oil), coal tar, creosote, dyestuff, and pyrolysis waste products are hydrocarbons, which are compounds made solely of carbon and hydrogen.

Note: In general, combustion is a provided or outgoing exothermic process, which indicates that energy is released. Typically, a combustion process releases heat and light.