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Found in: Page 472

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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# 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/m2 is 1.06.

See the step by step solution

## 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;

${{\mathbit{P}}}_{{\mathbf{O}}_{\mathbf{2}}}{\mathbf{=}}{\mathbf{ }}{\mathbit{f}}{\mathbit{r}}{\mathbit{a}}{\mathbit{c}}{\mathbit{t}}{\mathbit{i}}{\mathbit{o}}{\mathbit{n}}{\mathbf{ }}{\mathbf{ }}{\mathbit{o}}{\mathbit{f}}{\mathbf{ }}{\mathbf{ }}{{\mathbit{O}}}_{{\mathbf{2}}}{\mathbf{×}}{{\mathbit{P}}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ ………………………….(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;

${\mathbf{fractionofO}}_{\mathbf{2}}\mathbf{=}\mathbf{20}\mathbf{.}\mathbf{9}\mathbf{%}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{209}\phantom{\rule{0ex}{0ex}}{\mathbf{P}}_{\mathbf{total}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{01}\mathbf{×}{\mathbf{10}}^{\mathbf{5}}\mathbf{}\mathbit{N}\mathbf{/}{\mathbit{m}}^{\mathbf{2}}\phantom{\rule{0ex}{0ex}}$

Substitute these values in equation (1)

${}_{{\text{O}}_{2}}=1.01×{10}^{5}N/{m}^{2}×0.209\phantom{\rule{0ex}{0ex}}=2.111×{10}^{4}N/{m}^{2}$

## 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).

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