Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following equations is correct for the reaction \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) ?\) (a) \(3 \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{dt}}=2 \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{dt}}\) (b) \(2 \frac{\mathrm{d}\left[\mathrm{NH}_{2}\right]}{\mathrm{dt}}=-3 \frac{\mathrm{d}\left[\mathrm{H}_{3}\right]}{\mathrm{dt}}\) (c) \(2 \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{dt}}\) (d) \(3 \frac{\mathrm{d}\left[\mathrm{NH}_{2}\right]}{\mathrm{dt}}=-2 \frac{\mathrm{d}\left[\mathrm{H}_{3}\right]}{\mathrm{dt}}\)

Step-by-Step Solution

Answer

Option (a) is correct.

Step 1: Identify the Balanced Equation

The balanced chemical equation given is \( \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) \). This equation indicates that one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia.

Step 2: Derived Rate Expression from Stoichiometry

The stoichiometric coefficients relate the rates of consumption and formation of the reactants and products. For a balanced equation, the rates are related as follows:\[-\frac{1}{1} \frac{\mathrm{d}[\mathrm{N}_{2}]}{\mathrm{dt}} = -\frac{1}{3} \frac{\mathrm{d}[\mathrm{H}_{2}]}{\mathrm{dt}} = \frac{1}{2} \frac{\mathrm{d}[\mathrm{NH}_{3}]}{\mathrm{dt}}.\]This indicates that the nitrogen consumption, hydrogen consumption, and ammonia formation rates are related by the stoichiometric ratios.

Step 3: Analyze Each Option

Evaluate each option using the stoichiometric relationship:- (a) \(3 \frac{\mathrm{d}[\mathrm{NH}_{3}]}{\mathrm{dt}} = 2 \frac{\mathrm{d}[\mathrm{H}_{2}]}{\mathrm{dt}}\): After rearranging, this becomes \( \frac{1}{2} \frac{\mathrm{d}[\mathrm{NH}_{3}]}{\mathrm{dt}} = \frac{1}{3} \frac{\mathrm{d}[\mathrm{H}_{2}]}{\mathrm{dt}} \), which matches the stoichiometric ratio.- (b) and (c) involve incorrect species.- (d) involves incorrect stoichiometric coefficients and incorrect species.

Step 4: Select the Correct Option

Based on the analysis, option (a) correctly represents the stoichiometric relationship between the formation of \( \mathrm{NH}_{3} \) and the consumption of \( \mathrm{H}_{2} \). It follows the derived rate expression from the balanced equation.

Key Concepts

Stoichiometry

Stoichiometry comes into play whenever chemical reactions are involved. It is all about the quantitative relationship between reactants and products in a chemical reaction. This means using balanced chemical equations to figure out how much of each substance is involved. For example, in the formation of ammonia (\( \mathrm{N}_{2} + 3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3} \)), the stoichiometric coefficients are 1, 3, and 2, respectively. These coefficients help determine the proportions of molecules or moles that react or form during the reaction.
When we use stoichiometry, we can find out:

• How many moles of hydrogen are needed to react with one mole of nitrogen.
• How many moles of ammonia are produced from a given amount of reactants.

This concept is crucial for chemists to predict product yields and optimize reactions. Stoichiometry ensures the reaction components are just the right amount for complete transformation without leaving excess reactants behind.

Reaction Rates

In simple terms, reaction rates describe how fast or slow a reaction takes place. It's about the change in concentration of reactants or products over time. In the ammonia formation reaction, the rate of disappearance of hydrogen and nitrogen is related to the rate of formation of ammonia by their stoichiometric coefficients.
For example, the change per unit time in hydrogen concentration is three times that of nitrogen, because it takes three molecules of hydrogen to react with one molecule of nitrogen. The stoichiometric relationships provide a means to compare these rates and calculate one from the other:

• Disappearance rate of nitrogen: \(-\frac{1}{1} \frac{\mathrm{d}[\mathrm{N}_{2}]}{\mathrm{dt}}\)
• Disappearance rate of hydrogen: \(-\frac{1}{3} \frac{\mathrm{d}[\mathrm{H}_{2}]}{\mathrm{dt}}\)
• Formation rate of ammonia: \(\frac{1}{2} \frac{\mathrm{d}[\mathrm{NH}_{3}]}{\mathrm{dt}}\)

Understanding reaction rates is essential for controlling industrial processes, predicting reaction outcomes, and ensuring safety in chemical experiments.

Balanced Chemical Equation

A balanced chemical equation is the starting point for any stoichiometric calculation. It shows the exact numbers of atoms for each element involved, ensuring that matter is neither created nor destroyed. This principle is known as the law of conservation of mass.
In the ammonia formation reaction, the balanced equation \(\mathrm{N}_{2} + 3 \mathrm{H}_{2} \longrightarrow 2 \mathrm{NH}_{3}\) demonstrates that one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia. If this equation wasn’t balanced, we couldn’t accurately predict how much of each substance we need or produce.
Balancing equations involves making sure that the number of each type of atom is the same on both sides of the reaction. It's an essential skill in chemistry, critical for accurate calculations in lab settings or chemical manufacturing.

Ammonia Formation

Ammonia formation is a classic example in chemistry that illustrates not just stoichiometry but also reaction kinetics. The reaction, \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2\mathrm{NH}_{3}(\mathrm{~g})\), is widely used industrially in the Haber process to produce ammonia for fertilizers.
The conditions required for this reaction typically include high temperature and pressure, along with a catalyst to speed up the process. This shows how understanding both the stoichiometry and kinetics of a reaction are crucial for practical applications.
In our daily lives, ammonia is essential not only for fertilizer production but also as a building block for various chemicals. Its efficient production is vital for feeding the global population and contributing to sustainable agriculture practices. Ammonia's synthesis also highlights the application of chemistry in solving real-world problems, enhancing how we produce and sustain food supplies.