Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

\(10 \mathrm{~mL}\) of propane are mixed with \(70 \mathrm{~mL}\) of oxygen and exploded. What would be the volume of residual gases after explosion and after exposure of the residual gases to alkali? All volume measurements are made at the same temperature and pressure. (a) \(55 \mathrm{~mL}, 25 \mathrm{~mL}\) (b) \(40 \mathrm{~mL}, 15 \mathrm{~mL}\) (c) \(50 \mathrm{~mL}, 20 \mathrm{~mL}\) (d) \(35 \mathrm{~mL}, 40 \mathrm{~mL}\)

Step-by-Step Solution

Answer

The volume of residual gases is 50 mL, reducing to 20 mL after alkali exposure.

Step 1: Write the Balanced Equation

The combustion of propane, \[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]This equation shows that 1 mole of propane reacts with 5 moles of oxygen to produce 3 moles of carbon dioxide and 4 moles of water.

Step 2: Determine the Limiting Reactant

We have \(10 \text{ mL}\) of propane and \(70 \text{ mL}\) of oxygen. According to the balanced equation, \[1 \text{ mol (or L)} \, \text{C}_3\text{H}_8 \text{ requires } 5 \text{ mols (or L)} \text{O}_2\] Thus, \(10 \text{ mL}\) of propane requires \(50 \text{ mL}\) of oxygen. We have more oxygen (\(70 \text{ mL}\)), so propane is the limiting reactant.

Step 3: Calculate Remaining Oxygen

Since propane is fully consumed, the oxygen used is \(50 \text{ mL}\). Therefore, remaining oxygen:\[ \text{Remaining } \text{O}_2 = 70 \text{ mL} - 50 \text{ mL} = 20 \text{ mL} \]

Step 4: Assess Volume of Residual Gases

The combustion produces water and carbon dioxide, but water as a gas will condense out in regular conditions, leaving only gases. Thus, the final mixture contains the unreacted oxygen and carbon dioxide produced:\[\text{CO}_2 = 3 \times 10 \text{ mL} = 30 \text{ mL}\] Total residual gas volume\:\[\text{Residual gas} = 30 \text{ mL} + 20 \text{ mL} = 50 \text{ mL}\]

Step 5: Exposure to Alkali

Carbon dioxide (\(\text{CO}_2\)) reacts with alkali. If we treat the gas mixture with alkali (which absorbs \(\text{CO}_2\)), only unreacted oxygen remains:\(\text{Residual gas} = 20 \text{ mL}\)

Key Concepts

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that gets completely consumed first, limiting the amount of products formed. It's like running a bake sale where you have a finite amount of flour and sugar. Imagine if your flour runs out before sugar, you can't bake any more cookies, right? This is similar to how a limiting reactant curtails the chemical reaction's progress.

In our propane and oxygen example, we start with 10 mL of propane and 70 mL of oxygen. According to the balanced equation, 1 mL of propane needs 5 mL of oxygen for complete combustion. This means our 10 mL of propane would ideally require 50 mL of oxygen. Since we have more oxygen (70 mL) than needed, propane will be used up first, making it the limiting reactant. Once all the propane is gone, the reaction stops, no matter how much oxygen is left.

Chemical Reaction

A chemical reaction involves transformation of reactants into products through breaking and forming of chemical bonds. In the reaction of propane and oxygen, the process is known as combustion—a type of reaction that usually involves heat and produces carbon dioxide and water.

The balanced chemical equation for propane combustion is:

• \[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]

This equation tells us the proportion in which reactants combine and products are formed. For every 1 mole of propane, 5 moles of oxygen are consumed, resulting in 3 moles of carbon dioxide and 4 moles of water. Hence, maintaining a balance between reactants is key to how much product is ultimately formed. If something is off balance, the excess substance is leftover as residue, which is what we calculated in the problem.

Gas Laws

Gas laws are fundamental principles that describe how gases behave under different conditions of temperature, pressure, and volume. For the combustion of propane, the laws allow us to predict the volume of gases produced and leftover.

In this exercise, all volumes are measured at constant temperature and pressure, simplifying our calculations by keeping conditions ideal as per the ideal gas law. Upon completion of the reaction, water is usually present as vapor, but in regular conditions, it condenses out, leaving us with only the oxygen and carbon dioxide to consider when calculating total gas volume.

Following the reaction, we have 30 mL of carbon dioxide and 20 mL of unreacted oxygen, resulting in 50 mL of total residual gases. If we then treat this with an alkali, this alkali absorbs carbon dioxide, leaving just 20 mL of oxygen. These calculations hinge on understanding how gases interact and change under the constraints defined by gas laws.