A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?
The Correct Answer and Explanation is:
To convert the barometric pressure from millimeters of mercury (mm Hg) to both atmospheres (atm) and kilopascals (kPa), we use the following conversion factors:
- 1 atm = 760 mm Hg
- 1 atm = 101.325 kPa
Step 1: Convert mm Hg to atm
$$
\text{Pressure (atm)} = \frac{615 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} \approx 0.8092 \, \text{atm}
$$
Step 2: Convert atm to kPa
$$
\text{Pressure (kPa)} = 0.8092 \, \text{atm} \times 101.325 \, \text{kPa/atm} \approx 82.01 \, \text{kPa}
$$
✅ Final Answer:
- Atmospheres (atm): ≈ 0.809 atm
- Kilopascals (kPa): ≈ 82.01 kPa
✏️ Explanation (300+ words):
Barometric pressure is the pressure exerted by the weight of the atmosphere at a given point. It is commonly measured in millimeters of mercury (mm Hg), especially in older or clinical settings, but it can also be expressed in atmospheres (atm) or kilopascals (kPa) for scientific and international standard purposes.
Denver, Colorado, is known as the “Mile-High City” because its elevation is approximately 1,609 meters (5,280 feet) above sea level. Due to this high elevation, the atmospheric pressure is lower than at sea level. At sea level, the standard atmospheric pressure is 760 mm Hg, but in Denver, it’s typically around 615 mm Hg.
To compare Denver’s pressure to standard conditions or to use it in calculations involving gas laws (like Boyle’s, Charles’s, or the Ideal Gas Law), you often need to convert mm Hg into more standard scientific units like atm or kPa.
In this case, dividing 615 mm Hg by 760 mm Hg gives the pressure in atm, because 1 atm equals 760 mm Hg. This yields approximately 0.809 atm, indicating that the air pressure in Denver is about 80.9% of the sea-level pressure.
Then, converting from atm to kPa allows you to express the pressure in SI (International System) units. Since 1 atm equals 101.325 kPa, multiplying 0.809 atm by 101.325 gives about 82.01 kPa.
Understanding how atmospheric pressure varies with elevation is crucial in fields like meteorology, aviation, and medicine, particularly in interpreting oxygen availability and weather changes.
