Problem 68 - A Complete Resource Book in Chemistry for JEE Main

Question

In Haber's process, \(30 \mathrm{~L}\) of dihydrogen and \(30 \mathrm{~L}\) of dinitrogen were taken for reaction which yielded only \(50 \%\) of expected product. What is the composition of the gaseous mixture under afore-said conditions in the end? (a) \(20 \mathrm{~L} \mathrm{NH}_{3}, 25 \mathrm{~L} \mathrm{~N}_{2}, 15 \mathrm{~L} \mathrm{H}_{2}\) (b) \(20 \mathrm{~L} \mathrm{NH}_{3}, 20 \mathrm{~L} \mathrm{~N}_{2}, 20 \mathrm{~L} \mathrm{H}_{2}\) (c) \(10 \mathrm{~L} \mathrm{NH}_{3}, 25 \mathrm{~L} \mathrm{~N}_{2}, 15 \mathrm{~L} \mathrm{H}_{2}\) (d) \(20 \mathrm{~L} \mathrm{NH}_{3}, 10 \mathrm{~L} \mathrm{~N}_{2}, 30 \mathrm{~L} \mathrm{H}_{2}\)

Step-by-Step Solution

Answer

The composition is 10 L NH_3, 25 L N_2, 15 L H_2 (option c).

Step 1: Understanding the reaction

The Haber process involves the reaction of dihydrogen (H_2) and dinitrogen (N_2) to form ammonia (NH_3) as per the balanced equation: \[ N_2 + 3H_2 \rightarrow 2NH_3 \] According to this equation, 1 volume of N_2 reacts with 3 volumes of H_2 to form 2 volumes of NH_3.

Step 2: Determine limiting reactant

Given that the volumes of H_2 and N_2 are equal at 30 L each, and using the stoichiometric ratio from the balanced equation, H_2 is the limiting reactant because it requires 90 L of H_2 to fully react with 30 L of N_2 according to the equation.

Step 3: Calculate expected yield

The chemical equation suggests that 90 L of H_2 will produce 60 L of NH_3. With 30 L of H_2 available, the complete reaction would have produced \( \frac{60}{90} \times 30 = 20 \) L of NH_3. However, since the yield is only 50%, it actually produces \( \frac{50}{100} \times 20 = 10 \) L of NH_3.

Step 4: Calculate the composition of unreacted gases

From the reaction's stoichiometry, producing 10 L of NH_3 would consume \( \frac{3}{2} \times 10 = 15 \) L of H_2 and \( \frac{1}{2} \times 10 = 5 \) L of N_2.

Step 5: Determine the final mixture composition

Initially, there were 30 L of H_2, so the remaining H_2 would be \( 30 - 15 = 15 \) L. The initial 30 L of N_2 would reduce by the consumed amount, leaving \( 30 - 5 = 25 \) L. Therefore, the composition of the final gas mixture is 10 L of NH_3, 25 L of N_2, and 15 L of H_2.

Key Concepts

Limiting Reactant

In the Haber process for ammonia production, identifying the limiting reactant is crucial. It determines how much ammonia can be produced from available reactants. A limiting reactant is the substance that will be entirely consumed first, stopping the reaction. This happens because all reactants are needed in specific ratios to each other, and once one is used up, no further reaction can occur.
In the exercise provided, we have 30 liters of both dihydrogen (\( ext{H}_2 \)) and dinitrogen (\( ext{N}_2 \)). Using the balanced reaction equation:

• \( ext{N}_2 + 3 ext{H}_2 ightarrow 2 ext{NH}_3 \)

To react fully, 30 L of \( ext{N}_2 \) would need 90 L of \( ext{H}_2 \), as per the stoichiometric requirements (1 volume of \( ext{N}_2 \) reacts with 3 volumes of \( ext{H}_2 \)). Since only 30 L of \( ext{H}_2 \) is available, \( ext{H}_2 \) becomes the limiting reactant. It limits the production of ammonia, as we can't make more ammonia once \( ext{H}_2 \) is exhausted.

Stoichiometric Ratio

Understanding the stoichiometric ratio in chemical reactions provides a map for converting reactants to products. This ratio comes from the balanced chemical equation and tells you how many moles (or volumes, in case of gases under constant conditions) of each reactant are needed to form a given amount of product.
In the Haber process, the balanced equation:

• \( ext{N}_2 + 3 ext{H}_2 ightarrow 2 ext{NH}_3 \)

indicates that 1 volume of \( ext{N}_2 \) reacts with 3 volumes of \( ext{H}_2 \) to produce 2 volumes of \( ext{NH}_3 \). From this, you can calculate the amounts of all substances involved:

• If you start with 30 L of \( ext{N}_2 \), you need 90 L of \( ext{H}_2 \). You would theoretically produce 60 L of \( ext{NH}_3 \).
• The stoichiometric ratio helps in determining what portion is used up and helps in calculating the expected yield under varying initial conditions.

Such calculations ensure that you have a predictable understanding of how varying amounts of substances will react.

Chemical Yield

Chemical yield expresses the efficiency of a reaction in converting reactants into products. It is the actual amount of product obtained compared to the theoretical maximum, usually expressed as a percentage.
In our problem, chemical yield becomes crucial because only 50% of the expected product (ammonia) is obtained. This means if 20 L of ammonia is theoretically expected (from the limiting \( ext{H}_2 \)), only 10 L is practically produced:

• Theoretical yield: 20 L \( ext{NH}_3 \)
• Actual yield: 10 L \( ext{NH}_3 \)
• Yield percentage calculated as: \( \left( \frac{10}{20} \times 100 \right) \% = 50\% \)

Many factors, such as reaction conditions or side reactions, can influence chemical yield. Knowing this figure helps in adjusting the reaction conditions to improve productivity and efficiency in industrial settings.

Ammonia Production

Ammonia production via the Haber process is a cornerstone of modern chemistry, providing essential compounds for fertilizers, cleaning products, and more. The process works under high temperatures and pressures to increase reaction efficiency, crucial in maximizing ammonia yield.
For ammonia formation:

• \( ext{N}_2 + 3 ext{H}_2 ightarrow 2 ext{NH}_3 \)

Dihydrogen (\( ext{H}_2 \)) and dinitrogen (\( ext{N}_2 \)) are reacted in a 3:1 ratio respectively. The industrial process optimizes reactions through catalysts, making production more viable.
In the exercise, you start with 30 L of each gas but due to yield limitations, only 10 L of \( ext{NH}_3 \) is actually produced. This highlights real-world limitations where theoretical output is curtailed by practical conditions.
Understanding the chemistry at play allows producers to refine techniques and improve efficiency, ensuring ammonia remains affordable and available for various global applications.