When 10.0 g of a mixture of Ca1ClO322 and
Ca1ClO22 is heated to 700 °C in a 10.0-L vessel, both compounds
decompose, forming O21g2 and CaCl21s2. The final
pressure inside the vessel is 1.00 atm.
(b) What is the mass of each compound in the original
mixture?
Verified step by step guidance
1
Step 1: Write the balanced chemical equations for the decomposition of each compound. For calcium chlorate (Ca(ClO3)2), the decomposition reaction is: Ca(ClO3)2(s) → CaCl2(s) + 3O2(g). For calcium chlorite (Ca(ClO2)2), the decomposition reaction is: Ca(ClO2)2(s) → CaCl2(s) + 2O2(g).
Step 2: Use the ideal gas law to determine the total moles of O2 produced. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
Step 3: Let x be the moles of Ca(ClO3)2 and y be the moles of Ca(ClO2)2. From the stoichiometry of the reactions, the total moles of O2 produced can be expressed as 3x + 2y. Set up the equation 3x + 2y = total moles of O2 from Step 2.
Step 4: Convert the masses of Ca(ClO3)2 and Ca(ClO2)2 to moles using their molar masses. Set up the equation x * molar mass of Ca(ClO3)2 + y * molar mass of Ca(ClO2)2 = 10.0 g (total mass of the mixture).
Step 5: Solve the system of equations from Step 3 and Step 4 to find the values of x and y. Convert these moles back to grams to find the mass of each compound in the original mixture.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 will help relate the masses of the original compounds to the moles of products formed during decomposition.
Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The ideal gas law (PV=nRT) is particularly relevant here, as it allows us to relate the pressure of the gas produced to the number of moles and the volume of the container. Understanding these relationships is crucial for determining how the decomposition of the compounds affects the final pressure in the vessel.
Decomposition reactions involve a single compound breaking down into two or more simpler products, often requiring heat. In this scenario, both calcium hypochlorite (Ca(ClO)2) and calcium chloride (CaCl2) decompose upon heating, producing oxygen gas and solid calcium chloride. Recognizing the products of these reactions is essential for calculating the mass of each compound in the original mixture.
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