Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Question: A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01×10⁵ N/m². (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of 2.00×10⁶ N/m², what percent oxygen should it be to have the same oxygen partial pressure as at sea level?

Answer

The partial pressure of oxygen at sea level is 2.111×10⁴ N/m² and the percentage of oxygen at a pressure of 2.00×10⁶ N/m²is1.06.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of partial pressure

Partial pressure is the pressure exerted by individual gases in a mixture. Partial pressure is the product of the fraction of oxygen present and total pressure. The partial pressure of oxygen is expressed as follows;

$P_{O_{2}} = f r a c t i o n o f O_{2} \times P_{t o t a l}$ ………………………….(1)

Where is the partial pressure of oxygen and is the total pressure

Step 2: Solution of part a

The fraction of oxygen and the total pressure is given as;

${fractionofO}_{2} = 20.9 % = 0.209 P_{total} = 1.01 \times 10^{5} N / m^{2}$

Substitute these values in equation (1)

${}_{O_{2}}= 1.01 \times 10^{5} N / m^{2} \times 0.209 = 2.111 \times 10^{4} N / m^{2}$

Step 3: Solution of part b

In this scenario, the total pressure has changed to 2.00×10⁶ N/m². We have to calculate the percentage of oxygen with the calculated measurement of partial pressure at sea level. Substitute the values in equation (1).

$2.111 \times 10^{4} N / m^{2} = f r a c t i o n o f O_{2} \times 2.00 \times 10^{6} N / m^{2} f r a c t i o n o f O_{2} = \frac{2.111 \times 10^{4} N / m^{2}}{2.00 \times 10^{6} N / m^{2}} = 0.0106 = 1.06 %$

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College Physics (Urone)

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Short Answer

Step by Step Solution

Step 1: Definition of partial pressure

Step 2: Solution of part a

Step 3: Solution of part b

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College Physics (Urone)

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Step by Step Solution

Step 1: Definition of partial pressure

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Step 3: Solution of part b

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