Problem 24 - 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 (882 mbar) can be converted into: (a) approximately 0.8705 atmospheres, (b) approximately 661 torr, and (c) approximately 26.04 inches of \(\mathrm{Hg}\).

Step 1: (a) Conversion to atmospheres

To convert the pressure reading from mbar to atmospheres, we can use the following proportion: \(1 \ \ \mathrm{atm} \ = \ 1013.25 \ \ \mathrm{mbar}\) Thus, to convert the pressure of 882 mbar to atmospheres, we have the equation: \[\frac{1 \ \mathrm{atm}}{1013.25 \ \mathrm{mbar}} \ = \frac{x}{882 \ \mathrm{mbar}}\] Solve for x: \[ x = \frac{882 \ \mathrm{mbar}}{1013.25 \ \mathrm{mbar}} \times 1 \ \mathrm{atm} \] \[ x \approx 0.8705 \ \mathrm{atm} \]

Step 2: (b) Conversion to torr

To convert the pressure reading from mbar to torr, we can use the following proportion: \(1 \ \ \mathrm{atm} \ = \ 760 \ \ \mathrm{torr}\) Thus, to convert the pressure of 882 mbar to torr, we can first convert it to atm as in (a) and then multiply by the conversion factor for torr: \[ 882 \ \mathrm{mbar} \times \frac {1 \ \mathrm{atm}}{1013.25 \ \mathrm{mbar}} \times \frac {760 \ \mathrm{torr}}{1 \ \mathrm{atm}} \ = x \ \mathrm{torr} \] \[ x \approx 661 \ \mathrm{torr} \]

Step 3: (c) Conversion to inches of \(\mathrm{Hg}\)

To convert the pressure reading from mbar to inches of \(\mathrm{Hg}\), we can use the following proportion: \(1 \ \ \mathrm{atm} \ = \ 29.92 \ \ \mathrm{in\ of\ Hg}\) Thus, to convert the pressure of 882 mbar to inches of \(\mathrm{Hg}\), we can first convert it to atm as in (a) and then multiply by the conversion factor for inches of \(\mathrm{Hg}\): \[ 882 \ \mathrm{mbar} \times \frac {1 \ \mathrm{atm}}{1013.25 \ \mathrm{mbar}} \times \frac {29.92 \ \mathrm{in\ of\ Hg}}{1 \ \mathrm{atm}} \ = x \ \mathrm{in\ of\ Hg} \] \[ x \approx 26.04 \ \mathrm{in\ of\ Hg} \] So, the pressure of Hurricane Wilma is approximately: (a) 0.8705 atmospheres, (b) 661 torr, and (c) 26.04 inches of \(\mathrm{Hg}\).

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air in the atmosphere on a surface. This pressure is crucial for understanding weather patterns and is often measured in terms of atmospheric units. A standard atmosphere (atm) is defined as 1013.25 millibars (mbar), or equivalently, 760 torr.

This measurement is crucial for comparing atmospheric conditions across different geographical locations. During Hurricane Wilma, the recorded atmospheric pressure was 882 mbar, lower than the standard atmosphere, reflecting the intense nature of the hurricane.

To convert from mbar to atmospheres, we use the conversion factor: \(1\ \text{atm} = 1013.25\ \text{mbar}\). This gives us a simplified way to express pressures in terms that are more universally understood in scientific and meteorological contexts.

Torr

Torr is another unit of pressure named after Evangelista Torricelli, an Italian physicist. It is equivalent to the pressure exerted by a 1 mm column of mercury and is often used in scientific applications like vacuum pressures.

The equation involves converting millibars to atmospheres first, and then using the relationship \(1\ \text{atm} = 760\ \text{torr}\), we can easily convert to torr.

• Begin with mbar to atm conversion.
• Use atm to torr conversion factor.

This process yields a pressure of approximately 661 torr for the hurricane, highlighting how much lower it was compared to regular atmospheric pressure.

Inches of Mercury

Inches of mercury, abbreviated as in of Hg, is a unit of measurement that originated from the mercury barometer, one of the oldest tools for measuring air pressure. It is especially known in meteorological reports in the United States.

The conversion from millibars to inches of mercury begins by converting millibars to atmospheres, similar to the previous steps, and then using the conversion factor \(1\ \text{atm} = 29.92\ \text{in hinspace of hinspace Hg}\).

This provides a way to relate atmospheric pressure to a tangible concept that is easy to grasp. For the hurricane example, converting 882 mbar results in a reading of approximately 26.04 inches of Hg.