Ch.10 - Gases: Their Properties & Behavior

Problem 141

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Chapter 10, Problem 141

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?

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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

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

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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Related Practice

Textbook Question

When solid mercury(I) carbonate, Hg2CO3, is added to nitric acid, HNO3, a reaction occurs to give mercury(II) nitrate, Hg1NO322, water, and two gases A and B: Hg2CO31s2 + HNO31aq2¡ Hg1NO3221aq2 + H2O1l 2 + A1g2 + B1g2 (a) When the gases are placed in a 500.0-mL bulb at 20 °C, the pressure is 258 mm Hg. How many moles of gas are present?

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Open Question

Consider the combustion reaction of 0.148 g of a hydrocarbon with the formula CnH2n+2 in an excess of O2 within a 400.0-mL steel container. Before the reaction, the gaseous mixture had a temperature of 25.0 °C and a pressure of 2.000 atm. After complete combustion and heat loss, the products and excess O2 had a temperature of 125.0 °C and a pressure of 2.983 atm. (a) What is the formula and molar mass of the hydrocarbon? (b) What are the partial pressures in atmospheres of the reactants? (c) What are the partial pressures in atmospheres of the products and the excess O2?

Textbook Question

A mixture of CS21g2 and excess O21g2 is placed in a 10.0-L reaction vessel at 100.0 °C and a pressure of 3.00 atm. A spark causes the CS2 to ignite, burning it completely, according to the equation CS21g2 + 3 O21g2¡CO21g2 + 2 SO21g2 After reaction, the temperature returns to 100.0 °C, and the mixture of product gases (CO2, SO2, and unreacted O2) is found to have a pressure of 2.40 atm. What is the partial pressure of each gas in the product mixture?

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Textbook Question

When 10.0 g of a mixture of Ca(ClO₃)₂ and Ca(ClO)₂ is heated to 700 °C in a 10.0-L vessel, both compounds decompose, forming O₂(g) and CaCl₂(s). The final pressure inside the vessel is 1.00 atm. (a) Write balanced equations for the decomposition reactions.

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Textbook Question

A 5.00-L vessel contains 25.0 g of PCl3 and 3.00 g of O2 at 15 °C. The vessel is heated to 200.0 °C, and the contents react to give POCl3. What is the final pressure in the vessel, assuming that the reaction goes to completion and that all reactants and products are in the gas phase?

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Textbook Question

A steel container with a volume of 500.0 mL is evacuated, and 25.0 g of CaCO₃ is added. The container and contents are then heated to 1500 K, causing the CaCO₃ to decompose completely, according to the equation CaCO₃(s) → CaO(s) + CO₂(g). (a) Using the ideal gas law and ignoring the volume of any solids remaining in the container, calculate the pressure inside the container at 1500 K.

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