Problem 19 - Chemistry The Central Science In Si Units

Question

The highest barometric pressure ever recorded was 823.7 torr at Agata in Siberia, Russia on December 31,1968 . Convert this pressure to \((\mathbf{a})\) atm, (b) \(\mathrm{mm} \mathrm{Hg}\) (c) pascals, (d) bars, (e) psi.

Step-by-Step Solution

Answer

1.083 atm, 823.7 mm Hg, 109,855 Pa, 1.098 bars, 15.93 psi.

Step 1: Conversion from Torr to Atm

To convert torr to atm, we use the conversion factor: \(1 \text{ atm} = 760 \text{ torr}\). Therefore,\[\text{Pressure in atm} = \frac{823.7 \text{ torr}}{760} = 1.083289 \text{ atm.}\]

Step 2: Conversion from Torr to mm Hg

Since 1 torr is equivalent to 1 mm Hg by definition, the pressure in mm Hg will be the same as in torr. Therefore, \[\text{Pressure in mm Hg} = 823.7 \text{ mm Hg.}\]

Step 3: Conversion from Torr to Pascals

To convert torr to pascals (Pa), we use the conversion factor: \(1 \text{ torr} = 133.322 \text{ Pa}\). Hence,\[\text{Pressure in Pa} = 823.7 \times 133.322 = 109,854.8274 \text{ Pa.}\]

Step 4: Conversion from Torr to Bars

Convert torr to bars using the conversion factor: \(1 \text{ bar} = 750.062 \text{ torr}\). Thus,\[\text{Pressure in bars} = \frac{823.7 \text{ torr}}{750.062} = 1.097993 \text{ bars.}\]

Step 5: Conversion from Torr to Psi

To convert torr to psi, the conversion factor is \(1 \text{ psi} = 51.7149 \text{ torr}\). Therefore,\[\text{Pressure in psi} = \frac{823.7 \text{ torr}}{51.7149} = 15.928252 \text{ psi.}\]

Key Concepts

Barometric Pressure

Barometric pressure, often referred to as atmospheric pressure, is the force that the atmosphere exerts on a surface due to the weight of the air above it. This crucial concept in meteorology helps us understand weather patterns and altitude changes. In practical terms, barometric pressure is what makes your ears pop when you travel up a mountain or descend in an airplane. Because the column of atmosphere above you changes in height, it alters the weight exerted on you.
Measuring barometric pressure involves a barometer, which is a device specifically designed for this purpose. There are different types of barometers, including mercury-based barometers, aneroid barometers, and digital barometers. In scientific terms, barometric pressure is typically measured in units like torr, as seen in this exercise, where the record in Siberia was 823.7 torr.
Understanding barometric pressure is vital not only for weather prediction but also for various scientific and industrial applications.

Pressure Units

Pressure is a fundamental concept in physics and is defined as force applied perpendicular to the surface of an object per unit area. It is measured using different units depending on the context or country. In the exercise, we see pressure measured in torr, then converted into several other units.

• Atmosphere (atm): A standard unit used in many scientific contexts, where 1 atmosphere is the average atmospheric pressure at sea level, equal to 760 torr.
• Millimeters of Mercury (mm Hg): This is another common unit which is equivalent to torr; thus, 1 torr equals 1 mm Hg.
• Pascals (Pa): The SI unit of pressure, where even small pressures lead to large numerical values (1 atm = 101,325 Pa).
• Bars: Common in meteorological contexts, with 1 bar being slightly less than atmospheric pressure (1 bar = 100,000 Pa).
• Pounds per Square Inch (psi): Primarily used in the U.S., with 1 psi equating to 6894.76 pascals.

Choosing the right unit for pressure is crucial for clarity in communication across different industries and scientific fields.

Conversion Factors

Conversion factors are a bridge that helps in translating measurements from one unit to another. They are vital in scientific calculations to ensure consistency and accuracy across various systems of measurements. In our problem, we used several conversion factors to change from torr to different units of pressure.
For example, to convert from torr to atmospheres, we used the conversion factor of 1 atm = 760 torr. Similar conversion factors help us switch from torr to pascals, bars, and psi. The beauty of conversion factors is their simplicity: they typically involve straightforward multiplication or division. Understanding how to apply conversion factors requires careful attention to detail, as selecting the wrong factor or applying it incorrectly can lead to significant errors in calculations. Mastering these conversions is crucial in scientific and engineering work, where precision is key.

Measurement in Science

Measurement is the cornerstone of scientific inquiry. It allows us to quantify and analyze the world around us, leading to better understanding and advancements in technology and knowledge. In science, measurements must be both accurate (close to the true value) and precise (reproducible results).
Tools and units for measurement in science vary depending on what you are measuring. For pressure, as seen in the exercise, various instruments and units like barometers, torr, and pascals are employed. Proper calibration of these instruments is crucial to ensure reliable measurements.
Measurements require careful adjustments and considerations to eliminate errors. Environmental factors like temperature can affect measurements, particularly for pressure readings. Thus, scientific measurements often require corrections for these factors to maintain consistency. Understanding the intricacies of scientific measurement is essential in conducting experiments and research with reliability and credibility.