Problem 146 - General Chemistry: Principles and Modern Applications

Question

Nitric acid, \(\mathrm{HNO}_{3}\), can be manufactured from ammonia, \(\mathrm{NH}_{3}\), by using the three reactions shown below. $$\begin{aligned} &\text { Step 1: 4 NH }_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\\\ &\text { Step 2: } 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\\\ &\text { Step 3: } 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{aligned}$$ What is the maximum number of moles of \(\mathrm{HNO}_{3}\) that can be obtained from 4.00 moles of \(\mathrm{NH}_{3}\) ? (Assume that the NO produced in step 3 is not What is the maximum number of moles of \(\mathrm{HNO}_{3}\) that can be obtained from 4.00 moles of \(\mathrm{NH}_{3}\) ? (Assume that the NO produced in step 3 is not recycled back into step 2.) (a) 1.33 mol; (b) 2.00 mol; (c) 2.67 mol; (d) 4.00 mol; (e) 6.00 mol.

Step-by-Step Solution

Answer

(c) 2.67 mol

Step 1: Examine the first reaction

In the first reaction, 4 moles of ammonia (\(NH_{3}\)) react to produce 4 moles of \(NO\). Given that there are 4.00 moles of \(NH_{3}\), all of it will react and also produce 4 moles of \(NO\).

Step 2: Analyze the second reaction

The second reaction involves the reaction of \(NO\) with oxygen (\(O_{2}\)) to form \(NO_{2}\). Two moles of \(NO\) produce 2 moles of \(NO_{2}\); hence, the four moles of \(NO\) from the first reaction would yield 4 moles of \(NO_{2}\).

Step 3: Investigate the third reaction

The third reaction involves the reaction of \(NO_{2}\) with water (\(H_{2}O\)) to yield \(HNO_{3}\) and \(NO\). In this reaction, 3 moles of \(NO_{2}\) yield 2 moles of \(HNO_{3}\). Therefore, the 4 moles of \(NO_{2}\) obtained in step 2 will yield \(\frac{2}{3} \times 4 = 2.67\) moles of \(HNO_{3}\).

Step 4: Conclusion

The maximum number of moles of \(HNO_{3}\) that can be obtained from 4.00 moles of \(NH_{3}\) is 2.67 moles, assuming that the \(NO\) produced in step 3 is not recycled back into step 2. So, the answer is (c) 2.67 mol.

Key Concepts

Stoichiometry

Stoichiometry is a vital concept in chemistry that involves calculating the amounts of reactants and products in a chemical reaction. It is based on the conservation of mass where the quantity of each element must remain constant throughout a chemical reaction. To solve stoichiometric problems, one must understand the balanced chemical equation, which provides the mole ratio of reactants to products.

For example, in the production of nitric acid from ammonia, the balanced equations show specific ratios such as 4 moles of ammonia yielding 4 moles of nitric oxide in the first reaction. Using these ratios, one can predict the amount of products formed from a given quantity of reactants. In the exercise, we used stoichiometry to determine that 4.00 moles of ammonia would produce a maximum of 2.67 moles of nitric acid.

Key Points in Stoichiometry

• Stoichiometry is based on the balanced chemical equation.
• The mole ratio is essential for predicting product formation.
• Conservation of mass must be maintained in stoichiometry calculations.

Furthermore, it's important not to overlook coefficients in chemical equations as they are crucial for accurate calculations—each coefficient represents the number of moles of a given species.

Chemical Reactions

Chemical reactions are processes where reactants convert into products, often with observable changes such as energy release, color change, or the formation of a solid or gas. In the example of nitric acid production, we observed a multi-step chemical reaction where ammonia first reacts with oxygen to form nitric oxide and water, followed by the oxidation of nitric oxide to nitrogen dioxide, and finally the reaction of nitrogen dioxide with water to yield nitric acid and nitric oxide.

Understanding Chemical Reaction Steps

• Each step represents a distinct reaction with unique reactants and products.
• Sequential reactions can be part of a larger overall process.
• Products from one reaction can sometimes serve as reactants in subsequent reactions.

Grasping the complexities of these reactions helps in understanding why it's assumed that the nitric oxide produced in the final step isn't recycled—which is crucial for arriving at the correct stoichiometry and solving the problem.

Mole Concept

The mole concept is a foundational principle in chemistry that allows chemists to count atoms, molecules, and formula units by weighing them. One mole equals Avogadro's number (\(6.022 \times 10^{23}\) entities) and it relates the mass of a substance to its number of particles.

In the exercise, we dealt with the production of nitric acid where understanding the mole concept is essential. The exercise required converting moles of ammonia to moles of nitric acid, highlighting the direct role that this concept plays in quantitative chemistry.

Essentials of the Mole Concept

• The mole links mass to number of particles in a substance.
• It's critical for converting grams of a substance to moles and vice versa.
• Mole ratios from the balanced equation are the bridge between reactants and products.

Knowing how to use the mole concept in stoichiometric calculations allows students to easily determine the required number of moles of a reactant or yield of a product in a given chemical reaction.