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Chapter 5: Problem 54

The average lung capacity of a human is 6.0 L. How many moles of air are in your lungs when you are in the following situations? a. At sea level \((T=298 \mathrm{K}, P=1.00 \mathrm{atm})\) b. \(10 . \mathrm{m}\) below water \((T=298 \mathrm{K}, P=1.97 \mathrm{atm})\) c. At the top of Mount Everest \((T=200 . \mathrm{K}, P=0.296 \mathrm{atm})\)

Short Answer

Expert verified
In the three given situations, the number of moles of air in the lungs can be calculated as follows: a. At sea level (T=298 K, P=1.00 atm) - \(n = 0.246 \mathrm{mol}\) b. 10 m below water (T=298 K, P=1.97 atm) - \(n = 0.483 \mathrm{mol}\) c. At the top of Mount Everest (T=200 K, P=0.296 atm) - \(n = 0.108 \mathrm{mol}\)

Step by step solution

01

Write down the given variables

For this situation, we have: - P = 1.00 atm - V = 6.0 L - T = 298 K - R = 0.0821 Latm / Kmol (Ideal Gas Constant)
02

Calculate the number of moles (n) using the Ideal Gas Law

Rearrange the Ideal Gas Law formula to solve for n: \(n = \frac{PV}{RT}\) Plug in the given values and calculate n: \(n = \frac{(1.00 \mathrm{atm})(6.0 \mathrm{L})}{(0.0821 \frac{\mathrm{Latm}}{\mathrm{Kmol}}) (298 \mathrm{K})} = 0.246 \mathrm{mol}\) So, at sea level, there are 0.246 moles of air in the lungs. #b. 10 m below water (T=298 K, P=1.97 atm)#
03

Write down the given variables

For this situation, we have: - P = 1.97 atm - V = 6.0 L - T = 298 K - R = 0.0821 Latm / Kmol (Ideal Gas Constant)
04

Calculate the number of moles (n) using the Ideal Gas Law

Use the rearranged Ideal Gas Law formula to solve for n: \(n = \frac{PV}{RT}\) Plug in the given values and calculate n: \(n = \frac{(1.97 \mathrm{atm})(6.0 \mathrm{L})}{(0.0821 \frac{\mathrm{Latm}}{\mathrm{Kmol}}) (298 \mathrm{K})} = 0.483 \mathrm{mol}\) So, 10 meters below water, there are 0.483 moles of air in the lungs. #c. At the top of Mount Everest (T=200 K, P=0.296 atm)#
05

Write down the given variables

For this situation, we have: - P = 0.296 atm - V = 6.0 L - T = 200 K - R = 0.0821 Latm / Kmol (Ideal Gas Constant)
06

Calculate the number of moles (n) using the Ideal Gas Law

Use the rearranged Ideal Gas Law formula to solve for n: \(n = \frac{PV}{RT}\) Plug in the given values and calculate n: \(n = \frac{(0.296 \mathrm{atm})(6.0 \mathrm{L})}{(0.0821 \frac{\mathrm{Latm}}{\mathrm{Kmol}}) (200 \mathrm{K})} = 0.108 \mathrm{mol}\) So, at the top of Mount Everest, there are 0.108 moles of air in the lungs.

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Most popular questions from this chapter

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