Pakistan's K2 is the world's second-tallest mountain, with an altitude of 28,251 ft. Its base camp, where climbers stop to acclimate, is located about 16,400 ft above sea level. (c) Assuming the mole fraction of oxygen in air is 0.2095, what is the partial pressure of oxygen in mm Hg at the summit of K2?

Verified step by step guidance

1. Identify the total atmospheric pressure at the summit of K2 using the altitude given. You can use the barometric formula or an approximation that atmospheric pressure decreases by about 12% for every 1000 meters of altitude increase.
2. Calculate the partial pressure of oxygen at the summit by using the mole fraction of oxygen in air. The formula for partial pressure is: \( P_{O_2} = X_{O_2} \times P_{total} \), where \( P_{O_2} \) is the partial pressure of oxygen, \( X_{O_2} \) is the mole fraction of oxygen, and \( P_{total} \) is the total atmospheric pressure.
3. Convert the altitude from feet to meters for more accurate calculations, knowing that 1 meter equals approximately 3.28084 feet.
4. Apply the conversion factor to convert the calculated pressure in atmospheres (atm) to millimeters of mercury (mm Hg), using the conversion 1 atm = 760 mm Hg.
5. Ensure all units are consistent throughout the calculations to avoid any errors in the final result.

Key Concepts

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. In the context of atmospheric gases, it is calculated by multiplying the total pressure of the gas mixture by the mole fraction of the specific gas. This concept is crucial for understanding how gases behave in different altitudes, where total atmospheric pressure decreases.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. In this case, the mole fraction of oxygen in air is given as 0.2095, indicating that approximately 20.95% of the air is oxygen, which is essential for calculating its partial pressure.

Atmospheric Pressure at Altitude

Atmospheric pressure decreases with increasing altitude due to the reduction in the weight of the air above. At sea level, the average atmospheric pressure is about 760 mm Hg, but at higher altitudes, such as the summit of K2, this pressure is significantly lower. Understanding how to calculate the atmospheric pressure at different altitudes is vital for determining the partial pressure of gases like oxygen.