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. $(\mathbf{a})$ Convert this pressure to torr. $(\mathbf{b})$ Convert this pressure to atm.

Short answer

(a) The pressure in torr is 773.43 torr. (b) The pressure in atm is 1.0177 atm.

Step-by-step solution

(a) Convert the pressure to torr.

To convert 30.45 in. Hg to torr, we need to use the first two conversion factors: 1 in. Hg = 25.4 mm Hg 1 torr = 1 mm Hg Step 1: Convert inches of mercury to millimeters of mercury. $30.45in.Hg\ast \frac{25.4mmHg}{1in.Hg}=773.43mmHg$ Step 2: Convert millimeters of mercury to torr. $773.43mmHg\ast \frac{1torr}{1mmHg}=773.43torr$ So, the pressure in torr is 773.43 torr.

(b) Convert the pressure to atm.

To convert 30.45 in. Hg to atm, we will continue from the previously calculated pressure in torr and use the third conversion factor: 1 atm = 760 torr Step 3: Convert torr to atm. $773.43torr\ast \frac{1atm}{760torr}=1.0177atm$ So, the pressure in atm is 1.0177 atm.

Key concepts

Barometric Pressure

Barometric pressure is a measure of the weight that the atmosphere's column of air exerts on the surface of the Earth. It is a key component in weather forecasting as such air pressure affects weather patterns and conditions. Understanding barometric pressure can help predict changes in the weather, such as when a storm is approaching. Meteorologists typically report it in several different units, each suitable for different situations. Comprehending these units and being able to convert between them is crucial for scientific calculations and studies.

Inches of Mercury

Inches of mercury, denoted as in. Hg, is one of the units commonly used to measure barometric pressure, especially in the United States. The term originated from the traditional way of measuring atmospheric pressure using a mercury barometer. In such devices, atmospheric pressure is indicated by the height to which mercury rises in a glass tube.
This unit remains in common use due to its historical significance and ease of comprehension in daily weather reports. For example, a typical atmospheric pressure at sea level is around 29.92 inches of mercury. Converting from inches of mercury to other units like torr or atm involves a clear understanding of conversion factors which are used to maintain consistency across different pressure measurement systems.

Torr

The torr is another unit of pressure that is often used in scientific contexts, especially in physics and chemistry. Named after the Italian scientist Evangelista Torricelli, who invented the barometer, one torr is equivalent to one millimeter of mercury (mm Hg). Because of this, converting between these two units is straightforward, involving a direct one-to-one ratio.
When converting from inches of mercury to torr, a stepwise process is required: first converting inches to millimeters, and then millimeters to torr. This highlights the need for accuracy in scientific measurements and the importance of using the correct conversion factors to ensure precision.

Atmosphere (atm)

The atmosphere (atm) is a standard unit of pressure defined as being precisely equal to 101,325 Pa (pascals). This unit is very useful for scientific calculations, as it represents the average air pressure at sea level on Earth. Understanding how to convert from other pressure units to atm is important for scientists and engineers alike, as many scientific equations use atm as a baseline for pressure.
Pressure conversions, such as from torr to atm, commonly use the factor that 1 atm equals 760 torr. Mastery of these conversions allows for precise computations across various scientific disciplines. The ability to convert between units of pressure is essential for solving complex problems and understanding the underlying principles of physical science.