Problem 13 - A Complete Resource Book in Chemistry for JEE Main

Question

How many moles of potassium chlorate should be decomposed completely to obtain \(67.2\) litres of oxygen at STP? (a) 1 (b) 2 (c) 3 (d) 4

Step-by-Step Solution

Answer

2 moles of potassium chlorate are required.

Step 1: Understanding the Reaction

The decomposition of potassium chlorate (KCIO3) yields potassium chloride and oxygen gas. The balanced chemical equation is:\[ 2 ext{KClO}_3 ightarrow 2 ext{KCl} + 3 ext{O}_2 \]This equation shows that 2 moles of potassium chlorate produce 3 moles of oxygen.

Step 2: Using Ideal Gas Law Concepts

At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 liters. Therefore, we can use this fact to determine the amount of moles of oxygen produced from the given volume of oxygen gas.

Step 3: Calculate Moles of Oxygen

Given 67.2 liters of oxygen, we find how many moles this represents at STP using the relation where 1 mole is 22.4 liters:\[ ext{Moles of } O_2 = \frac{67.2 ext{ liters}}{22.4 ext{ liters/mole}} = 3 ext{ moles} \]

Step 4: Relate Moles of Oxygen to Potassium Chlorate

From the balanced equation, 3 moles of oxygen are produced by 2 moles of potassium chlorate. Thus, the moles of potassium chlorate needed can be calculated as follows:\[ ext{Moles of } ext{KClO}_3 = \frac{3 ext{ moles of } O_2}{3 ext{ moles of } O_2/2 ext{ moles of } ext{KClO}_3} \approx 2 ext{ moles} \]

Step 5: Final Calculation and Answer

We compute that 2 moles of potassium chlorate are needed to decompose fully to yield 67.2 liters of oxygen gas. Therefore, the correct answer is option (b) 2.

Key Concepts

Balanced Chemical Equations

Balanced chemical equations are central to understanding chemical reactions. In these equations, the number of atoms for each element is the same on both sides of the equation. This balance ensures the law of conservation of mass is upheld, which states that mass cannot be created or destroyed in a chemical reaction.

For the decomposition of potassium chlorate, the balanced equation is:

• 2 KClO extsubscript{3} → 2 KCl + 3 O extsubscript{2}

This equation tells us that two moles of potassium chlorate decompose to form two moles of potassium chloride and three moles of oxygen gas.

Balancing equations involves ensuring that the number of atoms for each element in the reactants equals the number in the products. It's a crucial skill in stoichiometry, allowing us to calculate how much of each substance is involved in a chemical reaction.

Ideal Gas Law

The Ideal Gas Law is a fundamental concept in chemistry that helps us relate the volume, pressure, temperature, and number of moles of a gas. At Standard Temperature and Pressure (STP), which is 0°C and 1 atm, the law simplifies certain calculations.

A key fact derived from the Ideal Gas Law at STP is that one mole of any gas occupies 22.4 liters. This knowledge is particularly useful when calculating how much gas is involved in a reaction, as seen in the potassium chlorate decomposition exercise.

By understanding this principle, we can determine the volume a given number of moles of gas will occupy under standard conditions. It's incredibly helpful in stoichiometry for predicting gas quantities and supporting balanced chemical equations.

Moles Calculation

Calculating moles is an essential part of solving chemical reaction problems. The mole is the unit for amount of substance in chemistry, providing a bridge between the atomic scale and real-world quantities.

In our example, we calculate the moles of oxygen gas produced by knowing its volume at STP:

• Moles of O extsubscript{2} = 67.2 liters / 22.4 liters per mole = 3 moles

This calculation shows how we can use volume measurements to find out the number of moles present, provided we have a basis like the 22.4 liters per mole at STP.

Accurate moles calculations allow chemists to quantify materials in reactions properly, ensuring correct proportions and outcomes.

Chemical Reactions

Chemical reactions are processes where substances transform into different substances through the breaking and forming of chemical bonds. They can be categorized into various types, such as synthesis, decomposition, single replacement, and double replacement reactions.

The decomposition reaction of potassium chlorate is a classic example. During the reaction:

• Potassium chlorate breaks down into potassium chloride and oxygen gas.

This particular reaction can be represented with the equation:

• 2 KClO extsubscript{3} → 2 KCl + 3 O extsubscript{2}

Understanding the type of reaction helps predict the products and determine the quantities of reactants and products involved. Recognizing these patterns across different reactions improves problem-solving skills in chemistry and enhances comprehension.