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When discussing scuba diving, understanding gas laws is crucial for ensuring diver safety. One of the primary gas laws applicable here is Boyle's Law, which relates the pressure and volume of a gas. According to Boyle's Law, the pressure of a gas is inversely proportional to its volume when temperature is constant. This means that as a diver descends and the water pressure increases, the volume of air in their lungs decreases. Conversely, as they ascend, decreasing pressure causes the volume to increase. Another important consideration is the effect of temperature on gases, as described by Charles's Law, indicating that the volume of a gas increases with temperature, provided the pressure is constant. In a real-world scenario like scuba diving, divers need to account for both pressure and temperature changes, which is where the Combined Gas Law comes into effect. This law helps ensure divers can calculate and anticipate how gases behave under varying conditions to avoid dangerous situations like decompression sickness.

Understanding the pressure-volume relationship is key to comprehending how gases behave. According to Boyle's Law, which is part of the foundation of the Combined Gas Law, the pressure (\text{P}) of a gas is inversely proportional to its volume (\text{V}), given that the temperature remains constant. The relationship can be mathematically expressed as: \[ P \times V = \text{constant} \] This means if the volume of a gas increases, its pressure decreases, and vice versa. For instance, in the given problem, the diver's air volume changes from 50.0 mL to 150.0 mL, while underwater. According to Boyle's Law, as the diver ascends and the water pressure decreases, the air volume expands. Adjusting to these changes is critical in avoiding lung over-expansion injuries and ensuring safe dive practices.

Temperature conversion is an essential step when working with gas law calculations. In most cases, temperatures given in Celsius need to be converted to Kelvin for accurate results. Kelvin is the SI unit for temperature and is used in gas law equations because it starts at absolute zero, making calculations straightforward. The conversion formula is: \[ T(K) = T(^{\bullet}C) + 273.15 \] For example, in the exercise above, we converted the initial temperature of 8°C to Kelvin: \[ T_1 = 8^{\bullet}C + 273.15 = 281 K \] Similarly, the final temperature of 37°C converted to Kelvin is: \[ T_2 = 37^{\bullet}C + 273.15 = 310 K \] Using Kelvin ensures consistency and accuracy in gas law calculations, allowing one to properly apply the Combined Gas Law in various conditions.

Ideal gas law calculations help in understanding the behavior of gases under different conditions. The Ideal Gas Law is expressed as: \[ PV = nRT \] where \text{P} is pressure, \text{V} is volume, \text{n} is the amount of substance in moles, \text{R} is the ideal gas constant, and \text{T} is temperature in Kelvin. This law provides a good approximation of the behavior of real gases under various conditions. In our exercise, we use a variant of the Ideal Gas Law known as the Combined Gas Law to deal with changing conditions of pressure, volume, and temperature while keeping the amount of gas constant: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] By substituting the known values from our problem into this equation, we can solve for the unknown final pressure (\text{P}_2): \[ \frac{3.00 \text{ atm} \times 50.0 \text{ mL}}{281 K} = \frac{P_2 \times 150.0 \text{ mL}}{310 K} \] Simplifying and solving, we find the final pressure (\text{P}_2) to be approximately 1.10 atm. This calculation helps us understand how the parameters interact and how to predict the behavior of gases in practical scenarios such as scuba diving.