Problem 19 - Chemistry: The Central Science

Question

The typical atmospheric pressure on top of Mt. Everest \((29,028 \mathrm{ft})\) is about 265 torr. Convert this pressure to (a) \(a \mathrm{tm}\), (b) \(\mathrm{mm} \mathrm{Hg}\), (c) pascals, (d) bars.

Step-by-Step Solution

Answer

The atmospheric pressure on top of Mt. Everest is approximately \(0.348 \mathrm{atm}\), \(265 \mathrm{mmHg}\), \(35261 \mathrm{Pa}\), and \(0.353 \mathrm{bars}\).

Step 1: (a) Convert the pressure to atm

First, let's convert the pressure in torr to atm. We can use the conversion factor \(\frac{1 \mathrm{atm}}{760 \mathrm{torr}}\). \(265 \mathrm{torr} \times \frac{1 \mathrm{atm}}{760 \mathrm{torr}} = a \mathrm{atm}\) Calculate the value of a: \(a = \frac{265}{760} \approx 0.348 \mathrm{atm}\)

Step 2: (b) Convert the pressure to mmHg

Since 1 torr is equal to 1 mmHg, the pressure value is already in mmHg. \(265 \mathrm{torr} = 265 \mathrm{mmHg}\)

Step 3: (c) Convert the pressure to pascals

To convert the pressure to pascals, we first convert it to atm (as we have already done in part (a)) and then use the conversion factor \(\frac{101325 \mathrm{Pa}}{1 \mathrm{atm}}\). \(0.348 \mathrm{atm} \times \frac{101325 \mathrm{Pa}}{1 \mathrm{atm}} = \mathrm{pascals}\) Calculate the value in pascals: \(0.348 \times 101325 \approx 35261 \mathrm{Pa}\)

Step 4: (d) Convert the pressure to bars

To convert the pressure to bars, we use the value we obtained in pascals and use the conversion factor \(\frac{1 \mathrm{bar}}{100000 \mathrm{Pa}}\). \(35261 \mathrm{Pa} \times \frac{1 \mathrm{bar}}{100000 \mathrm{Pa}} = \mathrm{bars}\) Calculate the value in bars: \(\frac{35261}{100000} \approx 0.353 \mathrm{bars}\) The pressure on top of Mt. Everest is approximately \(0.348 \mathrm{atm}\), \(265 \mathrm{mmHg}\), \(35261 \mathrm{Pa}\), and \(0.353 \mathrm{bars}\).

Key Concepts

atmospheric pressure

Atmospheric pressure is the weight of the air above us in the Earth's atmosphere, exerted on Earth's surface. This concept is crucial because it helps us understand how pressure changes based on altitude and weather conditions. At sea level, the standard atmospheric pressure is 1 atm, equivalent to 101,325 pascals or 760 torr. This value serves as a baseline used in various pressure conversion calculations. However, as you ascend in altitude, like climbing Mt. Everest, the atmospheric pressure decreases because there are fewer air molecules above exerting pressure. Understanding atmospheric pressure is important in numerous science and engineering fields, such as meteorology and aeronautics.

unit conversion

Unit conversion is a fundamental concept that involves changing a measurement from one unit to another. This skill is essential across scientific and engineering disciplines, where precise measurements matter. To perform unit conversions:

• Identify the original and desired units.
• Use a conversion factor, which is a numerical ratio or formula that equates one unit to another.
• Multiply the original measurement by the conversion factor to find the value in the new units.

Effective unit conversion often requires a reference for common conversion factors, such as 1 atm = 760 torr or 1 atm = 101,325 pascals. This process allows for consistent and accurate interpretation of measurements across different contexts, like converting the pressure on Mt. Everest from torr to atm.

Mt. Everest pressure

Mt. Everest, the highest peak on Earth, presents unique conditions including extremely low pressures compared to sea level. The reduced atmospheric pressure of 265 torr on top of Mt. Everest challenges both humans and equipment. For comparison, the sea level pressure is about 760 torr; thus, the pressure on Everest is significantly lower, providing less oxygen per breath. This factor is pivotal for climbers who must acclimate to avoid altitude sickness. Knowing and converting this pressure into units like atm or pascals assists in planning and managing the challenges of extreme altitude environments. For example, the 265 torr converts to approximately 0.348 atm, which is a useful measurement for understanding the thin air conditions at the summit.

torr to atm conversion

Converting from torr to atm is a straightforward yet essential calculation in understanding pressure changes, like those experienced on Mt. Everest. The key conversion factor here is that 1 atm is equal to 760 torr. Here's how you can do it:

• Start with the pressure value in torr.
• Apply the conversion factor: \(\frac{1 \, atm}{760 \, torr}\).
• Calculate to find the pressure in atm. For example, 265 torr converts to approximately 0.348 atm.

This conversion is vital in various fields such as aviation and medicine, where pressures are often described in more than one unit, making it necessary to switch between them for practical applications.