Problem 137 - A Complete Resource Book in Chemistry for JEE Main

Question

For the formation of \(3.65 \mathrm{gm}\) of \(\mathrm{HCl}\), what volume of \(\mathrm{H}_{2}\), and \(\mathrm{Cl}_{2}\) are needed at N.T.P? (a) \(1.12 \mathrm{~L}, 1.12 \mathrm{~L}\) (b) \(1.12 \mathrm{~L}, 2.24 \mathrm{~L}\) (c) \(3.65 \mathrm{~L}, 1.83 \mathrm{~L}\) (d) \(1 \mathrm{~L}, 1 \mathrm{~L}\)

Step-by-Step Solution

Answer

(a) 1.12 L, 1.12 L

Step 1: Calculate moles of HCl

First, determine the number of moles of HCl using its molar mass. The molar mass of HCl is approximately 36.5 g/mol. Given 3.65 g of HCl, the moles are calculated as follows:\[\text{Moles of HCl} = \frac{3.65 \text{ g}}{36.5 \text{ g/mol}} = 0.1 \text{ moles}\]

Step 2: Determine the moles of H2 and Cl2

The balanced chemical equation for the formation of HCl is:\[\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}\]From the equation, 1 mole of H2 and 1 mole of Cl2 produce 2 moles of HCl. Therefore, to produce 0.1 moles of HCl, we need 0.05 moles of H2 and 0.05 moles of Cl2.

Step 3: Calculate volume at N.T.P

At N.T.P (Normal Temperature and Pressure), 1 mole of any gas occupies 22.4 L. Thus, the required volumes of H2 and Cl2 can be calculated as follows:\[\text{Volume of H}_2 = 0.05 \text{ moles} \times 22.4 \text{ L/mole} = 1.12 \text{ L}\]\[\text{Volume of Cl}_2 = 0.05 \text{ moles} \times 22.4 \text{ L/mole} = 1.12 \text{ L}\]

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry that allows us to quantify substances in terms of their number of entities, such as atoms, molecules, ions, etc. One mole is defined as Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This is analogous to a dozen, which represents 12 items, but on a much larger scale.

When dealing with chemical substances, the use of the mole allows chemists to count particles by weighing them. The molar mass, usually expressed in grams per mole (g/mol), is the mass of one mole of a substance. It is numerically equivalent to the average atomic or molecular weight of the substance. For example, the molar mass of \(\text{HCl}\) is approximately \(36.5\, \text{g/mol}\), which means that 36.5 grams of \(\text{HCl}\) contains 1 mole of \(\text{HCl}\) molecules.

In this exercise, we calculated the moles of \(\text{HCl}\) by dividing the given mass by its molar mass:

• Moles of \(\text{HCl} = \frac{3.65\, \text{g}}{36.5\, \text{g/mol}} = 0.1\, \text{moles}\)

This calculation sets the foundation for determining the amount of reactants needed in a chemical reaction.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are represented by balanced chemical equations that adhere to the law of conservation of mass, meaning the number of atoms of each element must be the same on both sides of the equation. This ensures that mass is neither created nor destroyed in a chemical reaction.

A balanced chemical equation also indicates the stoichiometry of the reaction, which is the ratio of moles of reactants to products. For example, the reaction for the formation of \(\text{HCl}\) is:

• \(\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}\)

This equation shows that 1 mole of \(\text{H}_2\) reacts with 1 mole of \(\text{Cl}_2\) to yield 2 moles of \(\text{HCl}\). Hence, to produce 0.1 moles of \(\text{HCl}\), we need half the amount of moles of \(\text{H}_2\) and \(\text{Cl}_2\), calculated as follows:

• \(0.05\, \text{moles of H}_2\)
• \(0.05\, \text{moles of Cl}_2\)

By understanding the stoichiometry, we can predict the quantities involved in the chemical reaction.

Gas Laws

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. Key terms related to gas laws include:

• Boyle's Law: At constant temperature, pressure is inversely proportional to volume.
• Charles's Law: At constant pressure, volume is directly proportional to temperature.
• Avogadro's Law: At constant temperature and pressure, volume is directly proportional to the number of moles.

These laws collectively lead to the Ideal Gas Law, expressed as \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the gas constant, and \(T\) is temperature.

This exercise uses these gas laws to calculate the volume of gases needed for the reaction at Normal Temperature and Pressure (N.T.P). Understanding these laws aids in predicting how gases will react or change under different conditions.

Molar Volume at NTP

Molar volume refers to the volume occupied by one mole of a gas. At Normal Temperature and Pressure (N.T.P), which is defined as \(0°C\) and \(1\, \text{atm}\), the molar volume of an ideal gas is \(22.4\, \text{L/mole}\). This means that every mole of gas occupies a volume of 22.4 liters under these conditions.

Applying this information, the calculation of gas volumes needed for the formation of \(\text{HCl}\) in our exercise is straightforward. We already determined that \(0.05\) moles of \(\text{H}_2\) and \(\text{Cl}_2\) are required. Given the molar volume at N.T.P, the volume for each gas is:

• \(Volume = moles \times 22.4 \text{ L/mole} = 0.05 \times 22.4 = 1.12 \text{ L}\)

Thus, 1.12 liters of both \(\text{H}_2\) and \(\text{Cl}_2\) are required for the reaction. Understanding molar volumes is crucial when working with gases at standard conditions.