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. $$\left(\mathrm{NH}_{4}\right) 2 \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}$$ Write the mole ratios for this reaction that relate ammonium dichromate to the products.

Step-by-Step Solution

Answer

The mole ratios for this reaction that relate ammonium dichromate to the products are: Ammonium dichromate to nitrogen gas: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{1 \, \text{mol} \, \mathrm{N}_{2}}\] Ammonium dichromate to chromium(III) oxide: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{1 \, \text{mol} \, \mathrm{Cr}_{2} \mathrm{O}_{3}}\] Ammonium dichromate to water vapor: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{4 \, \text{mol} \, \mathrm{H}_{2} \mathrm{O}}\]

Step 1: Identify the coefficients in the balanced chemical equation

In the given chemical equation, we have the coefficients: - for ammonium dichromate: 1 - for nitrogen gas: 1 - for chromium(III) oxide: 1 - for water vapor: 4 Equation: \[\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\]

Step 2: Write the mole ratios

Now that we have the coefficients from the balanced chemical equation, we can write down the mole ratios for ammonium dichromate related to the products: Mole ratio of ammonium dichromate to nitrogen gas: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{1 \, \text{mol} \, \mathrm{N}_{2}}\] Mole ratio of ammonium dichromate to chromium(III) oxide: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{1 \, \text{mol} \, \mathrm{Cr}_{2} \mathrm{O}_{3}}\] Mole ratio of ammonium dichromate to water vapor: \[\frac{1 \, \text{mol} \, (\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7})}{4 \, \text{mol} \, \mathrm{H}_{2} \mathrm{O}}\]

Key Concepts

Mole Ratios

Mole ratios are an essential part of understanding chemical reactions. They tell us how substances in a reaction relate to each other in terms of moles. This is crucial when converting between amounts of different substances involved in a reaction. For the given decomposition reaction of ammonium dichromate, we can find the mole ratios from the coefficients in the balanced chemical equation.

• Mole ratio helps in predicting how much product can be formed from a given amount of reactant.
• It assists in calculating the required amount of reactants to produce a desired amount of product.

In our example, the decomposition of ammonium dichromate, we have:- Ammonium dichromate to nitrogen gas: \(1:1\)- Ammonium dichromate to chromium(III) oxide: \(1:1\)- Ammonium dichromate to water vapor: \(1:4\)These ratios tell us how many moles of each product you get from one mole of ammonium dichromate. Use these ratios to scale up or down your reaction as needed.

Balanced Chemical Equations

Balanced chemical equations are the foundation of accurately interpreting chemical reactions. A balanced equation has equal numbers of each type of atom on both sides, following the Law of Conservation of Mass.In the case of our exercise, the given reaction is:\[\mathrm{NH}_4 2 \mathrm{Cr}_2 \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\]This balanced equation ensures the number of atoms for nitrogen, chromium, oxygen, and hydrogen are the same before and after the reaction.

• Ensuring the equation is balanced is critical for stoichiometry calculations.
• It helps predict how substances will react and the quantities involved.

To balance an equation, adjust the coefficients—not the subscripts. In this reaction, the coefficients help determine the mole ratios and are crucial in determining how the reaction proceeds.

Decomposition Reactions

A decomposition reaction is when a single compound breaks down into two or more simpler substances. This type of reaction is characterized by having one reactant and multiple products.The reaction in our example:\[\left(\mathrm{NH}_{4}\right) 2 \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}\]illustrates decomposing ammonium dichromate into nitrogen gas, chromium(III) oxide, and water vapor.

• Decomposition often requires energy, such as heat, to proceed.
• Understanding this type of reaction is essential for applications in chemistry, like analyzing thermal stability of compounds.

In practical terms, decomposition reactions are used in various applications, such as decomposing compounds for analysis or as part of larger chemical processes.