Question

Write balanced equations to represent: (a) the decomposition, by heating, of solid ammonium nitrate to produce dinitrogen monoxide gas (laughing gas) and water vapor (b) the reaction of aqueous sodium carbonate with hydrochloric acid to produce water, carbon dioxide gas, and aqueous sodium chloride (c) the reaction of methane \(\left(\mathrm{CH}_{4}\right),\) ammonia, and oxygen gases to form gaseous hydrogen cyanide (HCN) and water vapor

Short answer

The balanced equations are: (a) \(\mathrm{NH}_4\mathrm{NO}_3 \rightarrow 2\mathrm{N}_2\mathrm{O} + 2\mathrm{H}_2\mathrm{O}\), (b) \(\mathrm{Na}_2\mathrm{CO}_3 + 2\mathrm{HCl} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2 + 2\mathrm{NaCl\), and (c) \(\mathrm{CH}_4 + 2\mathrm{NH}_3 + \frac{3}{2}\mathrm{O}_2 \rightarrow \mathrm{HCN} + 6\mathrm{H}_2\mathrm{O}\)

Step-by-step solution

Decomposition of solid ammonium nitrate by heating

The given decomposition reaction of solid ammonium nitrate is represented as follows: \[ \mathrm{NH}_4\mathrm{NO}_3 \rightarrow \mathrm{N}_2\mathrm{O} + \mathrm{H}_2\mathrm{O} \] Counting the atoms on each side of the equation shows this is unbalanced. Adding coefficients to the reactants and products to balance the atoms and energy give us: \[ \mathrm{NH}_4\mathrm{NO}_3 \rightarrow 2\mathrm{N}_2\mathrm{O} + 2\mathrm{H}_2\mathrm{O}\]

Reaction of aqueous sodium carbonate with hydrochloric acid

The given reaction of aqueous sodium carbonate with hydrochloric acid can be written as: \[ \mathrm{Na}_2\mathrm{CO}_3 + \mathrm{HCl} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2 + \mathrm{NaCl}\] This equation is unbalanced. After balancing it, the following equation is achieved: \[ \mathrm{Na}_2\mathrm{CO}_3 + 2\mathrm{HCl} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2 + 2\mathrm{NaCl}\]

Reaction of methane, ammonia, and oxygen gases

The given reaction of methane, ammonia, and oxygen gases can be represented as follows: \[ \mathrm{CH}_4 + \mathrm{NH}_3 + \mathrm{O}_2 \rightarrow \mathrm{HCN} + \mathrm{H}_2\mathrm{O}\] This equation is unbalanced. After balancing it, the following balanced chemical equation can be written down: \[ \mathrm{CH}_4 + 2\mathrm{NH}_3 + \frac{3}{2}\mathrm{O}_2 \rightarrow \mathrm{HCN} + 6\mathrm{H}_2\mathrm{O} \]

Key concepts

Decomposition Reactions

Decomposition reactions are chemical reactions where a single compound breaks down into two or more simpler products. These reactions usually require an input of energy like heat, light, or electricity. An excellent example of a decomposition reaction is the heating of solid ammonium nitrate \(\mathrm{NH}_4\mathrm{NO}_3\), which decomposes into dinitrogen monoxide \(\mathrm{N}_2\mathrm{O}\) and water \(\mathrm{H}_2\mathrm{O}\).

The goal is to ensure the mass and energy are conserved, so balancing the equation is crucial. For ammonium nitrate, notice how the original equation doesn’t have equivalent numbers of nitrogen, hydrogen, and oxygen atoms on both sides. By balancing, we adjust the coefficients to ensure the number of each type of atom is the same on either side of the equation:

• Start with the nitrogen atoms. One ammonium ion and one nitrate ion give a total of 2 nitrogen atoms, which matches the 2 nitrogen atoms in \(\mathrm{N}_2\mathrm{O}\).
• Then check the hydrogen, where 4 hydrogen atoms are balanced by \(2 \mathrm{H}_2\mathrm{O}\), giving 4 hydrogen atoms.
• Finally, balance the oxygen atoms; initial 1 oxygen in \(\mathrm{NH}_4\mathrm{NO}_3\) equals the oxygen in 2 water molecules and 1 \(\mathrm{N}_2\mathrm{O}\).

Balancing equations ensures no mass is lost in transition. Thus, understanding decomposition reactions is key to mastering chemical processes.

Acid-Base Reactions

Acid-base reactions are another fundamental type of chemical reaction. Typically, they involve an acid and a base reacting to produce a salt and water. One common acid-base interaction is between sodium carbonate \(\mathrm{Na}_2\mathrm{CO}_3\) and hydrochloric acid \(\mathrm{HCl}\).

In this particular acid-base reaction, when sodium carbonate and hydrochloric acid interact, products create water \(\mathrm{H}_2\mathrm{O}\), carbon dioxide \(\mathrm{CO}_2\), and sodium chloride \(\mathrm{NaCl}\). The balancing act for this reaction focuses on ensuring each element's atoms from the reactants equal those in the products. Here's how you balance it:

• There are 2 sodium atoms on the left, hence you require 2 sodium chloride on the right.
• 1 carbonate reacts with 2 hydrochloric acid molecules, producing 1 \(\mathrm{CO}_2\) and 1 \(\mathrm{H}_2\mathrm{O}\).
• Hydrogen and chlorine atoms balance out with 2 moles of \(\mathrm{HCl}\), ensuring atom parity across both sides.

Understanding acid-base reactions helps in many areas, such as environmental chemistry and pharmaceuticals, where neutralization is vital.

Combustion Reactions

Combustion reactions involve a substance reacting with oxygen to release energy. This energy is usually in the form of heat and light, commonly witnessed in burning processes. A combustion reaction discussed here involves methane \(\mathrm{CH}_4\), ammonia \(\mathrm{NH}_3\), and oxygen \(\mathrm{O}_2\).

Balancing such reactions can be tricky due to multiple reactants and products. The result of the reaction mentioned is hydrogen cyanide \(\mathrm{HCN}\) and a substantial amount of water \(\mathrm{H}_2\mathrm{O}\). Let's see how to balance this equation:

• Methane, with 1 carbon, collaborates towards forming \(\mathrm{HCN}\).
• For nitrogen, 2 molecules of \(\mathrm{NH}_3\) provide sufficient nitrogen for \(\mathrm{HCN}\) formation.
• Balancing oxygen requires careful adjustment. The initial unbalanced equation has fractional \(\frac{3}{2} \mathrm{O}_2\), but multiplying through by an appropriate factor can rid us of fractions.

Accurate balancing ensures that during combustion reactions, all substances are accounted for, making this concept central to industries like energy and manufacturing.