Problem 22 - Chemistry: The Central Science

Question

Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low-pressure reading of 882 mbar (millibars). Convert this reading into (a) atmospheres, (b) torr, and (c) inches of \(\mathrm{Hg}\) -

Step-by-Step Solution

Answer

The pressure of Hurricane Wilma in different units is approximately: (a) 0.87 atmospheres, (b) 660.6 torr, and (c) 0.260 inches of Hg.

Step 1: (a) Conversion to atmospheres (atm)

To convert the pressure from mbar to atm, we'll use the conversion factor for atmospheres: 1 atm = 1013.25 mbar First, we will divide the pressure in mbar (882 mbar) by the conversion factor: \(atm = \frac{882 \ mbar}{1013.25 \ mbar}\) Now, calculate the value of atm: \(atm = 0.870 \ atm\approx 0.87 \ atm\)

Step 2: (b) Conversion to torr

To convert the pressure from mbar to torr, we'll use the conversion factors for atmospheres and torr: 1 atm = 1013.25 mbar, 1 torr = \(\frac{1}{760}\) atm First, convert the pressure from mbar to atm as we did in part (a): \(atm = \frac{882 \ mbar}{1013.25 \ mbar} \approx 0.870 \ atm\) Now, we'll convert atm to torr using the conversion factor: \(torr = 0.87 \ atm \times 760 \ \frac{torr}{atm} \) Now, calculate the value of torr: \(torr \approx 660.6 \ torr\)

Step 3: (c) Conversion to inches of Hg

To convert the pressure from mbar to inches of Hg, we'll use the conversion factor for inches of Hg: 1 inch of Hg = 3386.39 mbar First, divide the pressure in mbar (882 mbar) by the conversion factor: \(inches \ of \ Hg = \frac{882 \ mbar}{3386.39 \ mbar}\) Now, calculate the value of inches of Hg: \(inches \ of \ Hg \approx 0.260 \ inches \ of \ Hg\) So, the pressure of Hurricane Wilma is approximately: - (a) 0.87 atmospheres, - (b) 660.6 torr, - (c) 0.260 inches of Hg.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted on a surface by the weight of the air above it. At sea level, this pressure is around 1013.25 millibars (mbar) or 1 atmosphere (atm).
It is a fundamental concept in meteorology and affects everyday weather conditions.

When discussing pressure, it's crucial to understand the average atmospheric pressure values that serve as baselines for calculations and conversions. For instance, in the context of hurricanes like Wilma, readings are significantly lower, which indicates intense storm systems.

• Standard atmospheric pressure at sea level: 1013.25 mbar
• Conversion to other units like atm or Pascals helps in understanding and comparing different pressure scenarios.

Understanding how pressure is converted between different units will enhance comprehension of how atmospheric conditions are measured and analyzed.

Torr

The torr is a unit of pressure, traditionally used in measuring partial vacuums. One torr is defined as 1/760 of an atmosphere.
It’s named after Evangelista Torricelli, an Italian physicist and mathematician who is credited with the invention of the barometer.

The pressure of gases, like air, can be measured using this unit which helps in applications ranging from industrial vacuum systems to scientific research.
When converting atmospheric pressure readings into torr, it’s critical to utilize proper conversion factors to ensure accuracy.

• 1 atm = 1013.25 mbar = 760 torr
• It’s beneficial, especially for chemistry and physics students, to learn to convert between different units as it aids in solving various practical and theoretical problems.

The concept of converting atmospheric pressure into torr provides insight into how pressures are standardized across different scientific fields.

Inches of Mercury

Inches of mercury (in Hg) is another unit used to measure pressure, particularly in weather forecasting and aviation. The unit originates from the pressure required to support a column of mercury one inch high in a barometer.
It is a traditional unit of measure and provides an easy-to-understand way to express atmospheric pressure.

It's still commonly used in weather reports across the United States and in some elements of aviation, thus its familiarity benefits various sectors.
To convert pressure into inches of mercury, conversion factors are necessary to provide equivalent values in different units.

• Standard sea level pressure is 29.92 inches of mercury.
• 1 inch of Hg = 3386.39 mbar, which gives an idea of the pressure in more relatable terms for observant areas.

Knowing how to convert pressure readings to inches of mercury can help in understanding forecasts and communicating with professionals in meteorology and aviation.