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Diving, particularly SCUBA (Self-Contained Underwater Breathing Apparatus) diving, subjects the body to increased pressure. Each \(10 .\) m (approximately \(33 \mathrm{ft}\) ) of water exerts an additional pressure of 1 atm on the body. (a) What is the pressure on the body at a depth of \(100 . \mathrm{ft} ?\) (b) The partial pressure of nitrogen gas in air at 1 atm is \(593 \mathrm{mm}\) Hg. Assuming a SCUBA diver breathes compressed air, what is the partial pressure of nitrogen entering the lungs from a breathing tank at a depth of \(100 . \mathrm{ft} ?\) (c) The partial pressure of oxygen gas in the air at 1 atm is \(158 \mathrm{mm}\) Hg. What is the partial pressure of oxygen in the air in the lungs at a depth of \(100 . \mathrm{ft} ?\) (d) Why is it absolutely essential to exhale vigorously in a rapid ascent from a depth of \(100 . \mathrm{ft?}\)

Step by step solution

01

Determine the Depth in Meters

First, convert the depth from feet to meters to align with the pressure increase per 10 meters of water depth. Given depth is \( 100 \text{ ft} \), and since \( 33 \text{ ft} \equiv 10 \text{ m} \), then \( 100 \text{ ft} = \frac{100}{33} \times 10 \approx 30.3 \) meters.

02

Calculate Pressure on the Body at 100 ft

For every \( 10 \text{ m} \) depth, the pressure increases by \( 1 \text{ atm} \). At the surface, pressure is \( 1 \text{ atm} \). At \( 30.3 \text{ m} \): \[ \text{Total pressure} = \text{surface pressure} + \frac{30.3}{10} \times 1 \approx 4.03 \text{ atm} \]

03

Find Partial Pressure of Nitrogen at 100 ft

At \( 1 \text{ atm} \), the partial pressure of nitrogen is \( 593 \text{ mm Hg} \). At \( 4.03 \text{ atm} \), use: \[ \text{Partial pressure of } N_2 = 593 \times 4.03 \approx 2388.79 \text{ mm Hg} \]

04

Find Partial Pressure of Oxygen at 100 ft

At \( 1 \text{ atm} \), the partial pressure of oxygen is \( 158 \text{ mm Hg} \). At \( 4.03 \text{ atm} \), use: \[ \text{Partial pressure of } O_2 = 158 \times 4.03 \approx 636.74 \text{ mm Hg} \]

05

Understand the Importance of Exhaling During Ascent

When ascending, the external pressure decreases. Without exhaling, the volume of gases in the lungs would expand. To prevent lung overexpansion and potential injury, it is vital to exhale and release this expanding air during ascent.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Pressure in SCUBA Diving

When diving, the deeper you go, the more water is above you. This increases the pressure exerted on your body. At sea level, pressure is 1 atmosphere (atm). Every additional 10 meters you dive adds another atmosphere of pressure. So, at 100 feet, which is about 30.3 meters, the total pressure is approximately 4.03 atm. This total accounts for the weight of the water above and the pressure at the water's surface. Understanding this is crucial because it influences how gases behave in your body and affects breathing equipment.

The Concept of Partial Pressure

Air is a mixture of gases, and each gas contributes to the total pressure based on its concentration, known as partial pressure. In SCUBA diving, understanding partial pressure helps predict how gases will affect you underwater. For example, if nitrogen makes up 78% of air, at 1 atm, its partial pressure is 593 mm Hg. At 4.03 atm, its partial pressure becomes about 2388.79 mm Hg. This is significant because certain gases can act differently under increased pressure, affecting everything from breathing to how your body processes gases.

The Role of Nitrogen in Diving

Nitrogen is the most abundant gas in air. While it's harmless when breathed at normal pressure, it can cause issues at higher pressures like those experienced while diving. With increased depth and pressure, nitrogen's partial pressure rises, which may lead to nitrogen narcosis—an intoxicating effect on divers. It can impair judgment, making it crucial for divers to understand and monitor nitrogen levels. Additionally, rapid ascent can cause nitrogen to form bubbles in the bloodstream, leading to decompression sickness, commonly known as 'the bends.'

Oxygen and Its Partial Pressure Underwater

Oxygen is vital for life and makes up about 21% of the air. At 1 atm, its partial pressure is 158 mm Hg. However, at a depth of 100 feet, increasing pressure causes its partial pressure to rise to approx 636.74 mm Hg. Divers must monitor this because high partial pressures of oxygen can be toxic, leading to oxygen toxicity. This can cause symptoms like vision impairment, dizziness, and seizures. Proper diving practices help mitigate these risks, ensuring safe and enjoyable dives.

Proper Breathing Techniques While Diving

Breathing is crucial in SCUBA diving, as it helps manage buoyancy and pressure changes. Divers use equipment to provide breathable air under high pressure. A major breathing concern is during ascent. As pressure decreases, the volume of air in the lungs expands. It's essential for divers to exhale during ascent to avoid lung over-expansion, which can cause serious injury. By releasing expanding gases safely, divers prevent potential problems and ensure a safe return to the surface.