Problem 166 - A Complete Resource Book in Chemistry for JEE Main

Question

What volume of hydrogen gas, at \(273 \mathrm{~K}\) and 1 atm pressure will be consumed in obtaining \(21.6 \mathrm{~g}\) of elemental boron (atomic mass \(=10.8\) ) from the reduction of boron trichloride by hydrogen? \([2003]\) (a) \(89.6 \mathrm{~L}\) (b) \(67.2 \mathrm{~L}\) (c) \(44.8 \mathrm{~L}\) (d) \(22.4 \mathrm{~L}\)

Step-by-Step Solution

Answer

The volume of hydrogen gas consumed is 67.2 liters, option (b).

Step 1: Understanding the Reaction

The reaction for reducing boron trichloride (\(\text{BCl}_3\)) with hydrogen (\(\text{H}_2\)) to produce boron (\(\text{B}\)) and hydrogen chloride (\(\text{HCl}\)) is:\[\text{2BCl}_3 + 3\text{H}_2 \rightarrow 2\text{B} + 6\text{HCl}\]From this equation, 2 moles of \(\text{BCl}_3\) react with 3 moles of \(\text{H}_2\) to produce 2 moles of boron (\(\text{B}\)).

Step 2: Calculate Moles of Boron Produced

First, calculate the moles of boron produced from the mass given. The atomic mass of boron is 10.8 g/mol. Thus, the moles of boron are:\[\text{Moles of B} = \frac{21.6 \text{ g}}{10.8 \text{ g/mol}} = 2 \text{ moles}\]

Step 3: Relate Moles of Boron to Moles of Hydrogen

According to the balanced equation, 2 moles of boron require 3 moles of \(\text{H}_2\). Thus, the moles of \(\text{H}_2\) required are:\[\text{Moles of } \text{H}_2 = 3\]

Step 4: Calculate Volume of Hydrogen Gas at STP

At standard temperature and pressure (STP: 273 K and 1 atm), 1 mole of any gas occupies 22.4 liters. Therefore, the volume of 3 moles of \(\text{H}_2\) is:\[\text{Volume of } \text{H}_2 = 3 \times 22.4 \text{ L} = 67.2 \text{ L}\]

Step 5: Conclude the Correct Option

Thus, the volume of hydrogen gas consumed is 67.2 liters. Therefore, the correct option is (b) 67.2 \(\text{L}\).

Key Concepts

Chemical Equations

When looking at chemical reactions, it's important to appreciate the role of balanced chemical equations. They represent how substances react with one another. In a balanced equation, the number of atoms of each element is the same on both sides of the equation. This reinforces the law of conservation of mass—matter cannot be created or destroyed. Let's examine the provided equation: 2BCl_3 + 3H_2 \rightarrow 2B + 6HClThis balanced equation tells us that:

• 2 moles of boron trichloride (\(\text{BCl}_3\)) react with 3 moles of hydrogen (\(\text{H}_2\)).
• The product of this reaction is 2 moles of elemental boron (\(\text{B}\)) and 6 moles of hydrogen chloride (\(\text{HCl}\)).

It conveys the stoichiometric relationships between reactants and products, which are crucial in predicting the quantities needed or produced.

Gas Laws

The behavior of gases in chemical reactions is often described by gas laws. When referring to gases, especially those at standard temperature and pressure (STP), we use these laws to predict how much space a given amount of gas will occupy. At STP (273 K and 1 atm), 1 mole of any ideal gas occupies 22.4 liters of volume. In our exercise, the focus is on hydrogen gas. Since 3 moles of hydrogen are involved, the calculated volume under these conditions is:\[\text{Volume of } \text{H}_2 = 3 \times 22.4 \text{ L} = 67.2 \text{ L}\]This calculation relies on the ideal gas law, which states that under constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. Therefore, in predictable conditions such as STP, we can easily translate moles into volume, simplifying the stoichiometric calculation.

Mole Concept

The mole concept underpins much of chemistry, providing a bridge between the atomic scale and the macroscopic world. A mole is a unit for measuring the amount of substance, allowing chemists to count particles by weighing them. In this exercise, understanding the mole concept is key to deciphering how much hydrogen gas is needed.By using the molar mass of boron, calculated as \(10.8 \text{ g/mol}\), we first compute the number of moles from the given mass of 21.6 g of boron:\[\text{Moles of B} = \frac{21.6 \text{ g}}{10.8 \text{ g/mol}} = 2 \text{ moles}\]Then, from the balanced equation, we know that 2 moles of \(\text{B}\) correspond to 3 moles of \(\text{H}_2\). This stoichiometric relationship helps to calculate the total volume of hydrogen gas consumed, using the gas laws and reinforcing the crucial role of the mole concept in stoichiometry.