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Get Full Access to University Physics - 13 Edition - Chapter 18 - Problem 66p
Get Full Access to University Physics - 13 Edition - Chapter 18 - Problem 66p

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# BIO A person at rest inhales 0.50 L of air with each

ISBN: 9780321675460 31

## Solution for problem 66P Chapter 18

University Physics | 13th Edition

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Problem 66P

BIO A person at rest inhales 0.50 L of air with each breath at a pressure of 1.00 atm and a temperature of 20.0o C. The inhaled air is 21.0% oxygen. (a) How many oxygen molecules does this person inhale with each breath? (b) Suppose this person is now resting at an elevation of 2000 m but the temperature is still 20.0o C. Assuming that the oxygen percentage and volume per inhalation are the same as stated above, how many oxygen molecules does this person now inhale with each breath? (c) Given that the body still requires the same number of oxygen molecules per second as at sea level to maintain its functions, explain why some people report “shortness of breath” at high elevations.

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Solution 66P Here, we shall have to use the ideal gas equation PV = nRT and the equation for change RTy in pressure with height P = P e 0 . Here, P= pressure, V = volume, R = gas constant, T= absolute temperature, n = number of moles, M = molar mass of the gas, g = acceleration due to gravity and y = altitude Given, volume V = 0.5 L = 0.5 × 10 3m = 5.0 × 10 4 m 3 5 P = 1.00 atm = 1.01 × 10 Pa = 101000 Pa 0 T = 20 C = 293 K R = 8.314 J/mol.K (a) ow, substituting these values in the ideal gas equation, PV = nRT 4 3 101000 Pa × 5.0 × 10 m = n × 8.314 × 293 K n = 0.02 moles Therefore, the number of molecules of air, N = n × 6.02 × 10 23 = 0.02 × 6.02 × 10 23 = 0.120 × 10 23 Now, 21% of these molecules is oxygen, therefore the number of oxygen molecules is N = 21 × 0.120 × 10 23 molecules O2 100 21 N O2 = 2.52 × 10 molecules Therefore, the person inhales 2.52 × 10 21 molecules of O with each breath. 2 (b) Now, for air molar mass M = 0.029 kg/mol 2 g = 9.8 m/s y = 2000 m From the equation, Mgy P = P e0 RT 5 0.029 kg/mol×9.8 m/s ×2000 m P = 1.01 × 10 Pa × e 8.314 J/mol.K×293 K P = 101000 Pa × e 0.23 P = 101000/1.25 Pa = 80800 Pa Using this value of P in the ideal gas equation, 80800 Pa × 5.0 × 10 4 m = n × 8.314 J/mol.K × 293 K n = 0.016 moles 23 23 The number of air molecules = 0.016 × 6.02 × 10 molecules = 0.096 × 10 molecules Now, 21% of these molecules is oxygen, therefore the number of oxygen molecules is 21 23 N O 2= 100 × 0.096 × 10 molecules N O = 2.016 × 10 21 molecules 2 21 Therefore, the person now inhales 2.01 × 10 molecules of O wit2 each breath. (c) The number of oxygen molecules inhaled decreases with height as seen from the calculation in part b. This decrease may result in shortness of breath as the person does not get enough oxygen to breath at the given height unlike the sea level.

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##### ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13. The full step-by-step solution to problem: 66P from chapter: 18 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 66P from 18 chapter was answered, more than 342 students have viewed the full step-by-step answer. This full solution covers the following key subjects: oxygen, Person, breath, Molecules, air. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “BIO A person at rest inhales 0.50 L of air with each breath at a pressure of 1.00 atm and a temperature of 20.0o C. The inhaled air is 21.0% oxygen. (a) How many oxygen molecules does this person inhale with each breath? (b) Suppose this person is now resting at an elevation of 2000 m but the temperature is still 20.0o C. Assuming that the oxygen percentage and volume per inhalation are the same as stated above, how many oxygen molecules does this person now inhale with each breath? (c) Given that the body still requires the same number of oxygen molecules per second as at sea level to maintain its functions, explain why some people report “shortness of breath” at high elevations.” is broken down into a number of easy to follow steps, and 124 words.

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