Problem 62 - General Chemistry: Principles and Modern Applications

Question

Use information from this chapter and previous chapters to write plausible chemical equations to represent the following: (a) the reaction of silver metal with \(\mathrm{HNO}_{3}(\mathrm{aq})\) (b) the complete combustion of the rocket fuel, unsymmetrical dimethylhydrazine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2}\) (c) the preparation of sodium triphosphate by heating a mixture of sodium dihydrogen phosphate and sodium hydrogen phosphate.

Step-by-Step Solution

Answer

The balanced chemical equations are as follows: \n (a) \( 3Ag + 4HNO_{3} \rightarrow 3AgNO_{3} + 2H_{2}O + NO_{2} \) \n (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2} + 3O_{2} \rightarrow 2CO_{2} + 5H_{2}O + N_{2}\) \n (c) \(2NaH_{2}PO_{4} + \mathrm{Na}_{2} \mathrm{HPO}_{4} \rightarrow \mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10} + 2H_{2}O\).

Step 1: Reaction of Silver with Nitric Acid (HNO3)

The chemical reaction for this follows the pattern of a displacement reaction, where silver displaces hydrogen in nitric acid, resulting in the formation of silver nitrate and water, along with nitrogen dioxide. So, we'll write our reactants: \( Ag + HNO_{3}\), and our products: \(AgNO_{3} + H_{2}O + NO_{2}\). We then balance this equation to get the final relation: \( 3Ag + 4HNO_{3} \rightarrow 3AgNO_{3} + 2H_{2}O + NO_{2} \).

Step 2: Combustion of unsymmetrical dimethylhydrazine

The rocket fueler, unsymmetrical dimethylhydrazine reacts with oxygen from the atmosphere to produce carbon dioxide, water, and nitrogen. The reactants are \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2} + O_{2}\), and the products are \(CO_{2}, H_{2}O, N_{2}\). Balancing the equation, we get \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2} + 3O_{2} \rightarrow 2CO_{2} + 5H_{2}O + N_{2}\).

Step 3: Preparation of Sodium Triphosphate

The reaction involves heating a mixture of sodium dihydrogen phosphate, \(NaH_{2}PO_{4}\), and sodium hydrogen phosphate, \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\), to produce sodium triphosphate, \(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\), and water. Let's write our reactants \(NaH_{2}PO_{4} + \mathrm{Na}_{2} \mathrm{HPO}_{4}\), and specify the products as \(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10} + H_{2}O\). Balancing this gives us the equation: \(2NaH_{2}PO_{4} + \mathrm{Na}_{2} \mathrm{HPO}_{4} \rightarrow \mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10} + 2H_{2}O\).

Key Concepts

Silver Nitrate Formation

The formation of silver nitrate is a classic example of a displacement reaction, which is a type of chemical reaction where one element is replaced by another in a compound. In this case, silver (Ag) reacts with nitric acid (HNO₃) to form silver nitrate (AgNO₃), water (H₂O), and nitrogen dioxide (NO₂).

The overall balanced chemical equation for this reaction is:

• Reactants: 3Ag + 4HNO₃
• Products: 3AgNO₃ + 2H₂O + NO₂

Here's how it works:

• Silver displaces hydrogen ions from nitric acid.
• This displacement forms silver nitrate and nitrogen dioxide, which are typical products when metals react with strong acids like nitric acid.

The nitrogen dioxide formed is a brown gas, which indicates that the reaction has occurred. This reaction is often used in laboratories to teach the concepts of metal reactivity and displacement reactions.

Combustion Reaction

Combustion is a chemical process in which a substance reacts rapidly with oxygen and releases energy in the form of light and heat. A well-known example is the combustion of fuels, such as unsymmetrical dimethylhydrazine, which is used as rocket fuel.

The chemical formula of unsymmetrical dimethylhydrazine is \( ext{( ext{CH}_3)_2 ext{NNH}_2}\), and its combustion with oxygen \( ext{O}_2\) can be shown in the following combustion reaction:

• Reactants: \\(\text{( ext{CH}_3)_2 ext{NNH}_2} + ext{3} ext{O}_2\)
• Products: 2CO₂ + 5H₂O + N₂

Balancing equations is crucial in combustion reactions:

• The reaction above produces carbon dioxide (CO₂), water (H₂O), and nitrogen gas (N₂).
• Ensure the same number of each type of atom on both sides of the equation.

This reaction is exothermic, releasing energy that propels rockets. The complete combustion ensures all fuel molecules react, producing maximum energy output.

Sodium Triphosphate Synthesis

Synthesis reactions are when two or more reactants combine to form a single product. In the case of sodium triphosphate, the synthesis involves the combination of sodium dihydrogen phosphate and sodium hydrogen phosphate.

The chemical equation representing this synthesis is:

• Reactants: \(2NaH_2PO_4 + ext{Na}_2HPO_4\)
• Product: \( ext{Na}_5P_3O_{10} + 2 ext{H}_2O\)

Here's the process explained:

• Both phosphates are heated together, facilitating the removal of water and allowing the combination to form sodium triphosphate.
• The reaction balance ensures the conservation of mass, with all reactant atoms appearing in the product.

Sodium triphosphate is often used in detergents, enhancing their cleaning efficiency by preventing dirt from redepositing on clothes. Understanding synthesis reactions is crucial for producing complex compounds from simpler substances.