A mixture containing KClO3, K2CO3, KHCO3, and KCl was heated, producing CO2, O2, and H2O gases according to the following equations: 2 KClO31s2¡2 KCl1s2 + 3 O21g2 2 KHCO31s2¡K2O1s2 + H2O1g2 + 2 CO21g2 K2CO31s2¡K2O1s2 + CO21g2 The KCl does not react under the conditions of the reaction. If 100.0 g of the mixture produces 1.80 g of H2O, 13.20 g of CO2, and 4.00 g of O2, what was the composition of the original mixture? (Assume complete decomposition of the mixture.) How many grams of K2CO3 were in the original mixture?

Verified step by step guidance

1. Identify the chemical reactions involved and the products formed: \(2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2\), \(2 \text{KHCO}_3 \rightarrow \text{K}_2\text{O} + \text{H}_2\text{O} + 2 \text{CO}_2\), \(\text{K}_2\text{CO}_3 \rightarrow \text{K}_2\text{O} + \text{CO}_2\).
2. Calculate the moles of each gas produced using their respective molar masses: \(\text{H}_2\text{O}\), \(\text{CO}_2\), and \(\text{O}_2\).
3. Use stoichiometry to determine the moles of each reactant that decomposed to produce the given moles of gases.
4. Convert the moles of each reactant back to grams using their molar masses to find the mass of each component in the original mixture.
5. Subtract the masses of \(\text{KClO}_3\), \(\text{KHCO}_3\), and \(\text{K}_2\text{CO}_3\) from the total mass of the mixture to find the mass of \(\text{KCl}\).

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry is essential for relating the masses of the gases produced to the amounts of the original compounds in the mixture.

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, temperature, and the number of moles. Understanding these laws helps in calculating the expected volumes or masses of gases produced in a reaction. In this scenario, the production of gases like CO2, O2, and H2O must be analyzed to determine the original composition of the solid mixture.

Decomposition Reactions

Decomposition reactions involve the breakdown of a compound into simpler substances, often producing gases. In this question, the decomposition of KClO3, KHCO3, and K2CO3 is crucial to understanding how the original mixture generates the observed gases. Recognizing the specific products formed from each compound allows for the calculation of their initial amounts in the mixture.