Problem 21 - Chemistry The Central Science In Si Units

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. Hg. (a) Convert this pressure to torr. (b) Convert this pressure to atm.

Step-by-Step Solution

Answer

30.45 in. Hg is 773.43 torr and 1.018 atm.

Step 1: Understand the Units and Conversion Factors

Barometric pressure in inches of mercury (in. Hg) can be converted to other pressure units like torr and atm. The conversion factor for inches of mercury to torr is 1 in. Hg is equivalent to 25.4 torr. Similarly, 1 atm is equivalent to 29.92 in. Hg.

Step 2: Convert inches of mercury (in. Hg) to torr

We start with the given pressure of 30.45 in. Hg and convert it to torr using the conversion factor 1 in. Hg = 25.4 torr. Thus, we calculate: \[30.45 \text{ in. Hg} \times 25.4 \text{ torr/in. Hg} = 773.43 \text{ torr} \]

Step 3: Convert inches of mercury (in. Hg) to atm

Next, we convert the same pressure to atmosphere (atm) using the conversion factor 1 atm = 29.92 in. Hg. We calculate: \[ \frac{30.45 \text{ in. Hg}}{29.92 \text{ in. Hg/atm}} = 1.018 \text{ atm} \]

Key Concepts

Inches of Mercury

Inches of Mercury, often abbreviated as in. Hg, is a unit of pressure that originated from the design of barometers. Barometers are devices used to measure atmospheric pressure. They operate by using a column of mercury within a tube.
The weight of the air pushes on a reservoir of mercury, causing it to rise or fall in the tube. The height of mercury in the tube is proportional to atmospheric pressure. This measurement is what we refer to as inches of mercury.
It's a traditional measurement still commonly used, especially in the United States for weather forecasts and aviation. Though somewhat outdated, it remains a familiar unit for many, making understanding conversions essential for modern scientific work.

Torr

The torr is another unit of pressure named after Evangelista Torricelli, an Italian scientist who invented the barometer. One torr is defined as exactly 1/760th of a standard atmosphere (atm).
In practical terms, when converting inches of mercury to torr, we use the conversion factor where 1 in. Hg is equivalent to 25.4 torr. This relationship makes it relatively straightforward to convert between these units, helping in scientific calculations where precise measurements of pressure are necessary.
Understanding "torr" is crucial in fields such as physics and chemistry, where vacuum pressure measurements are commonplace. It offers a robust alternative to atmospheric pressure units and allows minute differences in atmospheric pressure to be measured quickly and easily.

Atmospheres

Atmospheres, denoted as atm, is a standard unit of pressure. It's defined as being precisely equivalent to 101,325 Pascals, which is another metric unit of pressure.
One atmosphere is roughly the pressure exerted by a 760 mm column of mercury at sea level and is commonly used in both scientific and engineering settings. This makes it a convenient and intuitive measure for atmospheric pressures and other applications.
Converting between units like inches of mercury and atmospheres is a necessary skill, especially when dealing with multi-national projects or scientific literature that uses various systems of measurement. Using the conversion factor 1 atm = 29.92 in. Hg assists in making these conversions painless.

Conversion Factors

Conversion factors are pre-determined values used to switch from one unit of measurement to another. They are extremely useful for maintaining consistency across different scientific disciplines and industries.
For pressure conversions, knowing the right factor is crucial. For example, converting from inches of mercury to torr requires multiplying by 25.4, while converting from inches of mercury to atmospheres involves dividing by 29.92.
Understanding and using conversion factors correctly ensures accuracy in calculations. This accuracy is especially important in scientific research, meteorological readings, and engineering tasks. A solid grasp of these principles not only aids in converting units but also in better comprehending the relevance and scale of measurements across fields.