Question

Convert the following pressures into units of \(m m H g.\) a. 0.9975 atm c. 99.7 kPa b. \(225,400 \mathrm{Pa}\) d. 1.078 atm

Short answer

a. 758.3 mmHg b. 1690.29 mmHg c. 748.21 mmHg d. 819.28 mmHg

Step-by-step solution

Conversion Factors

To convert the given pressures into mmHg, we need to remember the following conversion factors: 1 atm = 760 mmHg 1 kPa = 7.50062 mmHg 1 Pa = 0.00750062 mmHg

Convert 0.9975 atm to mmHg

Given pressure: 0.9975 atm Use the conversion factor: 1 atm = 760 mmHg 0.9975 atm × (760 mmHg / 1 atm) = \(760 \times 0.9975\) mmHg = 758.3 mmHg

Convert 99.7 kPa to mmHg

Given pressure: 99.7 kPa Use the conversion factor: 1 kPa = 7.50062 mmHg 99.7 kPa × (7.50062 mmHg / 1 kPa) = \(7.50062 \times 99.7\) mmHg = 748.21 mmHg

Convert 225,400 Pa to mmHg

Given pressure: 225,400 Pa Use the conversion factor: 1 Pa = 0.00750062 mmHg 225,400 Pa × (0.00750062 mmHg / 1 Pa) = \(0.00750062 \times 225,400\) mmHg = 1690.29 mmHg

Convert 1.078 atm to mmHg

Given pressure: 1.078 atm Use the conversion factor: 1 atm = 760 mmHg 1.078 atm × (760 mmHg / 1 atm) = \(1.078 \times 760\) mmHg = 819.28 mmHg In summary, we've converted the following pressures into mmHg: a. 0.9975 atm = 758.3 mmHg b. 225,400 Pa = 1690.29 mmHg c. 99.7 kPa = 748.21 mmHg d. 1.078 atm = 819.28 mmHg

Key concepts

Atmospheric Pressure

Understanding the weight of the air surrounding us is essential in grasping the concept of atmospheric pressure. It refers to the force exerted by the Earth's atmosphere in all directions at a given point. Often expressed in units of 'atmospheres' (atm), this pressure is crucial for numerous scientific and weather-related calculations. At sea level, atmospheric pressure is standardized to be around 1 atm, which is equivalent to 760 mmHg, 101.325 kilopascals (kPa), or 101,325 pascals (Pa). This benchmark is used to calibrate instruments like barometers, which measure atmospheric pressure and help predict weather changes.
In everyday life, we may not feel the pressure due to the equal forces exerted from all directions, and our bodies are adapted to balance the internal and external pressures. However, changes in atmospheric pressure can affect our environment and health, for example, causing discomfort in our ears during flights or changes in altitude.

Pascal (Pa)

The Pascal is the SI unit of pressure and it is fundamental in understanding pressure conversion. One Pascal is defined as one newton of force applied over an area of one square meter. It is a relatively small unit, which leads to its common multiples being used in practice, such as the kilopascal (kPa) for ease of measurement and calculations.
When dealing with real-world scenarios like tire pressure, weather forecasting, or engineering applications, converting between units should be done with precision. Given the small magnitude of the Pascal, professional fields often use higher multiples of the unit to avoid dealing with large numbers. For instance, atmospheric pressure at sea level, which is about 101,325 Pa, is more commonly referred to as 101.325 kPa.

Kilopascal (kPa)

When working with pressures, the use of kilopascals (kPa) often simplifies understanding and calculations. The kilopascal is a multiple of the Pascal, with 1 kPa being equal to 1,000 Pa. This unit is widely used in science and engineering to measure things like gas pressures, tensile strength, and more.
Conversion from kPa to other units such as millimeters of mercury (mmHg) is important in many practical applications. For instance, blood pressure is commonly measured in mmHg but may also be represented in kPa in some medical instruments. Understanding how to convert between these units is not only vital for interpreting the results correctly but also enables a universal understanding of pressure values in different formats.

Millimeters of Mercury (mmHg)

The unit millimeters of mercury (mmHg) has historical roots in medicine and science, originating from the use of mercury in barometers. It conveys how high mercury is raised in a column by the pressure exerted on it. Primarily used in the medical field for blood pressure measurement, mmHg represents a direct and tangible way to understand pressure levels.
When you see a weather forecast or a medical report with pressure in mmHg, it directly corresponds to the height a mercury column is displaced by the atmospheric pressure. In the context of conversions, knowing that 760 mmHg equates to standard atmospheric pressure enables us to visualize and relate to the concept of atmospheric pressure on a practical level. When engaging in pressure conversions, recognizing the relationship to physical properties like the displacement of mercury adds a tangible component to the concept of pressure.