Problem 11 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(5 \mathrm{~L}\) of an alkane requires \(25 \mathrm{~L}\) of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is : (a) Isobutane (b) Ethane (c) Butane (d) Propane

Step-by-Step Solution

Answer

The alkane is Propane (option d).

Step 1: Write the Combustion Reaction

The general combustion reaction for an alkane is \( C_nH_{2n+2} + \frac{3n+1}{2} O_2 ightarrow nCO_2 + (n+1)H_2O \). Determine how much oxygen is needed for 1 L of the alkane.

Step 2: Determine Oxygen to Alkane Ratio

Given in the problem, 5 L of the alkane requires 25 L of oxygen, which gives an oxygen to alkane ratio of \( \frac{25}{5} = 5 \). This matches the coefficient of \( O_2 \) in the reaction.

Step 3: Match Ratio with Alkane Formula

Substitute values into \( \frac{3n+1}{2} = 5 \) to find \( n \).\[ \frac{3n+1}{2} = 5 \]Multiply both sides by 2:\[ 3n+1 = 10 \]Subtract 1 from both sides:\[ 3n = 9 \]Divide by 3 to solve for \( n \):\[ n = 3 \]

Step 4: Identify the Alkane

With \( n = 3 \), the alkane is \( C_3H_8 \), which is propane. Therefore, the alkane given in the problem is propane.

Key Concepts

Combustion Reaction

In chemistry, a combustion reaction is a type of chemical reaction where a fuel reacts with an oxidant, often oxygen, to produce heat and light. This process is commonly seen in everyday activities such as burning wood in a fireplace or the combustion of gasoline in car engines. For alkanes, which are hydrocarbons, the combustion reaction leads to the formation of carbon dioxide and water. Alkanes are saturated hydrocarbons with the general formula \( C_nH_{2n+2} \). The complete combustion of an alkane can be represented by the equation:\[ C_nH_{2n+2} + \frac{3n+1}{2} O_2 \rightarrow nCO_2 + (n+1)H_2O \]In the reaction, the alkane combines with oxygen, which is required to completely convert the carbon atoms into carbon dioxide and hydrogen atoms into water. The reaction is exothermic, meaning it releases energy in the form of heat, and is dependent on having an adequate supply of oxygen to ensure complete combustion, avoiding incomplete combustion that would produce carbon monoxide instead.

Stoichiometry

Stoichiometry is an integral part of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the law of conservation of mass where the mass of the reactants must equal the mass of the products. For calculating stoichiometry in a combustion reaction, we rely on the balanced chemical equation. Each component has a stoichiometric coefficient, telling you how many moles of each reactant are required, and how many moles of each product will form.In the case of the given problem, stoichiometry is utilized to determine how much oxygen is needed to completely combust a specific volume of alkane. This is done by comparing stoichiometric coefficients, which for oxygen in the general combustion equation was determined to be 5 times the volume of the alkane based on the reaction equation:\[ \frac{3n+1}{2} = 5 \]Understanding these coefficients helps chemists calculate the exact amounts needed for a reaction without wastage or deficit.

Hydrocarbon Chemistry

Hydrocarbon chemistry primarily deals with the study of hydrocarbons, which are organic compounds consisting entirely of carbon and hydrogen. Alkanes are a significant family within this category, known for their simple single-bonded carbon structure, making them saturated hydrocarbons.Alkanes are generally nonpolar and relatively unreactive due to the strength of the C–H bond, making them stable compounds. However, they react readily with oxygen under the right conditions, leading to combustion reactions.Key types of hydrocarbons include:

• Alkanes: General formula \( C_nH_{2n+2} \), single bond, and saturated.
• Alkenes: General formula \( C_nH_{2n} \), double bond, and unsaturated.
• Alkynes: General formula \( C_nH_{2n-2} \), triple bond, and unsaturated.

Understanding the properties and reactions of these hydrocarbons is essential in various applications, from fuels for combustion engines to the synthesis of everyday chemicals and materials.