Question

Balance the following equation for the synthesis of hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\), a substance used as rocket fuel. $$ \mathrm{NH}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{NH}_{4} \mathrm{Cl}(s) $$

Short answer

The balanced equation is: 3\(\mathrm{NH}_3\) + 3\(\mathrm{Cl}_2\) \(\longrightarrow \mathrm{N}_2\mathrm{H}_4\) + 3\(\mathrm{NH}_4\mathrm{Cl}\).

Step-by-step solution

Write the Unbalanced Equation

First, write down the unbalanced chemical equation: \( \mathrm{NH}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{N}_{2}\mathrm{H}_{4}(l)+\mathrm{NH}_{4} \mathrm{Cl}(s) \). This shows the reactants and products in the chemical reaction.

List the Number of Atoms

Count the number of each type of atom present on both sides of the equation. \( \mathrm{NH}_3 \) has 1 N and 3 H, \( \mathrm{Cl}_2 \) has 2 Cl. On the product side, \( \mathrm{N}_2\mathrm{H}_4 \) has 2 N and 4 H, and \( \mathrm{NH}_4 \mathrm{Cl} \) has 1 N, 4 H, and 1 Cl.

Balance Nitrogen Atoms

Balance the nitrogen atoms. There are 2 N on the product side in \( \mathrm{N}_2\mathrm{H}_4 \) and 1 N in \( \mathrm{NH}_4 \mathrm{Cl} \), making a total of 3 N. Put a coefficient of 3 before \( \mathrm{NH}_3 \) to balance the N atoms: \( 3 \mathrm{NH}_{3} + \mathrm{Cl}_{2} \longrightarrow \mathrm{N}_{2}\mathrm{H}_{4} + \mathrm{NH}_{4}\mathrm{Cl} \).

Balance Hydrogen Atoms

Now balance the hydrogen atoms. On the product side, there are 4 H in \( \mathrm{N}_2\mathrm{H}_4 \) and 4 H in \( \mathrm{NH}_4\mathrm{Cl} \), totaling 8 H. On the reactant side, \( 3 \mathrm{NH}_{3} \) provides 9 H, so no changes are needed for hydrogen, it stays balanced.

Balance Chlorine Atoms

Balance the number of chlorine atoms. On the product side, there is 1 Cl atom in \( \mathrm{NH}_4 \mathrm{Cl} \), so put a coefficient of 3 before \( \mathrm{Cl}_2 \) to balance the equation: \( 3 \mathrm{NH}_{3} + 3 \mathrm{Cl}_{2} \longrightarrow \mathrm{N}_{2}\mathrm{H}_{4} + 3 \mathrm{NH}_{4}\mathrm{Cl} \).

Finalize the Balanced Equation

The final balanced equation is: \( 3\mathrm{NH}_{3} + 3\mathrm{Cl}_{2} \longrightarrow \mathrm{N}_{2}\mathrm{H}_{4} + 3\mathrm{NH}_{4}\mathrm{Cl} \). Double-check each type of atom to confirm they are balanced on both sides of the equation.

Key concepts

Hydrazine Synthesis

Hydrazine, \( \mathrm{N}_{2}\mathrm{H}_{4} \), plays a critical role as a fuel, especially in the aerospace industry. It is often synthesized from ammonia, \( \mathrm{NH}_{3} \), through a chemical process that includes chlorine, \( \mathrm{Cl}_{2} \). The hydrazine synthesis equation expresses the transformation of these reactants into products:

• \( \mathrm{NH}_{3} (g) + \mathrm{Cl}_{2} (g) \rightarrow \mathrm{N}_{2}\mathrm{H}_{4} (l) + \mathrm{NH}_{4}\mathrm{Cl} (s) \)

In this reaction, ammonia undergoes a transformation to become hydrazine and ammonium chloride. Understanding the synthesis process is important for ensuring efficient production and minimizing unwanted by-products.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It is a fundamental part of balancing equations like the hydrazine synthesis. Such calculations allow us to predict the amounts of substances consumed and produced. The balanced hydrazine synthesis is represented as:

• \( 3 \mathrm{NH}_{3} + 3 \mathrm{Cl}_{2} \rightarrow \mathrm{N}_{2}\mathrm{H}_{4} + 3 \mathrm{NH}_{4}\mathrm{Cl} \)

This equation tells us that 3 molecules of ammonia react with 3 molecules of chlorine, yielding 1 molecule of hydrazine and 3 molecules of ammonium chloride. Each coefficient in the equation corresponds to the exact ratio in which substances react. Hence, stoichiometry allows chemists to efficiently design reactions with specific outputs.

Nitrogen Balancing

Balancing nitrogen atoms is key in the synthesis of hydrazine. Initially, we notice that the reactants and products need careful accounting of nitrogen atoms. On the product side, there are two nitrogens in hydrazine (\( \mathrm{N}_{2}\mathrm{H}_{4} \)) and one in ammonium chloride (\( \mathrm{NH}_{4}\mathrm{Cl} \)), making three total nitrogens. To balance nitrogen atoms, three ammonia molecules (\( \mathrm{NH}_{3} \)) on the reactant side are used, because each ammonia has one nitrogen atom:

• \( \rightarrow 3 \mathrm{NH}_{3} \)

This simple adjustment ensures the molecule ratios correctly represent nitrogen distribution across the reaction, keeping the law of conservation of mass intact.

Chemical Reactions

Chemical reactions involve the transformation of substances through a rearrangement of atoms. In the synthesis of hydrazine, reactants like \( \mathrm{NH}_{3} \) and \( \mathrm{Cl}_{2} \) react together under certain conditions to form new products, hydrazine and ammonium chloride. The equation needs alignment with the law of conservation of mass. This law dictates that matter is neither created nor destroyed. As a result, balancing ensures that each type of atom has the same quantity on both sides of the equation:

• Reactants: \( 3 \mathrm{NH}_{3} + 3 \mathrm{Cl}_{2} \)
• Products: \( \mathrm{N}_{2}\mathrm{H}_{4} + 3 \mathrm{NH}_{4}\mathrm{Cl} \)

By following these principles, chemists effectively predict and manage chemical reactions, ensuring successful outcomes.