Problem 21 - Chemistry Central Science

Question

In the United States, barometric pressures are generally reported in inches of mercury (in. \(\mathrm{Hg}\) ). On a beautiful summer day in Chicago the barometric pressure is \(30.45\) in. Hg. (a) Convert this pressure to torr. (b) A meteorologist explains the nice weather by referring to a "high-pressure area." In light of your answer to part (a), explain why this term makes sense.

Step-by-Step Solution

Answer

The given pressure in inches of Hg is 30.45 in. Hg. To convert this measurement to torr, we can use the conversion factor: 1 in. Hg = 25.4 torr. \( Pressure_{torr} = 30.45 \ in. Hg \times \frac{25.4 \ torr}{1 \ in.Hg} \) \( Pressure_{torr} \approx 773.43 \ torr \) The term "high-pressure area" makes sense because the pressure of 773.43 torr is higher than the surrounding region. High pressure in an area prevents cloud formation and precipitation, resulting in clear and sunny weather conditions.

Step 1: Identify the conversion factor between inches of Hg and torr

The conversion factor between inches of Hg and torr is 1 in. Hg = 25.4 mm Hg. And we know that 1 mm Hg = 1 torr. Therefore, to convert the given pressure measurement to torr, we can use this conversion factor.

Step 2: Convert the given pressure to torr

The given pressure is 30.45 in. Hg. Using the conversion factor, we can convert this to torr as follows: \( Pressure_{torr} = Pressure_{in.Hg} \times \frac{25.4 \ torr}{1 \ in.Hg} \) \( Pressure_{torr} = 30.45 \ in. Hg \times \frac{25.4 \ torr}{1 \ in.Hg} \) \( Pressure_{torr} \approx 773.43 \ torr \)

Step 3: Explain why the term "high-pressure area" makes sense

A high-pressure area refers to a region where the atmospheric pressure is higher than the surrounding region. The higher pressure pushes down on the air, preventing the air from rising, which in turn, inhibits cloud formation and precipitation. This results in clear and sunny weather conditions. The given pressure of 30.45 in. Hg (or about 773.43 torr) indicates a high-pressure area, and this explains the nice weather in Chicago. In general, a pressure above around 760 torr is considered high pressure, while pressures below that value are considered low pressure.

Key Concepts

Inches of Mercury

Inches of mercury (in. Hg) is a widely used unit of measurement for barometric pressure, particularly in the United States. This unit originates from the process of measuring atmospheric pressure using a mercury barometer. In this setup, the pressure exerted by the atmosphere supports a column of mercury in a glass tube. The height of this column, measured in inches, gives the barometric pressure.

Despite the widespread use of electronic devices today, this term remains popular. It's a historical nod to older methods and provides a tangible way of understanding barometric pressure. If you visualize a column of mercury, each inch represents a certain amount of atmospheric pressure pressing down on the mercury.

Torr Conversion

Converting barometric pressure from inches of mercury to torr involves an established conversion factor. The relationship between these two units is based on the understanding that 1 inch of mercury (in. Hg) equals 25.4 millimeters of mercury (mm Hg). Since a torr is equivalent to 1 mm Hg, you can see that 1 in. Hg equals 25.4 torr.

The conversion process is straightforward: multiply the pressure value in inches of mercury by 25.4 to convert it to torr. For instance, if you have a barometric pressure of 30.45 in. Hg, the conversion to torr would be:

• Use the conversion: \[ Pressure_{torr} = Pressure_{in.Hg} \times \frac{25.4 \, \text{torr}}{1 \, \text{in.Hg}} \]
• Calculate for 30.45 in. Hg: \[ Pressure_{torr} = 30.45 \, \text{in. Hg} \times 25.4 \, \text{torr/in. Hg} \approx 773.43 \, \text{torr} \]

High-Pressure Area

A high-pressure area, often referred to in weather forecasts, is a key meteorological phenomenon. It occurs when the atmospheric pressure is higher than the surrounding areas. This relatively higher pressure influences weather patterns significantly.

High-pressure systems are associated with sinking air. This descending air suppresses cloud formation, leading to clearer skies. As a result, high-pressure areas are typically linked to fair and sunny weather. When meteorologists talk about a high-pressure system bringing nice weather, they refer to this calming effect on the weather.

• Above-average atmospheric pressure compared to the surroundings.
• Generally described with values exceeding 760 torr.
• Promotes dry, stable weather conditions due to descending air.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere of Earth. It is a crucial element in weather prediction and understanding climatic conditions. It varies with altitude and weather systems, playing a significant role in meteorological observations.

At sea level, the standard atmospheric pressure is often defined as 1013.25 hPa (hectopascals) or 760 mm Hg (torr). Essentially, atmospheric pressure affects how air moves and interacts, impacting everything from cloud formation to wind patterns. Recognizing how pressure changes can help predict different weather scenarios, making it a valuable tool for meteorologists.