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: Write the Balanced Chemical Equation

The chemical reaction for the formation of HCl from hydrogen 8\mathrm{H}_2\u00de and chlorine 8\mathrm{Cl}_2\u00de gases is: \[\mathrm{H}_2 + \mathrm{Cl}_2 \rightarrow 2\mathrm{HCl}.\] This equation shows that 1 mole of \(\mathrm{H}_2\) reacts with 1 mole of \(\mathrm{Cl}_2\) to produce 2 moles of \(\mathrm{HCl}\).

Step 2: Calculate the Moles of HCl

The molar mass of \(\mathrm{HCl}\) is approximately \(1 + 35.5 = 36.5\, \mathrm{g/mol}\). Given mass of \(\mathrm{HCl}\) is \(3.65\, \mathrm{gm}\). Calculate the moles of \(\mathrm{HCl}\): \[\text{Moles of } \mathrm{HCl} = \frac{3.65}{36.5} = 0.1\, \text{moles}.\]

Step 3: Determine the Required Moles of \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\)

According to the balanced equation, 2 moles of \(\mathrm{HCl}\) are produced from 1 mole of \(\mathrm{H}_2\) and 1 mole of \(\mathrm{Cl}_2\). Therefore, to produce 0.1 moles of \(\mathrm{HCl}\), we need \(\frac{0.1}{2} = 0.05\) moles of \(\mathrm{H}_2\) and \(0.05\) moles of \(\mathrm{Cl}_2\).

Step 4: Calculate Volume of Gases at N.T.P

At Normal Temperature and Pressure (N.T.P), 1 mole of any ideal gas occupies \(22.4\, \mathrm{L}\). Calculate the volume for \(0.05\) moles of \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\): \[\text{Volume of } \mathrm{H}_2 = 0.05 \times 22.4 = 1.12\, \mathrm{L},\] \[\text{Volume of } \mathrm{Cl}_2 = 0.05 \times 22.4 = 1.12\, \mathrm{L}.\]

Step 5: Choose the Correct Answer

Based on our calculations, the volumes needed at N.T.P for both \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\) are \(1.12\, \mathrm{L}\) each. Therefore, the correct answer is (a) \(1.12\, \mathrm{L}, 1.12\, \mathrm{L}\).

Key Concepts

chemical equations

Chemical equations are a shorthand way of expressing chemical reactions. They show how reactants transform into products. In a chemical equation, each element or compound is represented by its chemical formula, and the state of each substance (whether it's solid, liquid, gas, or aqueous) might be indicated in parentheses.

• Reactants are placed on the left-hand side of the equation.
• Products are placed on the right-hand side.
• An arrow pointing from left to right indicates the direction of the reaction.

In the given exercise, the chemical equation for the formation of hydrochloric acid (HCl) is written as \(\mathrm{H}_2 + \mathrm{Cl}_2 \rightarrow 2\mathrm{HCl} \). This equation tells us that hydrogen gas \((\mathrm{H}_2)\) and chlorine gas \((\mathrm{Cl}_2)\) combine to form hydrochloric acid \((\mathrm{HCl})\). The coefficients in front of each substance show the ratio in which they react. In this case, 1 mole of hydrogen reacts with 1 mole of chlorine to form 2 moles of hydrochloric acid.

molar volume at NTP

Molar volume is the volume occupied by one mole of any gas at a specified set of conditions. Normally, when we talk about NTP (Normal Temperature and Pressure), it means a temperature of 0°C and pressure of 1 atm.

• At NTP, the molar volume of any ideal gas is 22.4 liters.

This means, 1 mole of any gas (like hydrogen, oxygen, chlorine) would occupy 22.4 liters of volume at NTP. This relation is handy when calculating the volume of gases involved in reactions, especially when you know the amount in moles. For example, in our problem, we use this concept to determine the volume of hydrogen \((\mathrm{H}_2)\) and chlorine \((\mathrm{Cl}_2)\) needed to produce the required amount of hydrochloric acid.

moles calculation

Calculating moles is fundamental to stoichiometry, as it lets you convert between mass and the number of particles or volumes of substances.

• The mole is a unit of measurement that helps chemists count particles like atoms and molecules efficiently.
• To find the number of moles, you divide the mass of a substance by its molar mass.

In the exercise, you know the mass of \(\mathrm{HCl}\) you want to produce, which is 3.65 grams. Knowing the molar mass of \(\mathrm{HCl}\) is 36.5 grams per mole, you can calculate the moles of \(\mathrm{HCl}\) as: \[\text{Moles of } \mathrm{HCl} = \frac{3.65}{36.5} = 0.1 \text{ moles}\]This calculation lets you determine directly how much \(\mathrm{H}_2\) and \(\mathrm{Cl}_2\) you will need, which is critical for finding the volumes of gas required in this reaction.

balanced chemical reactions

Balanced chemical reactions are essential for maintaining the law of conservation of mass in a chemical process. In a balanced equation, the number of atoms of each element is the same on both the reactant and product sides.

• Balancing ensures that all atoms present in the reactants are accounted for in the products.

For the formation of \(\mathrm{HCl}\), the balanced equation \(\mathrm{H}_2 + \mathrm{Cl}_2 \rightarrow 2\mathrm{HCl} \) shows that 2 moles of \(\mathrm{HCl}\) are formed from 1 mole of \(\mathrm{H}_2\) and 1 mole of \(\mathrm{Cl}_2\). By knowing this ratio, you can calculate how much of each reactant you need. As the equation tells us 2 moles of \(\mathrm{HCl}\) are made from 1 mole of each gas, it helps in scaling the reaction up or down based on the desired amount of the product. This step is crucial in industry and laboratory settings where efficiency and exact amounts are necessary.