Question

A rule of thumb for scuba diving is that the external pressure increases by 1 atm for every \(10 \mathrm{~m}\) of depth. A diver using a compressed air tank is planning to descend to a depth of \(25 \mathrm{~m}\) (a) What is the external pressure at this depth? (Remember that the pressure at sea level is 1 atm.) (b) Assuming that the tank contains \(20 \%\) oxygen and \(80 \%\) nitrogen, what is the partial pressure of each gas in the diver's lungs at this depth?

Short answer

(a) 3.5 atm; (b) Oxygen: 0.7 atm, Nitrogen: 2.8 atm.

Step-by-step solution

Determine the Depth Pressure Increase

For every 10 meters of depth, the pressure increases by 1 atm. At 25 meters, calculate the number of 10-meter increments: \( \frac{25}{10} = 2.5 \). This means there is an increase of 2.5 atm due to the depth.

Calculate the Total External Pressure

The external pressure at the surface of the water is 1 atm. Add the pressure increase due to the 25 meters depth to the surface pressure: \( 1 + 2.5 = 3.5 \text{ atm} \). Therefore, the total external pressure at 25 meters deep is 3.5 atm.

Calculate Oxygen Partial Pressure

The partial pressure of a gas is calculated as the total pressure multiplied by the percentage of that gas. For oxygen: \( 3.5 \times 0.20 = 0.7 \text{ atm} \). Thus, the partial pressure of oxygen is 0.7 atm.

Calculate Nitrogen Partial Pressure

Similarly, calculate the partial pressure for nitrogen, which is 80% of the total pressure: \( 3.5 \times 0.80 = 2.8 \text{ atm} \). Therefore, the partial pressure of nitrogen is 2.8 atm.

Key concepts

External Pressure

When considering scuba diving, one of the most critical factors is understanding how external pressure changes with depth. At sea level, or when you are not submerged in water, the pressure exerted by the air on your body is 1 atmosphere (atm). This is a reference point for other pressure measurements. When you dive deeper, the pressure around you increases significantly because of the weight of the water above you.

For every 10 meters you dive deeper, the external pressure increases by 1 atm. This increase is due to the dense water exerting more pressure than air. For example, at a depth of 25 meters, the external pressure calculation is straightforward:

• Divide 25 meters by 10 meters per atm increase, resulting in an increase of 2.5 atm.
• Combining this with the atmospheric pressure at sea level gives a total of 3.5 atm.

Understanding external pressure is vital, not just for safety but also for managing your body's physiological responses while diving.

Gas Mixtures

Scuba divers breathe a mixture of gases, typically composed of oxygen and nitrogen, from their tanks. It's important to grasp that the air supply does not magically change when you dive; however, its effect on the body alters due to increased external pressure. Gas mixtures under pressure behave distinctly, which is why it's crucial to understand partial pressures—the pressure that each gas in a mixture would exert if it alone occupied the entire volume. In our example, the air in the tank contains 20% oxygen and 80% nitrogen:

• To find the partial pressure of the oxygen at 25 meters, multiply the total external pressure (3.5 atm) by 0.20. This gives 0.7 atm for oxygen.
• Similarly, for nitrogen, you multiply the total pressure by 0.80, resulting in a partial pressure of 2.8 atm.

These partial pressures help determine how each gas will behave in your body at different depths, as the body’s absorption and reaction to each gas can lead to significant physiological effects.

Scuba Diving Depth

Diving deeper into the ocean brings many changes due to increased pressures. As a diver goes further below the surface, understanding these changes in pressure becomes essential not only for safety but also for managing air supplies and preventing unwanted physiological effects such as nitrogen narcosis or oxygen toxicity. The effect of depth on pressure can help divers calculate:

• How long their air supply will last, as higher pressure increases air consumption.
• The type of dive equipment needed to handle varying pressure levels.

Understanding how depth affects pressure is a crucial aspect for divers. It informs them about how pressure impacts gas uptake in tissues and how to conduct dives safely to avoid complications like decompression sickness.