Ch.10 - Gases

Problem 66

Chapter 10, Problem 66

A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, 0.900 mm * 0.300 mm * 10.0 mm, contains 4% Xe in a 1:1 Ne:He mixture at a total pressure of 66.66 kPa. Calculate the number of Ne atoms in the cell and state the assumptions you need to make in your calculation.

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Convert the dimensions of the plasma cell from millimeters to meters to find the volume in cubic meters.

Calculate the total volume of the plasma cell using the formula: \( V = \text{length} \times \text{width} \times \text{height} \).

Use the ideal gas law \( PV = nRT \) to find the total number of moles of gas in the cell, assuming ideal gas behavior.

Determine the mole fraction of Ne in the mixture. Since the mixture is 4% Xe and a 1:1 Ne:He mixture, calculate the mole fraction of Ne.

Calculate the number of Ne atoms by multiplying the moles of Ne by Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol).

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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 gas particles in a given volume under specific conditions. In this problem, it will help determine the number of moles of the gas mixture in the plasma cell, which can then be converted to the number of atoms.

Partial Pressure

Partial pressure is the pressure that each gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of its individual components. This concept is crucial for calculating the contribution of neon (Ne) to the total pressure in the plasma cell, allowing for the determination of its mole fraction.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles of all components. In this scenario, knowing the mole fraction of neon in the gas mixture will enable the calculation of the total number of Ne atoms present in the plasma cell, based on the total number of moles derived from the Ideal Gas Law.

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Related Practice

Open Question

A mixture containing 0.50 mol H2(g), 1.00 mol O2(g), and 3.50 mol N2(g) is confined in a 25.0-L vessel at 25 °C. Calculate the partial pressure of H2, O2, and N2.

Open Question

A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 °C.

Textbook Question

The atmospheric concentration of CO2 gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every 106 L of the atmosphere are CO2). What is the mole fraction of CO2 in the atmosphere?.

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Textbook Question

A piece of dry ice (solid carbon dioxide) with a mass of 20.0 g is placed in a 25.0-L vessel that already contains air at 50.66 kPa and 25 °C. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO2 gas, and the total pressure in the container at 25 °C?

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Textbook Question

A sample of 5.00 mL of diethylether 1C2H5OC2H5, density = 0.7134 g>mL2 is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are PN2 = 21.08 kPa and PO2 = 76.1 kPa. The temperature is held at 35.0 °C, and the diethylether totally evaporates. (b) Calculate the total pressure in the container.

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Textbook Question

A rigid vessel containing a 3:1 mol ratio of carbon dioxide and water vapor is held at 200 °C where it has a total pressure of 202.7 kPa. If the vessel is cooled to 10 °C so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

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