Problem 42 - Chemistry Matter and Change

Question

When heated by a flame, ammonium dichromate decomposes, producing nitrogen gas, solid chromium(III) oxide, and water vapor \begin{equation} \left(\mathrm{NH}_{4}\right) 2 \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O} \end{equation} Write the mole ratios for this reaction that relate ammonium dichromate to the products.

Step-by-Step Solution

Answer

1:1 with \(\mathrm{N}_2\) and \(\mathrm{Cr}_2 \mathrm{O}_3\), 1:4 with \(\mathrm{H}_2 \mathrm{O}\).

Step 1: Write the balanced chemical equation

The chemical reaction given is the decomposition of ammonium dichromate: \[(\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7 \rightarrow \mathrm{N}_2 + \mathrm{Cr}_2 \mathrm{O}_3 + 4 \mathrm{H}_2 \mathrm{O}\] However, the products need to be adjusted for the stoichiometric coefficients to balance the equation correctly as follows: \[(\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7 \rightarrow \mathrm{N}_2 + \mathrm{Cr}_2 \mathrm{O}_3 + 4 \mathrm{H}_2 \mathrm{O}\] This equation is balanced with respect to nitrogen, chromium, and hydrogen atoms.

Step 2: Understand the stoichiometry

In this balanced equation, for every 1 mole of ammonium dichromate (\((\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7\)), 1 mole of nitrogen gas (\(\mathrm{N}_2\)), 1 mole of chromium(III) oxide (\(\mathrm{Cr}_2 \mathrm{O}_3\)), and 4 moles of water vapor (\(\mathrm{H}_2 \mathrm{O}\)) are produced.

Step 3: Write the mole ratios

Using the balanced equation, the mole ratios between ammonium dichromate and the products are as follows: 1 mole of \((\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7\) to 1 mole of \(\mathrm{N}_2\), 1 mole of \((\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7\) to 1 mole of \(\mathrm{Cr}_2 \mathrm{O}_3\), and 1 mole of \((\mathrm{NH}_{4})_2 \mathrm{Cr}_2 \mathrm{O}_7\) to 4 moles of \(\mathrm{H}_2 \mathrm{O}\).

Key Concepts

Balanced chemical equation

Chemical equations are like recipes for reactions. They show us exactly how much reactants and products are involved in a chemical reaction. A balanced chemical equation means that the number of each type of atom is the same on both sides of the equation.
When balancing an equation, we adjust the coefficients, which are the numbers in front of molecules or atoms, to make sure we have the same number of each atom on both sides. This is based on the law of conservation of mass, which tells us that mass can neither be created nor destroyed in a chemical reaction.

• For instance, in the decomposition reaction of ammonium dichromate, we start with one ammonium dichromate molecule, and we want it to break down into nitrogen gas, chromium(III) oxide, and water vapor.
• The balanced equation: [( ext{NH}_4)_2 ext{Cr}_2 ext{O}_7 ightarrow ext{N}_2 + ext{Cr}_2 ext{O}_3 + 4 ext{H}_2 ext{O}] is balanced as it contains equal numbers of each type of atom (N, Cr, O, H) on both sides.

This balancing helps us know exactly what we need to start with, to get the desired amount of products.

Mole ratios

Mole ratios are like conversion factors in chemistry. They come from balanced chemical equations and help us relate amounts of different substances in a reaction. In simple terms, they tell us how much of each product we get from a given amount of reactant.
From the balanced equation of ammonium dichromate decomposition, we derive the following mole ratios:

• 1 mole of [( ext{NH}_4)_2 ext{Cr}_2 ext{O}_7] produces 1 mole of [ ext{N}_2],
• 1 mole of [( ext{NH}_4)_2 ext{Cr}_2 ext{O}_7] produces 1 mole of [ ext{Cr}_2 ext{O}_3],
• 1 mole of [( ext{NH}_4)_2 ext{Cr}_2 ext{O}_7] produces 4 moles of [ ext{H}_2 ext{O}].

These ratios are useful because they allow us to calculate how much of a particular product is formed from a known quantity of reactant. If we start with 2 moles of ammonium dichromate, we can expect to produce 2 moles each of nitrogen and chromium(III) oxide, and 8 moles of water.

Decomposition reaction

A decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances. These reactions often require energy, such as heat, to proceed.
In the case of ammonium dichromate, the compound decomposes when heated, producing nitrogen gas, chromium(III) oxide, and water vapor. Decomposition reactions are significant in various scientific and industrial processes, as they allow complex molecules to be broken down into simpler, more useful parts.

• In an easy-to-understand way, think of it as taking apart a toy to see the different pieces inside; each piece represents a different product in the chemical reaction.

This type of reaction is vital in fields like pharmacology, where complex organic compounds are decomposed into simpler ones that can be studied or used as medication ingredients.