Ch.10 - Gases: Their Properties & Behavior

Problem 140

Chapter 10, Problem 140

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?

Verified step by step guidance

Write the balanced chemical equation for the reaction: CS2(g) + 3 O2(g) → CO2(g) + 2 SO2(g).

Use the ideal gas law (PV = nRT) to calculate the initial moles of CS2 and O2 before the reaction, assuming all gases behave ideally.

Apply stoichiometry to determine the moles of CO2 and SO2 produced, and the moles of O2 remaining, based on the initial moles of CS2 and O2 and the balanced equation.

Calculate the total moles of gas present after the reaction by summing the moles of CO2, SO2, and unreacted O2.

Use the ideal gas law again to find the partial pressures of CO2, SO2, and O2 in the product mixture by multiplying the mole fraction of each gas by the total pressure of 2.40 atm.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under varying conditions and is crucial for calculating the changes in pressure and volume during chemical reactions.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of each individual gas. This principle is vital for determining the partial pressures of the gases produced in the reaction, as it allows us to relate the total pressure of the gas mixture to the contributions from each component.

Stoichiometry of Chemical Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. Understanding stoichiometry is crucial for determining the amounts of products formed from a given amount of reactants, which in this case helps in calculating the partial pressures of CO2, SO2, and unreacted O2 after the combustion of CS2.

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Textbook Question

The apparatus shown consists of three temperature-jacketed 1.000-L bulbs connected by stopcocks. Bulb A contains a mixture of H₂O(g), CO₂(g), and N₂(g) at 25 °C and a total pressure of 564 mm Hg. Bulb B is empty and is held at a temperature of -70 °C. Bulb C is also empty and is held at a temperature of -190 °C. The stopcocks are closed, and the volume of the lines connecting the bulbs is zero. CO₂ sublimes at -78 °C, and N₂ boils at -196 °C.

(b) How many moles of H₂O are in the system?

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Textbook Question

When solid mercury(I) carbonate, Hg2CO3, is added tonitric 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 gasare present?

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Textbook Question

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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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?

749

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