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 33.6 kPa, which can be converted to atmospheres using the formula (atm) = (kPa) / 101.3. Plugging in the values, we get (atm) = 33.6 / 101.3 ≈ 0.331 atm. The pressure at the top of Mount Everest is much lower than the pressure at sea level (1 atm), with a difference of approximately 33.1%.

Step 1: Pressure conversion formula

To convert the pressure from kilopascals (kPa) to atmospheres (atm), we can use the following formula: (atm) = (kPa) / 101.3 Here, we're given the pressure in kPa (33.6) and we want to find the pressure in atm.

Step 2: Plugging in the values

Plug the value of the pressure atop Mount Everest (33.6 kPa) into the formula: (atm) = (33.6 kPa) / 101.3

Step 3: Calculating the pressure in atm

Now, let's perform the calculation: (atm) = 33.6 / 101.3 ≈ 0.331 atm

Step 4: Comparing the pressure with sea level

The pressure atop Mount Everest (0.331 atm) is much lower than the pressure at sea level (1 atm). To see the difference in percentage, we can compare them by dividing the pressure at the top of Mount Everest by the pressure at sea level: Difference = (Pressure atop Mount Everest) / (Pressure at sea level) * 100 Difference = (0.331 atm / 1 atm) * 100 ≈ 33.1 % The pressure atop Mount Everest is approximately 33.1% of the atmospheric pressure at sea level.

Key Concepts

Understanding Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us in the atmosphere. It is a vital concept in meteorology and various scientific fields. In simpler terms, it is the pressure that the air exerts on everything at the surface of the Earth. This pressure is created by the gravitational pull on the air above the surface.

Here are some key points to understand about atmospheric pressure:

• Atmospheric pressure decreases with altitude. The higher you go above sea level, the less pressure there is, because there is less air above you.
• It is measured using barometers, and standard atmospheric pressure at sea level is defined as 101.3 kilopascals (kPa) or 1 atmosphere (atm).
• Changin atmospheric pressure can influence weather patterns and is a core principle in aviation and environmental science.

Pressure at Sea Level

The pressure at sea level is a standard reference point known as 1 atmosphere (atm). This is the baseline for many scientific calculations and is crucial for understanding deviations in pressure at different altitudes.

At sea level, the pressure is about 101.3 kPa or 1 atm. This standardization helps scientists and engineers compare and convert pressure readings from different locations. Pressure at sea level supports life by maintaining the right balance of gases necessary for breathing and numerous other biological processes.

It is important to recognize how changes in elevation affect pressure readings. For example, when you ascend a mountain, the pressure decreases because there is less air above you. The air is less dense, which is why breathing becomes more challenging at altitudes like those found at the top of Mount Everest.

Kilopascals to Atmospheres Conversion

Converting pressure from kilopascals (kPa) to atmospheres (atm) is a useful skill in scientific calculations, especially when dealing with various altitudinal measurements. Atmospheric pressure at sea level is 101.3 kPa, which equates to 1 atm.

To perform the conversion, use the formula:

• \[\text{(atm)} = \frac{\text{(kPa)}}{101.3}\]
• Simply plug in the known value of pressure in kPa and divide by 101.3 to find the equivalent in atm.
• Example: If the pressure is 33.6 kPa, the calculation will be \(\frac{33.6}{101.3}\), yielding approximately 0.331 atm.

This conversion is particularly useful in understanding how much less pressure there is at higher altitudes compared to sea level. Knowing how to switch between these units is essential for scientists and students examining atmospheric conditions across various terrains.