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 L.

Step 1: Write the Balanced Chemical Equation

The reaction given involves the reduction of boron trichloride (\(\text{BCl}_3\)) by hydrogen gas (\(\text{H}_2\)) to produce elemental boron (\(\text{B}\)) and hydrochloric acid (\(\text{HCl}\)). The balanced chemical equation for the reaction is: \\[ 2\text{BCl}_3 + 3\text{H}_2 \rightarrow 2\text{B} + 6\text{HCl} \] This equation shows that 2 moles of boron trichloride react with 3 moles of hydrogen gas to yield 2 moles of elemental boron.

Step 2: Calculate Moles of Boron Needed

We are given that 21.6 g of boron is produced. Using the atomic mass of boron (10.8 g/mol), we can calculate the number of moles of boron produced:\[ \text{Moles of Boron} = \frac{\text{Mass of Boron}}{\text{Molar Mass of Boron}} = \frac{21.6 \text{ g}}{10.8 \text{ g/mol}} = 2 \text{ moles} \] Thus, 2 moles of boron are produced in the reaction.

Step 3: Relate Moles of Boron and Hydrogen

From the balanced chemical equation, we know that 2 moles of boron are produced from 3 moles of hydrogen gas. Since we have calculated that we need 2 moles of boron, the necessary moles of hydrogen gas are:\[ \frac{3 \text{ moles of } \text{H}_2}{2 \text{ moles of } \text{B}} \times 2 \text{ moles of } \text{B} = 3 \text{ moles of } \text{H}_2 \] Therefore, we need 3 moles of hydrogen gas for the complete reaction.

Step 4: Convert Moles of Hydrogen to Volume at STP

Under the conditions of standard temperature and pressure (STP: 0°C or 273 K and 1 atm), 1 mole of any gas occupies a volume of 22.4 L. Therefore, the volume of 3 moles of hydrogen gas is:\[ \text{Volume of } \text{H}_2 = 3 \text{ moles} \times 22.4 \text{ L/mol} = 67.2 \text{ L} \] Thus, 67.2 liters of hydrogen gas are consumed in the reaction.

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is a fundamental part of chemical reactions. It ensures that there are equal numbers of each type of atom on both sides of the equation. This reflects the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.

Let's break down the balanced equation from the original problem:

• Given: \(2\text{BCl}_3 + 3\text{H}_2 \rightarrow 2\text{B} + 6\text{HCl}\)
• This shows that 2 molecules of boron trichloride react with 3 molecules of hydrogen to produce 2 atoms of boron and 6 molecules of hydrochloric acid.
• This balancing tells us the stoichiometric coefficients—the numbers before each compound—that allow us to predict the amounts of reactants and products involved.

The importance of a balanced chemical equation lies in its ability to accurately represent the moles of reactants and products involved in the chemical process, making it possible to quantify materials needed or produced in reactions.

Mole Concept

The mole concept is pivotal in chemistry because it provides a bridge between the atomic scale and the macroscopic world. It allows chemists to convert given masses into measurable quantities called `moles`.

Here's a quick explanation:

• A mole represents \(6.022 \times 10^{23}\) particles of a substance, be it atoms, molecules, or ions. This number is known as Avogadro's number.
• Using the atomic mass, which is the weight of one mole of atoms, we can convert grams to moles. For instance, in the problem, boron with an atomic mass of \(10.8 \text{ g/mol}\), allows calculation of moles from the given mass.
• The formula used: \(\text{Moles of Boron} = \frac{\text{Mass of Boron}}{\text{Molar Mass of Boron}} = \frac{21.6}{10.8}= 2\text{ moles}\)

The mole concept is essential in stoichiometry, helping us relate the mass of substances to their amount in moles, allowing precise calculations and predictions in chemical reactions.

Gas Laws

Gas laws relate to the properties and behavior of gases, such as pressure, volume, and temperature. These laws are crucial when working with gaseous substances in chemistry.

In the problem at hand, understanding the behavior of hydrogen gas under standard conditions is key.

• At standard temperature and pressure (STP: 273 K and 1 atm), one mole of any gas occupies 22.4 L of volume.
• Using this knowledge, you can convert moles of gas to volume. For the hydrogen gas in the exercise, knowing there are 3 moles needed, we use: \(\text{Volume of } \text{H}_2 = 3 \text{ moles} \times 22.4 \text{ L/mol} = 67.2 \text{ L}\).
• This prediction or calculation is made based on the ideal gas law properties, which gas laws like Boyle's and Charles' laws describe in further detail.

Understanding gas laws and how they apply in different conditions helps chemists accurately describe and predict gas behavior in reactions.