Problem 47 - Chemistry Matter and Change

Question

Mountain Climbing The pressure atop the world's highest mountain, Mount Everest, is usually about 33.6 kPa. Convert the pressure to atmospheres. How does the pressure compare with the pressure at sea level?

Step-by-Step Solution

Answer

The pressure atop Mount Everest is approximately 0.332 atm, which is about one-third of sea level pressure.

Step 1: Understanding Pressure Units

Pressure is measured in various units, most commonly in pascals (Pa), kilopascals (kPa), and atmospheres (atm). At sea level, atmospheric pressure is about 101.3 kPa or 1 atm.

Step 2: Conversion Factor

To convert from kPa to atm, use the conversion factor: 1 atm = 101.3 kPa.

Step 3: Calculate Pressure in Atmospheres

Apply the conversion factor to change the pressure from kPa to atm. Use the formula: \( \text{Pressure in atm} = \frac{\text{Pressure in kPa}}{101.3} \). Thus, \( \text{Pressure in atm} = \frac{33.6}{101.3} \approx 0.332 \), round this to three decimal places.

Step 4: Compare with Sea Level Pressure

At sea level, the pressure is approximately 1 atm. The pressure atop Mount Everest is 0.332 atm, meaning it is much lower than sea level pressure, just about one-third of it.

Key Concepts

Pressure Units

Pressure is a way of expressing force applied over an area. It has various units that help in measuring it accurately in different contexts. Some common pressure units include:

• Pascals (Pa) - the standard unit of pressure in the metric system.
• Kilopascals (kPa) - 1 kPa is equal to 1,000 Pascals, often used for larger values.
• Atmospheres (atm) - a unit based on average sea level pressure, where 1 atm equals 101.3 kPa.

Each of these units helps in understanding pressure in different environments. Scientists and engineers frequently convert between these units to make data interpretable and comparable. Understanding these units lays a strong foundation for solving problems related to pressure in various conditions.

Atmospheric Pressure

Atmospheric pressure is the weight of the air pressing down on the Earth. It changes with elevation and weather patterns. At sea level, atmospheric pressure typically measures about 101.3 kPa or 1 atm. This pressure is considered standard because it is what the human body is accustomed to at sea level.

• With altitude increase, atmospheric pressure decreases because there is less air above.
• Understanding how atmospheric pressure shifts is crucial for activities like mountain climbing, aviation, and weather forecasting.
• Changes in atmospheric pressure can affect how we feel and function. Adjustments in our body may be required as we move between zones of different pressures, such as moving from sea level to higher altitudes.

Mount Everest Pressure

Standing at around 8,848 meters, Mount Everest exhibits significantly different atmospheric pressure compared to sea level. On the top of Everest, the atmospheric pressure is around 33.6 kPa, which is much lower than the pressure at sea level.

• The pressure at the summit is about 0.332 atm when you convert kPa into atm, meaning it's roughly a third of sea level pressure.
• This lower pressure means there is less oxygen available, which is why climbers must acclimatize or use supplemental oxygen.
• Familiarity with pressure changes at high altitudes can better prepare climbers for the challenges they face while ascending and descending the mountain.

Sea Level Pressure

Sea level pressure is considered a baseline for atmospheric pressure measurements. It is approximately 101.3 kPa or equivalently, 1 atmosphere (atm).

• It's the pressure exerted by the weight of air above at sea level, where most human activities are concentrated.
• Variations from this pressure can signal different weather patterns. For instance, higher than standard pressure often indicates good weather, while lower can suggest storms.
• Understanding sea level pressure helps in comparing pressure conditions found at various altitudes and in applying these comparisons to real-world scenarios like weather prediction or planning high-altitude expeditions.