A scuba diver breathing normal air descends to \(100 \mathrm{~m}\) of depth, where the total pressure is \(11 \mathrm{~atm}\). What is the partial pressure of oxygen that the diver experiences at this depth? Is the diver in danger of experiencing oxygen toxicity?

Understanding Dalton's Law of Partial Pressures is vital when discussing gases involved in scuba diving and similar activities. This law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the individual gases' partial pressures. A partial pressure is basically what the pressure of a single gas would be if it occupied the entire volume on its own, at the same temperature.

Let's imagine our scuba diver's tank is filled with normal air, which is approximately 21% oxygen. To calculate the partial pressure of oxygen that the diver breathes in at a depth of 100 m, where the total pressure is 11 atmospheres (atm), we simply multiply the percentage of oxygen in the air (0.21) by the total pressure, following Dalton's Law. Therefore, the partial pressure of oxygen, or \( P_{\text{O}_2} \), is \( 0.21 \times 11 \) atm. It is this concept that helps us understand how gas pressures behave under different conditions and is crucial for dives planning and safety.

Oxygen, while essential for life, can become toxic under certain conditions, particularly when diving. This is known as oxygen toxicity, and it occurs when the partial pressure of oxygen in the body becomes too high. The risk increases with depth since the partial pressure of gases increases with the total pressure according to Dalton's Law.

There are two main types of oxygen toxicity: pulmonary and central nervous system (CNS) toxicity. Pulmonary toxicity can lead to lung damage and long-term health issues, while CNS toxicity can cause symptoms like dizziness, seizures, or even unconsciousness, both potentially fatal for a diver.

For recreational scuba divers, it is generally accepted that a partial pressure of oxygen up to 1.4 atm is safe. Beyond this threshold, as our example of the diver at 100 m shows, the danger of oxygen toxicity increases, indicating the critical importance of monitoring oxygen exposure during a dive.

In scuba diving, understanding the relationship between depth and pressure is indispensable since it directly affects a diver's safety. As a diver descends, the pressure from the water's weight increases. At sea level, humans are used to a pressure of 1 atm, but for every 10 meters of water depth, an additional atmosphere of pressure is added.

So, at 100 meters, our diver is exposed to 11 atm, which is 10 atm from water depth plus the 1 atm of pressure we experience at sea level. This significantly increases the partial pressures of the gases being breathed, as shown with oxygen in our example. Due to these changes, divers need to manage the time spent at various depths and control their ascent to prevent decompression sickness, often referred to as 'the bends'.

It is these principles of physics that are the basis for dive planning and the development of dive tables, which help to calculate safe ascent times and stops, ensuring divers do not ascend too quickly and risk their health.