Problem 48 - Chemistry Matter and Change

Question

High Altitude The atmospheric pressure in Denver, Colorado, is usually about 84.0 \(\mathrm{kP}\) a. What is this pres- sure in atm and torr units?

Step-by-Step Solution

Answer

Pressure in Denver is approximately 0.829 atm and 630 torr.

Step 1: Understand the Units

The problem gives atmospheric pressure in kilopascals (kPa) and asks to convert this measurement into both atmospheres (atm) and torr. Knowing the conversion factors helps: \(1\, ext{atm} = 101.325\, ext{kPa}\) and \(1\, ext{atm} = 760\, ext{torr}\).

Step 2: Convert from kPa to atm

Use the conversion factor to change kilopascals to atmospheres. Set up the conversion: \[\text{Pressure in atm} = \frac{84.0 \, ext{kPa}}{101.325 \, ext{kPa/atm}}\]. Calculate it by performing the division to find the pressure in atm.

Step 3: Perform Conversion Calculations (kPa to atm)

Compute the division: \(\frac{84.0}{101.325} \approx 0.829\). Therefore, the pressure in Denver is approximately \(0.829 \, ext{atm}\).

Step 4: Convert from atm to torr

Now convert the pressure from atmospheres to torr using the conversion factor \(1\, ext{atm} = 760\, ext{torr}\). Multiply the atmospheric pressure in atm by 760: \[0.829\, ext{atm} \times 760\, ext{torr/atm} \].

Step 5: Perform Conversion Calculations (atm to torr)

Compute the multiplication: \(0.829 \times 760 \approx 630\). Therefore, the pressure in Denver is approximately \(630 \, ext{torr}\).

Key Concepts

Atmospheric Pressure

Atmospheric pressure is a vital concept that refers to the force exerted by the weight of the atmosphere above us. It varies with elevation, as the higher you go, the less atmosphere there is weighing down on you. That's why in places like Denver, Colorado, which is at a higher altitude, atmospheric pressure is lower than in places at sea level. Imagine stacking a column of air molecules one on top of the other reaching from the ground to the edge of space. This stacked column exerts pressure, similar to how water in a glass exerts pressure on the bottom.

Several factors influence atmospheric pressure:

• Altitude: Higher altitude usually means lower atmospheric pressure.
• Weather patterns: High pressure often indicates calm, clear weather, while low pressure might signal storms.
• Temperature: Warmer air expands, leading to lower pressure, while cooler air is denser, creating higher pressure.

This concept helps explain why boiling points of water are lower on a mountain compared to sea level, due to lower atmospheric pressure. Understanding atmospheric pressure is essential for meteorology, physics, and even cooking!

Units of Pressure

When discussing pressure, it's crucial to understand the units in which it is measured. Pressure is commonly expressed in several units, depending on context and region. This can often confuse students, as there are several common systems:

• Pascal (Pa): The SI unit of pressure. It's very small, so often kilopascals (kPa) are used in everyday situations.
• Atmosphere (atm): A standard unit used to express atmospheric pressure. Normal atmospheric pressure at sea level is 1 atm.
• Torr: Named after Evangelista Torricelli, it's used especially in scientific contexts. 1 atm is equivalent to 760 torr.

Understanding each unit's relation is key to converting between them. For example, the exercise requires you to move from kilopascals to atmospheres and then to torr, making knowledge of these units critical. Remember, conversion among these units is a vital skill in both academic settings and practical applications.

Conversion Factors

Conversion factors are an essential tool in solving problems involving different units of measure. They act as a bridge to help move from one unit to another. In the context of pressure, conversion factors allow us to translate measurements into familiar or useful units.

Let's look at the key conversion factors:

• Converting from kilopascals to atmospheres requires knowing that 1 atm = 101.325 kPa. This means to convert kPa to atm, you divide the pressure in kPa by 101.325.
• To convert from atmospheres to torr, you use the fact that 1 atm = 760 torr, thus multiplying the atmospheric value by 760.

These factors let you transform pressure measurements appropriately. Careful handling of these conversions ensures precise results, which is crucial in scientific calculations, engineering, and even day-to-day tasks like understanding weather.