Problem 75 - Chemistry The Science in Context

Question

How can the first two of the following reactions be combined to obtain the third reaction? a. \(\mathrm{CO}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g)\)

Step-by-Step Solution

Answer

Answer: To obtain the third reaction, we should reverse Reaction b and then add it to Reaction a. This will cancel out the intermediate products and result in the desired reactants and products for Reaction c.

Step 1: Identify reactants and products in each reaction

In this step, we list down the reactants and products for each reaction. Reaction a: Reactants: CO(g), NH3(g) Products: HCN(g), H2O(g) Reaction b: Reactants: CO(g), 3H2(g) Products: CH4(g), H2O(g) Reaction c (target): Reactants: CH4(g), NH3(g) Products: HCN(g), 3H2(g)

Step 2: Find a relationship between Reaction a and Reaction b

We can see that Reaction a produces HCN(g) as a product, and Reaction b produces CH4(g) as a product, which are part of the reactants in Reaction c. To obtain Reaction c from combining these two reactions, we should reverse Reaction b because that will cancel the unwanted H2O product in Reaction a and have the needed reactants for Reaction c. Reversed Reaction b: Reactants: CH4(g), H2O(g) Products: CO(g), 3H2(g)

Step 3: Combine Reaction a and Reversed Reaction b

Now, we combine the two reactions and cancel out any intermediates that appear on both sides of the equation. Reaction a: CO(g) + NH3(g) -> HCN(g) + H2O(g) Reversed Reaction b: CH4(g) + H2O(g) -> CO(g) + 3H2(g) Adding both reactions together: [CO(g) + NH3(g)] + [CH4(g) + H2O(g)] -> [HCN(g) + H2O(g)] + [CO(g) + 3H2(g)] Now cancel out the common terms (CO(g) and H2O(g)): CH4(g) + NH3(g) -> HCN(g) + 3H2(g) This is the same as Reaction c. So, combining Reaction a with the reversed Reaction b gives us Reaction c.

Key Concepts

Chemical Reactions

Chemical reactions are fundamental processes where substances called reactants transform into different substances known as products. In our exercise, we are dealing with three reactions. The aim is to combine the first two reactions to achieve the third one. Understanding how reactants interact and transform is critical. When looking at these reactions, each has distinct reactants and products:

• Reaction (a): CO and NH3 transform into HCN and H2O.
• Reaction (b): CO and 3H2 produce CH4 and H2O.
• Reaction (c): CH4 and NH3 result in HCN and 3H2.

The goal is to recognize how these transformations occur and how we can manipulate them to form new desired reactions. By understanding the fundamentals of chemical reactions, students can better grasp how substances interact and change.

Stoichiometry

Stoichiometry is a key concept in chemistry that deals with the relationships between the quantities of reactants and products in a chemical reaction. It allows chemists to predict how much of a product will form from given reactants. In our exercise, stoichiometry helps us see how Reaction (a) and Reaction (b) add up to Reaction (c). For instance, Reaction (a) shows that each molecule of CO and NH3 produces one molecule of HCN and H2O. Similarly, Reaction (b) indicates that CO and three molecules of H2 produce CH4 and H2O. By reversing Reaction (b) during our exercise, we can subtract and balance out the products and reactants that appear on both sides of the equation. We align the products of one reaction with the reactants of another to accomplish the desired transformation. Understanding stoichiometry helps to clarify how these reactions can be combined systematically.

Thermodynamics

Thermodynamics involves the study of energy changes that accompany chemical reactions. It's vital to understand that in the exercise, we're indirectly dealing with energy concepts when combining reactions. The study of reaction energies can tell us whether a reaction will proceed, in which direction, and to what extent. Both Reaction (a) and Reaction (b) result in energy changes. However, when reversing Reaction (b), we don't just reverse the reaction's flow but also the energy change. The reversed process can either consume or release energy. Understanding thermodynamics in this context doesn't require deep energy calculations but a comprehension of how energy balance impacts reaction direction and rate. This conceptual insight aids students in recognizing why some reaction combinations are viable, leading to desired products, like Reaction (c).

Reversibility of Reactions

Reversibility in chemical reactions refers to whether the reaction can proceed in both forward and backward directions. Identifying reversible reactions is crucial for altering and combining reaction pathways. In our problem, reversing Reaction (b) is key. By reversing this reaction, we change the products back into reactants, enabling us to cancel out intermediates like CO and H2O, aligning the process towards Reaction (c). This concept extends to real-world applications where reactions are manipulated in both directions to optimize desired outcomes, be it in industrial settings or experimental laboratories. Understanding reversibility helps students grasp that reactions aren't just static events; they can be dynamic processes, adjustable to meet specific chemical goals.