Problem 21 - Chemistry: The Central Science in SI Units, Global Edition

Question

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. \(\mathrm{Hg}\). (a) Convert this pressure to torr. (b) Convert this pressure to atm.

Step-by-Step Solution

Answer

(a) To convert the given pressure of 30.45 in. Hg to torr, we first convert inches of mercury to millimeters of mercury using the conversion factor 1 in. Hg = 25.4 mm Hg: \(30.45 \,\text{in. Hg} \times \frac{25.4 \,\text{mm Hg}}{1\, \text{in. Hg}} = 772.83\, \text{mm Hg}\) Since 1 torr is equal to 1 mm Hg, the pressure in torr is the same as the pressure in millimeters of mercury: 772.83 torr. (b) To convert the pressure from torr to atm, we use the conversion factor 1 atm = 760 torr: \(772.83 \, \text{torr} \times \frac{1\, \text{atm}}{760\, \text{torr}} \approx 1.017\, \text{atm}\) So, the barometric pressure is approximately 1.017 atm.

Step 1: (Step 1: Write down the given information.)

The given barometric pressure in Chicago on a beautiful summer day is 30.45 in. Hg.

Step 2: (Step 2: Convert inches of mercury to millimeters of mercury)

In order to convert inches of mercury to millimeters of mercury, we'll use the conversion factor 1 in. Hg = 25.4 mm Hg: \(30.45 \,\text{in. Hg} \times \frac{25.4 \,\text{mm Hg}}{1\, \text{in. Hg}}\) Now, perform the multiplication: \(30.45 \times 25.4 = 772.83\, \text{mm Hg}\) So, the pressure in millimeters of mercury is 772.83 mm Hg.

Step 3: (Step 3: Convert millimeters of mercury to torr)

Since 1 torr is equal to 1 mm Hg, the pressure in torr is the same as the pressure in millimeters of mercury: 772.83 mm Hg = 772.83 torr So, the pressure in torr is 772.83 torr.

Step 4: (Step 4: Convert torr to atmospheres)

Now we will use the conversion factor between torr and atmospheres (1 atm = 760 torr) to convert the pressure from torr to atm: \(772.83 \, \text{torr} \times \frac{1\, \text{atm}}{760\, \text{torr}}\) Now, perform the multiplication: \(\frac{772.83}{760} \approx 1.017\, \text{atm}\) So, the pressure in atmospheres is approximately 1.017 atm. In summary: (a) The barometric pressure in torr is 772.83 torr. (b) The barometric pressure in atm is approximately 1.017 atm.

Key Concepts

Barometric Pressure

Barometric pressure is a measure of the weight or force that the atmosphere exerts over a certain area. This force is typically measured using a barometer, and the pressure is often reported in inches of mercury (in. Hg), particularly in the United States. The measurement indicates how much mercury in a barometer's tube rises or falls, responding directly to the atmospheric conditions.
Barometric pressure is crucial in weather forecasting and has significant impacts on how weather is experienced. It affects wind patterns, how air moves, and even our comfort levels. For example:

• A high barometric pressure day often means clear skies and settled weather.
• Low barometric pressure typically indicates storms or unsettled weather ahead.

The value of barometric pressure on a "beautiful summer day" in Chicago as mentioned, showcases these pleasant and stable conditions.

Atmospheric Pressure

Atmospheric pressure, sometimes referred to as air pressure, is the force that air exerts on any surface it comes into contact with. It is measured in various units like millimeters of mercury (mm Hg), torr, or atmospheres (atm).
This pressure comes from the weight of air in the Earth's atmosphere pressing down on us. At sea level, the average atmospheric pressure is about 1013.25 millibars, which equals 760 mm Hg or 1 atm. Atmospheric pressure decreases with altitude because there is less air above to exert pressure.
Understanding atmospheric pressure is important for various fields such as aviation, meteorology, and even medicine. For meteorologists, changes in atmospheric pressure can indicate approaching weather systems, while pilots need to be aware of changing pressures to maintain altitude.

Unit Conversion

Unit conversion is an essential skill in science and engineering that allows us to express measurements in different units. This is vital for clarity and accuracy, especially when communicating scientific information across countries and disciplines that use different units of measure.
To convert barometric pressure from one unit to another, such as from inches of mercury to torr, we need a conversion factor. In our example:

• 1 inch of mercury (in. Hg) is equivalent to 25.4 millimeters of mercury (mm Hg).
• Since 1 torr is equal to 1 mm Hg, conversion between these two is straightforward.
• To convert torr to atmospheres, we use the ratio of 1 atm = 760 torr.

Through these conversions, the barometric pressure in Chicago can be expressed as 30.45 in. Hg, 772.83 torr, or approximately 1.017 atm. Understanding these steps ensures precise and consistent reporting of meteorological data.