Ch.10 - Gases: Their Properties & Behavior

Problem 137b

Chapter 10, Problem 137b

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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Determine the partial pressure of H2O(g) in Bulb A. Since the total pressure is given, use Dalton's Law of Partial Pressures which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual component in the gas mixture.

Calculate the mole fraction of H2O(g) in Bulb A. The mole fraction can be found by dividing the partial pressure of H2O(g) by the total pressure.

Use the ideal gas law to find the total number of moles of gas in Bulb A at 25 °C. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

Multiply the total number of moles of gas by the mole fraction of H2O to find the number of moles of H2O in Bulb A.

Since Bulbs B and C are initially empty and the stopcocks are closed, all the H2O remains in Bulb A. Therefore, the number of moles calculated in the previous step represents the total moles of H2O in the system.

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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 calculating the number of moles of a gas in a given volume and pressure, making it a fundamental tool in gas calculations. In this scenario, it can be used to determine the moles of H2O present in Bulb A.

Phase Changes and Sublimation

Understanding phase changes, such as sublimation and boiling, is crucial for this problem. CO2 sublimates at -78 °C, meaning it transitions from solid to gas at this temperature, while N2 boils at -196 °C. These phase changes affect the composition of gases in the bulbs when the system is cooled, influencing the calculations of moles of H2O.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas. This concept is vital for determining the contribution of H2O to the total pressure in Bulb A, allowing for the calculation of its moles based on the total pressure and the known pressures of CO2 and N2.

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Related Practice

Textbook Question

Pakistan's K2 is the world's second-tallest mountain, with an altitude of 28,251 ft. Its base camp, where climbers stop to acclimate, is located about 16,400 ft above sea level. (c) Assuming the mole fraction of oxygen in air is 0.2095, what is the partial pressure of oxygen in mm Hg at the summit of K2?

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Textbook Question

Assume that you take a flask, evacuate it to remove all the air, and find its mass to be 478.1 g. You then fill the flask with argon to a pressure of 2.15 atm and reweigh it. What would the balance read in grams if the flask has a volume of 7.35 L and the temperature is 20.0 °C?

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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.

(a) The stopcock between A and B is opened, and the system is allowed to come to equilibrium. The pressure in A and B is now 219 mm Hg. What do bulbs A and B contain?

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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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