Chapter 8: Problem 5
A typical barometric pressure in Denver, Colorado, is \(615 \mathrm{mm}\) Hg. What is this pressure in atmospheres and kilopascals?
Short Answer
Expert verified
The pressure in Denver, Colorado, is approximately 0.8092 atmospheres (atm) and 81.99 kilopascals (kPa).
Step by step solution
01
Convert pressure from mmHg to atmospheres
Use the conversion factor that 1 atmosphere (atm) is equivalent to 760 mmHg. To convert mmHg to atm, divide the given pressure in mmHg by the conversion factor: \[ \text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760} \]
02
Calculate the pressure in atmospheres
Calculate the pressure in atm for Denver using the given pressure: \[ \text{Pressure in atm} = \frac{615 \, \mathrm{mm} \, \mathrm{Hg}}{760 \, \mathrm{mm} \, \mathrm{Hg}/\mathrm{atm}} = 0.8092 \, \mathrm{atm} \]
03
Convert pressure from atm to kilopascals
Use the conversion factor that 1 atm is equivalent to 101.325 kPa. To convert atm to kPa, multiply the pressure in atm by the conversion factor: \[ \text{Pressure in kPa} = \text{Pressure in atm} \times 101.325 \, \mathrm{kPa}/\mathrm{atm} \]
04
Calculate the pressure in kilopascals
Calculate the pressure in kPa for Denver using the pressure in atm: \[ \text{Pressure in kPa} = 0.8092 \, \mathrm{atm} \times 101.325 \, \mathrm{kPa}/\mathrm{atm} = 81.99 \, \mathrm{kPa} \]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Pressure Units Conversion
Understanding how to convert between different units of pressure is crucial in fields like chemistry and meteorology. Pressure measurement indicates the force applied per unit area, and it can be expressed in various units, such as millimeters of mercury (mmHg), atmospheres (atm), or kilopascals (kPa).
To convert between these units, we utilize conversion factors. A conversion factor is a value that allows us to change one unit to another by multiplying or dividing the quantity of interest. For instance, know that 1 atmosphere is equivalent to 760 mmHg, so to convert mmHg to atm, you would divide the pressure value in mmHg by 760. Conversely, converting atm to kPa involves multiplying by 101.325, since 1 atm equals 101.325 kPa.
When performing conversions, it's essential to keep track of units and use the correct conversion factor. This ensures accuracy in your calculations, whether you're analyzing a chemical reaction or forecasting the weather.
To convert between these units, we utilize conversion factors. A conversion factor is a value that allows us to change one unit to another by multiplying or dividing the quantity of interest. For instance, know that 1 atmosphere is equivalent to 760 mmHg, so to convert mmHg to atm, you would divide the pressure value in mmHg by 760. Conversely, converting atm to kPa involves multiplying by 101.325, since 1 atm equals 101.325 kPa.
When performing conversions, it's essential to keep track of units and use the correct conversion factor. This ensures accuracy in your calculations, whether you're analyzing a chemical reaction or forecasting the weather.
Atmospheric Pressure
Atmospheric pressure is the force per unit area exerted against a surface by the weight of the air above that surface in the Earth's atmosphere. It's a vital concept in meteorology, as it influences weather patterns and can affect altitude measurements.
At sea level, standard atmospheric pressure is defined as 101.325 kilopascals (kPa), 760 millimeters of mercury (mmHg), or 1 atmosphere (atm). However, at higher elevations, like Denver, Colorado, the atmospheric pressure is lower because there is less air above exerting pressure. This phenomenon can impact breathing and the boiling point of liquids, which is why understanding atmospheric pressure is not only scientific but also has practical day-to-day implications.
At sea level, standard atmospheric pressure is defined as 101.325 kilopascals (kPa), 760 millimeters of mercury (mmHg), or 1 atmosphere (atm). However, at higher elevations, like Denver, Colorado, the atmospheric pressure is lower because there is less air above exerting pressure. This phenomenon can impact breathing and the boiling point of liquids, which is why understanding atmospheric pressure is not only scientific but also has practical day-to-day implications.
Kilopascals (kPa)
Kilopascals (kPa) are a unit of pressure in the International System of Units (SI), and they are widely used in science, especially in the fields of physics and engineering. One kilopascal equals 1,000 pascals, and the pascal is defined as one newton of force applied over an area of one square meter.
In the context of atmospheric pressure, kilopascals allow us to measure the pressure exerted by the atmosphere with a fine degree of precision. The standard atmosphere at sea level is 101.325 kPa, while higher altitudes, such as in Denver, exhibit lower kPa values due to the reduced atmospheric mass above. Kilopascals are especially convenient for calculations in scientific studies and industrial applications, as they align with the decimal system.
In the context of atmospheric pressure, kilopascals allow us to measure the pressure exerted by the atmosphere with a fine degree of precision. The standard atmosphere at sea level is 101.325 kPa, while higher altitudes, such as in Denver, exhibit lower kPa values due to the reduced atmospheric mass above. Kilopascals are especially convenient for calculations in scientific studies and industrial applications, as they align with the decimal system.
Measurement and Conversion in Chemistry
Chemists routinely deal with measurements and conversions as they work with various physical quantities like pressure, volume, and temperature. Accurate measurements and conversions are critical for experiments, calculations, and understanding physical properties of substances.
To measure pressure, chemists might use a manometer which often gives readings in mmHg. Since standard units in science are typically SI units, such as kilopascals for pressure, conversions are frequently necessary for reporting and comparing results. The reliability of experimental results and the reproducibility of experiments depend on the precise conversion of these measurements.
Understanding how to convert units like mmHg to kPa, especially in the calculation of gas laws or when working with barometric pressures, is essential. This knowledge ensures that chemists and students alike can effectively communicate and interpret scientific data.
To measure pressure, chemists might use a manometer which often gives readings in mmHg. Since standard units in science are typically SI units, such as kilopascals for pressure, conversions are frequently necessary for reporting and comparing results. The reliability of experimental results and the reproducibility of experiments depend on the precise conversion of these measurements.
Understanding how to convert units like mmHg to kPa, especially in the calculation of gas laws or when working with barometric pressures, is essential. This knowledge ensures that chemists and students alike can effectively communicate and interpret scientific data.