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Chapter 20: Problem 95

The atmosphere contains \(9.0 \times 10^{-6} \%\) Xe by volume at \(1.0 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\). a. Calculate the mass of Xe in a room \(7.26 \mathrm{~m}\) by \(8.80 \mathrm{~m}\) by \(5.67 \mathrm{~m} .\) b. A typical person takes in about \(2 \mathrm{~L}\) of air during a breath. How many Xe atoms are inhaled in each breath?

Short Answer

Expert verified
a. The mass of Xe in the room is approximately 0.849 g. b. A person inhales about \(1.16 × 10^{14}\) Xe atoms in each breath.

Step by step solution

01

Calculate the volume of the room

The volume of the room can be calculated using the formula for the volume of a rectangular prism, which is the product of its length, width, and height. In this case: Volume = Length × Width × Height So, we need to multiply the given dimensions of the room: Volume = \(7.26 m × 8.80 m × 5.67 m\)
02

Calculate the number of moles of Xe in the room

First, we need to find the moles of air in the room. The Ideal Gas Law helps us to find the number of moles (n) of a gas, using the formula: n = \(PV/RT\) Where: - P is the pressure (1.0 atm) - V is the volume (calculated in Step 1) - R is the gas constant (0.0821 L*atm/(K*mol)) - T is the temperature (25°C = 298 K) Next, we need to determine the number of moles of Xe in the room. As the atmosphere contains \(9.0 × 10^{-6} \%\) Xe by volume, we can use this proportion to calculate the number of moles of Xe from the total moles of air in the room.
03

Calculate the mass of Xe in the room

To find the mass of Xe in the room, use the formula: Mass = moles of Xe × molar mass of Xe (131 g/mol) Now we need to multiply the moles of Xe calculated in the previous step by the molar mass of Xe.
04

Calculate the number of Xe atoms inhaled per breath

We are given that a person takes in about 2 L of air during a breath. To find out how many Xe atoms are inhaled in each breath, we need first to calculate the moles of Xe in 2 L of air. Using the Ideal Gas Law formula n = \(PV/RT\), calculate the moles of air in 2 L at 1 atm and 25°C: - P= 1 atm - V = 2 L - R = 0.0821 L*atm/(K*mol) - T = 298 K Now, find the moles of Xe in 2 L of air by using the proportion of Xe in the air (as we did in Step 2). Finally, to find the number of Xe atoms, we must convert the moles of Xe inhaled to the number of atoms using Avogadro's number (6.022 × 10^23 atoms/mol). Multiply the moles of Xe by Avogadro's number to get the number of Xe atoms in each breath.

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Most popular questions from this chapter

What is a disproportionation reaction? Use the following reduction potentials \(\mathrm{ClO}_{3}^{-}+3 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}_{2}+\mathrm{H}_{2} \mathrm{O} \quad \mathscr{E}^{\circ}=1.21 \mathrm{~V}\) \(\mathrm{HClO}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}+\mathrm{H}_{2} \mathrm{O} \quad \mathscr{E}^{\circ}=1.65 \mathrm{~V}\) to predict whether \(\mathrm{HClO}_{2}\) will disproportionate.

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