Question

Perform the following conversions: (a) $0.850$ atm to torr, (b) 785 torr to kilopascals, (c) $655\mathrm{mm}\mathrm{Hg}$ to atmospheres, (d) $1.323\times {10}^5$ Pa to atmospheres, (e) $2.50$ atm to bars.

Short answer

(a) 646 torr, (b) 105.230 kPa, (c) 0.8618 atm, (d) 1.306 atm, (e) 2.53312 bars

Step-by-step solution

a) 0.850 atm to torr

Using the relationship between atm and torr, we have: 1 atm = 760 torr To convert 0.850 atm to torr, we can use the following proportion: $0.850\text{atm}\times \frac{760\text{torr}}{1\text{atm}}$ When we perform the calculation, we get: $0.850\times 760=646\text{torr}$ So, 0.850 atm is equal to 646 torr.

b) 785 torr to kilopascals

Using the relationships between torr, atm, and kilopascals, we can convert 785 torr to kilopascals: 1 torr = 1 mmHg 1 atm = 760 torr 1 atm = 101325 Pa = 101.325 kPa We set up a proportion to convert 785 torr to kilopascals: $785\text{torr}\times \frac{1\text{atm}}{760\text{torr}}\times \frac{101.325\text{kPa}}{1\text{atm}}$ After performing the calculation, we get: $\frac{785}{760}\times 101.325\approx 105.230\text{kPa}$ So, 785 torr is equal to approximately 105.230 kPa.

c) 655 mmHg to atmospheres

Using the relationships between mmHg and atmospheres, we can convert 655 mmHg to atmospheres: 1 torr = 1 mmHg 1 atm = 760 torr We set up a proportion to convert 655 mmHg to atmospheres: $655\text{mmHg}\times \frac{1\text{atm}}{760\text{mmHg}}$ After performing the calculation, we get: $\frac{655}{760}\approx 0.8618\text{atm}$ So, 655 mmHg is equal to approximately 0.8618 atm.

d) 1.323 x 10^5 Pa to atmospheres

Using the relationships between Pa and atmospheres, we can convert 1.323 x 10^5 Pa to atmospheres: 1 atm = 101325 Pa We set up a proportion to convert 1.323 x 10^5 Pa to atmospheres: $1.323\times {10}^5\text{Pa}\times \frac{1\text{atm}}{101325\text{Pa}}$ After performing the calculation, we get: $\frac{1.323\times {10}^5}{101325}\approx 1.306\text{atm}$ So, 1.323 x 10^5 Pa is equal to approximately 1.306 atm.

e) 2.50 atm to bars

Using the relationships between atm and bars, we can convert 2.50 atm to bars: 1 atm = 1.01325 bar We set up a proportion to convert 2.50 atm to bars: $2.50\text{atm}\times \frac{1.01325\text{bar}}{1\text{atm}}$ After performing the calculation, we get: $2.50\times 1.01325=2.53312\text{bar}$ So, 2.50 atm is equal to 2.53312 bars.

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air in the atmosphere of Earth. This pressure is generated by the collision of air molecules and gravitation acting upon the gases in the atmosphere. It can vary based on altitude and weather conditions but at sea level, it is typically considered to be 101,325 Pascals (Pa), which is equivalent to 1 atmosphere (atm). This standard measurement serves as a base unit for various pressure unit conversions and is often used to calibrate instruments and specify conditions in scientific contexts.

For instance, meteorologists use atmospheric pressure to predict weather patterns. High atmospheric pressure generally correlates with clear skies, while low pressure may indicate stormy weather. In daily life, you might encounter atmospheric pressure when dealing with tire pressures, vacuum systems, or understanding recipes that rely on pressure cooking. Comprehending atmospheric pressure is essential for conversions, such as determining the equivalent in torr or kilopascals, which are commonly used in different scientific and industrial settings.

Torr to Kilopascals

The conversion from torr to kilopascals (kPa) is a common exercise in pressure unit translation. One torr is defined as 1/760th of an atmosphere because the unit originated from the use of mercury (mmHg) in barometers, which measures pressure. Therefore, when converting from torr to kilopascals, one must take into account the equivalent of one atmosphere in Pascals, since a kilopascal is merely a multiple of the Pascal unit, specifically a thousand (one kPa is 1000 Pa).

To perform this conversion, a two-step process is employed: first, convert the torr value to atmospheres by dividing by 760, and then convert that atmosphere value to kilopascals using the conversion factor that 1 atm equals 101.325 kPa. This process is fundamental to many scientific calculations, particularly in fields where pressure measurements are routine, such as physics, engineering, and meteorology.

Pascals to Atmospheres

Pascals (Pa) to atmospheres (atm) conversion is essential for scientists and engineers working with various pressure measurements. Since the Pascal is a much smaller unit of pressure, representing the force of one Newton per square meter, it takes a large number of Pascals to equal one atmosphere. Specifically, the equivalent is 101,325 Pascals to 1 atmosphere.

Converting Pascals to atmospheres involves dividing the given Pascal value by 101,325. This conversion is commonly used in the study of atmospheric science, aeronautics, and other disciplines where understanding the pressure exerted by gases is crucial. Although the calculation is straightforward, accurate application allows for precise interpretation of conditions and behaviors within the context of atmospheric pressure.

mmHg to atm

The millimeter of mercury (mmHg) unit is commonly used in medicine and physiology, particularly when measuring blood pressure. The conversion from mmHg to atmosphere (atm) units is based on the relationship that 760 mmHg equals one atm, as this is the amount of mercury displacement in a barometer caused by the standard atmospheric pressure at sea level.

To convert mmHg to atm, simply divide the mmHg value by 760. The outcome represents the pressure in terms of the atmosphere, with practical implications in various fields like healthcare, where understanding blood pressure readings is tied to atmospheric pressure units. This conversion demonstrates the close relationships between units of pressure and further emphasizes the interconnectivity of different scientific and medical measurements.

atm to Bars

Bars are another unit of pressure that is particularly popular in the European Union and in the field of oceanography. One bar is slightly less than the atmospheric pressure at sea level, with 1 bar being defined as 100,000 Pascals (Pa). When converting atmospheres to bars, we use the equivalence of 1 atm to 1.01325 bars.

The conversion is straightforward: one multiplies the value in atmospheres by 1.01325 to get the pressure in bars. This is particularly useful for applications within the fields of geology and oceanography, where conveying pressure in terms of bars is standard. In such conversions, understanding the proportional relationship between atmospheres and bars is key. This precision in converting pressure units ensures that scientists and professionals across different disciplines can communicate and understand pressure-related data consistently.