Question

The rocket fuel hydrazine \(\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)\) is made by the three-step Raschig process, which has the following overall equation: $$ \mathrm{NaOCl}(a q)+2 \mathrm{NH}_{3}(a q) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(a q)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ What is the percent atom economy of this process?

Short answer

The percent atom economy is approximately 29.5%.

Step-by-step solution

- Write Down the Balanced Equation

Write the provided balanced chemical equation for the reaction: \( \mathrm{NaOCl}(aq) + 2 \mathrm{NH}_{3}(aq) \rightarrow \mathrm{N}_{2} \mathrm{H}_{4}(aq) + \mathrm{NaCl}(aq) + \mathrm{H}_{2} \mathrm{O}(l) \)

- Identify Molar Masses of Reactants and Products

Calculate the molar masses of each reactant and product.For NaOCl: \( \mathrm{Na} (23) + \mathrm{O} (16) + \mathrm{Cl} (35.5) = 74.5 \ g/mol \)For NH₃: \( 2 \times (14 + 3 \times 1) = 34 \ g/mol \)For N₂H₄: \( 2 \times 14 + 4 \times 1 = 32 \ g/mol \)For NaCl: \( 23 + 35.5 = 58.5 \ g/mol \)For H₂O: \( 2 \times 1 + 16 = 18 \ g/mol \)

- Calculate Total Molar Mass of Reactants

Calculate total molar mass of reactants:\( 74.5 + 2 \times 17 = 74.5 + 34 = 108.5 \ g/mol \)

- Calculate Total Molar Mass of Desired Products

Identify the desired product which is N₂H₄.Molar mass of desired product (N₂H₄) is 32 g/mol

- Calculate Percent Atom Economy

Use the formula for percent atom economy: \[ \text{Percent Atom Economy} = \frac{\text{Molar Mass of Desired Product}}{\text{Total Molar Mass of Reactants}} \times 100 \]\[ \text{Percent Atom Economy} = \frac{32}{108.5} \times 100 \approx 29.5 \% \]

Key concepts

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with the same number of atoms for each element on both the reactant and product sides. This ensures the conservation of mass. In the given exercise, the overall reaction from the Raschig process is:

aqt{NaOCl (aq) + 2 NH₃ (aq) → Na₂H₄ (aq) + NaCl (aq) + H₂O (l)}aqt
This means for every 1 mole of sodium hypochlorite (NaOCl) and 2 moles of ammonia (NH₃), we get 1 mole of hydrazine (N₂H₄), 1 mole of sodium chloride (NaCl), and 1 mole of water (H₂O). Balancing the equation involves making sure the same number of atoms for each element is present on both sides.

• Na: 1 atom on both sides
• O: 1 atom on both sides
• Cl: 1 atom on both sides
• N: 2 atoms on both sides
• H: 8 atoms on both sides

Balancing chemical equations is critical for accurate stoichiometric calculations, including percent atom economy.

Molar Mass Calculation

Calculating molar masses involves summing the atomic masses of all atoms in a molecule. For instance, in the given equation:

• NaOCl: Na (23 g/mol) + O (16 g/mol) + Cl (35.5 g/mol) = 74.5 g/mol
• NH₃: 14 (N) + 3 * 1 (H) = 17 g/mol. Since there are 2 NH₃, we get 34 g/mol
• N₂H₄: 2 * 14 (N) + 4 * 1 (H) = 32 g/mol
• NaCl: Na (23 g/mol) + Cl (35.5 g/mol) = 58.5 g/mol
• H₂O: 2 * 1 (H) + 16 (O) = 18 g/mol

Using these molar mass values, we calculate the total molar mass of the reactants. It is 74.5 g/mol for NaOCl plus 34 g/mol for 2 NH₃, resulting in 108.5 g/mol. Molar mass calculations are pivotal in understanding the quantities of substances involved in reactions, which helps in analyzing efficiencies like atom economy.

Rocket Fuel Chemistry

Hydrazine (N₂H₄) is a valuable compound used as rocket fuel due to its high energy content and the exothermic nature of its decomposition. Related to the given Raschig process equation:

aqt{NaOCl (aq) + 2 NH₃ (aq) → N₂H₄ (aq) + NaCl (aq) + H₂O (l)}aqt

Hydrazine's efficient production and combustion are vital in the chemical propulsion of rockets:

• High-energy output from its combustion
• Easy storage and handling compared to some alternative propellants
• Provides thrust necessary for rocket propulsion

The proficiency of hydrazine as a rocket fuel underscores why processes like the Raschig process are essential in rocket fuel chemistry. Understanding how this fuel is synthesized ensures its reliable and efficient use in aerospace applications.

Raschig Process

The Raschig process is a key industrial method for synthesizing hydrazine (N₂H₄). It involves a series of chemical reactions starting from ammonia and sodium hypochlorite. The given overall equation for the process is:

aqt{NaOCl (aq) + 2 NH₃ (aq) → N₂H₄ (aq) + NaCl (aq) + H₂O (l)}aqt

This three-step process includes:

• Reaction of NaOCl with NH₃ to form chloramine (NH₂Cl)
• Further reaction of NH₂Cl with NH₃ to form hydrazine (N₂H₄)
• Generation of by-products like NaCl and H₂O

The Raschig process ensures the efficient production of hydrazine, which is not only used as a rocket fuel but also in various industrial applications such as water treatment and polymerization processes. Mastering the Raschig process helps in optimizing the synthesis and yields of hydrazine, making it economically viable and environmentally friendly.