Question

Convert the following pressures into mm Hg. a. 0.903 atm c. \(445 \mathrm{kPa}\) b. \(2.1240 \times 10^{6} \mathrm{Pa}\) d. 342 torr

Short answer

a. 686.28 mm Hg c. 3340.26 mm Hg b. 15942.32 mm Hg d. 342 mm Hg

Step-by-step solution

a. Convert 0.903 atm to mm Hg

Use the conversion factor 1 atm = 760 mm Hg. Multiply 0.903 atm by the conversion factor: \(0.903~\text{atm} \times \frac{760~\text{mm Hg}}{1~\text{atm}} = 686.28~\text{mm Hg}\)

c. Convert 445 kPa to mm Hg

Use the conversion factor 1 kPa = 7.50062 mm Hg. Multiply 445 kPa by the conversion factor: \(445~\text{kPa} \times \frac{7.50062~\text{mm Hg}}{1~\text{kPa}} = 3340.26~\text{mm Hg}\)

b. Convert \(2.1240 \times 10^{6}\) Pa to mm Hg

Use the conversion factor 1 Pa = 0.00750062 mm Hg. Multiply \(2.1240 \times 10^{6}~\text{Pa}\) by the conversion factor: \((2.1240 \times 10^{6}~\text{Pa}) \times \frac{0.00750062~\text{mm Hg}}{1~\text{Pa}} = 15942.32~\text{mm Hg}\)

d. Convert 342 torr to mm Hg

Since torr and mm Hg are the same unit, no conversion is needed. 342 torr = 342 mm Hg

Key concepts

Pressure Conversion

Pressure conversion is a useful skill, especially in fields like physics and engineering where different units are used. The purpose of pressure conversion is to translate a pressure value from one unit to another, making it possible to compare, analyse, or integrate data effectively.

There are several pressure units, with common ones including atmospheres (atm), pascals (Pa), torr, and millimeters of mercury (mm Hg). Each unit has its own conversion factor when converting between other units.

• To convert from atmospheres to mm Hg, use the conversion factor of 1 atm = 760 mm Hg.
• To convert from kilopascals (kPa) to mm Hg, use 1 kPa = 7.50062 mm Hg.
• For pascals to mm Hg, use 1 Pa = 0.00750062 mm Hg.
• Torr and mm Hg are effectively equivalent, so converting them is straightforward with a conversion ratio of 1:1.

Use these conversion factors and multiply them with the given value to obtain the desired unit. Memorizing these basic conversions can simplify many calculations.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the atmosphere on a surface area. It's a vital concept in meteorology and physical sciences.

The atmospheric pressure at sea level is considered to be 1 atmosphere (atm). This is approximately equivalent to:

• 101,325 pascals (Pa)
• 760 mm Hg (millimeters of mercury)
• 760 torr
• 14.696 psi (pounds per square inch)

Atmospheric pressure decreases as altitude increases. This is because there is less air above the surface exerting downward force. Understanding the standard value of atmospheric pressure in various units is crucial for calculations involving pressure changes due to elevation or weather conditions.

Pascal

The Pascal (Pa) is the SI unit of pressure and it is defined as one newton per square meter. In scientific and engineering contexts, pascals are often used because they align with the International System of Units (SI), making it a universal measure sure to support global standardization.

However, due to their small size, pascals are often used in conjunction with a prefix like kilo (kPa) to represent 1,000 pascals, allowing for more convenient numbers:

• 1 Pascal = 0.00000987 atm (approximately)
• 1 Pascal = 0.00750062 mm Hg
• 1,000 Pascals = 1 kPa

Using these relations, we can easily convert between pascals and other units of pressure depending on what's required for the problem or data analysis.

Torr

The Torr is a unit of pressure based on an absolute scale, named after Evangelista Torricelli, an Italian physicist. It is used particularly in high-vacuum physics and engineering contexts.

One torr equates to one millimeter of mercury or mm Hg, which reflects its origin in measuring atmospheric pressure using a mercury barometer. Consequently:

• 1 Torr = 1 mm Hg
• 1 Torr ≈ 133.322 Pa (pascals)
• Torr is the preferred unit when dealing with vacuum systems or when precise atmospheric pressure readings are necessary.

Since 1 Torr is effectively 1 mm Hg, converting between the two is direct and requires no mathematical manipulation, making it a convenient unit to work with when comparing measurements in millimeters of mercury.