Problem 19 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

The atmospheric pressure on top of Mount Everest is approximately \(0.3487 \,atm\), \(265 \,mmHg\), \(35342 \,Pa\), \(0.3534 \,bar\), and \(5.12 \,psi\).

Step 1: Convert to atmospheres (atm)

To convert the pressure to atmospheres (atm), we will use the conversion factor 1 atm = 760 torr: \(Pressure_{atm} = \frac{Pressure_{torr}}{760 \,torr} = \frac{265 \,torr}{760 \,torr} = 0.3487 \,atm\)

Step 2: Convert to millimeters of mercury (mmHg)

Since 1 torr is equivalent to 1 mmHg, the pressure in mmHg is the same as the given pressure in torr: \(Pressure_{mmHg} = 265 \,mmHg\)

Step 3: Convert to pascals (Pa)

To convert the pressure to pascals (Pa), we will first convert the pressure to atmospheres using the conversion factor 1 atm = 760 torr, and then use the conversion factor 1 atm = 101325 Pa: \(Pressure_{Pa} = Pressure_{atm} * 101325 \,Pa = 0.3487 \,atm * 101325 \,Pa = 35342 \,Pa\)

Step 4: Convert to bars

To convert the pressure to bars, we will first convert the pressure to atmospheres using the conversion factor 1 atm = 760 torr, and then use the conversion factor 1 atm = 1.01325 bar: \(Pressure_{bar} = Pressure_{atm} * 1.01325 \,bar = 0.3487 \,atm * 1.01325 \,bar = 0.3534 \,bar\)

Step 5: Convert to pounds per square inch (psi)

To convert the pressure to pounds per square inch (psi), we will first convert the pressure to atmospheres using the conversion factor 1 atm = 760 torr, and then use the conversion factor 1 atm = 14.696 psi: \(Pressure_{psi} = Pressure_{atm} * 14.696 \,psi = 0.3487 \,atm * 14.696 \,psi = 5.12 \,psi\) The atmospheric pressure on top of Mount Everest, in various units, is as follows: a) 0.3487 atm b) 265 mmHg c) 35342 Pa d) 0.3534 bar e) 5.12 psi

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere. It is a fundamental concept in meteorology and earth sciences. At sea level, we typically experience an atmospheric pressure of 1 atmosphere (atm), which is equivalent to 101325 pascals or 760 millimeters of mercury (mmHg). However, as we move to higher altitudes, such as the peak of Mount Everest, atmospheric pressure decreases significantly due to the thinner air.
This is why climbers often require supplemental oxygen to breathe at such high altitudes. Understanding atmospheric pressure allows us to measure weather changes and analyze environmental conditions in various locations. It's also crucial when converting pressure units to comprehend these variations effectively.
When studying atmospheric pressure, it's important to consider the factors affecting it, such as altitude, temperature, and humidity. These factors can cause pressure differences that are critical in predicting weather patterns and understanding air movement.

Unit Conversion

Unit conversion is an essential mathematical skill, especially when dealing with different measurements in scientific calculations. In the context of atmospheric pressure, understanding how to convert between units like atm, torr, Pascal (Pa), and bars is crucial.
Steps to convert units effectively include:

• Identify the unit you start with and the unit you need to convert to.
• Use the appropriate conversion factor for the units. For instance, converting torr to atm involves using the conversion factor 1 atm = 760 torr.
• Apply the conversion factor: divide or multiply the given value by the conversion factor, depending on whether you're converting to a larger or smaller unit.

Let's take converting 265 torr on Mount Everest to different units as an example: - From torr to atm: divide 265 by 760. - From torr to mmHg: it's directly equal, so 265 mmHg. - From atm to Pascal: multiply the atm value by 101325. - From atm to bars: multiply the atm value by 1.01325. - From atm to psi: multiply the atm value by 14.696.
Accurate unit conversion ensures that scientific data remains consistent and comparable.

Mount Everest Pressure Measurement

The atmospheric pressure at the summit of Mount Everest is considerably lower than at sea level. Measured at around 265 torr, this pressure is influenced by the mountain's extreme altitude of 29,028 feet. This low pressure impacts not only respiration for climbers but also the boiling point of water and other physical phenomena.
Given the lower atmospheric pressure, climbers can experience hypoxia, a condition where body tissues don't receive enough oxygen. To address this, many climbers use oxygen tanks to ensure adequate oxygen levels.

• The pressure value of 265 torr indicates that the air is less dense, leading to decreased oxygen availability.
• Converting this measure across various units helps in preparing equipment and resources needed for scientific or climbing expeditions.

Understanding these measures is vital for safety and preparation when attempting to summit one of the world's highest peaks.