Problem 49 - Chemistry Matter and Change

Question

At an ocean depth of \(76.2 \mathrm{m},\) the pressure is about 8.4 \(\mathrm{atm} .\) Convert the pressure to \(\mathrm{mm} \mathrm{Hg}\) and kPa units.

Step-by-Step Solution

Answer

8.4 atm equals 6384 mm Hg and 850.92 kPa.

Step 1: Understanding Atmospheric Pressure

Atmospheric pressure at sea level is known to be approximately 101.3 kPa or 760 mm Hg (millimeters of mercury). We will use these as conversion factors to convert pressure from atmospheres to other units.

Step 2: Convert Atmospheres to mm Hg

To convert from atmospheres to mm Hg, use the conversion factor: 1 atm = 760 mm Hg. Therefore, multiply the pressure in atm by 760 mm Hg/atm.\[8.4 \text{ atm} \times 760 \frac{\text{mm Hg}}{\text{atm}} = 6384 \text{ mm Hg}\]

Step 3: Convert Atmospheres to kPa

To convert from atmospheres to kPa, use the conversion factor: 1 atm = 101.3 kPa. Therefore, multiply the pressure in atm by 101.3 kPa/atm.\[8.4 \text{ atm} \times 101.3 \frac{\text{kPa}}{\text{atm}} = 850.92 \text{ kPa}\]

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the atmosphere on a surface. At sea level, it is typically measured as 1 atmosphere (atm). This standard atmospheric pressure is crucial for many scientific calculations related to pressure throughout our atmosphere and within various liquids. When we talk about atmospheric pressure:

• The standard that many calculations start from is 101.3 kilopascals (kPa)
• It's also equivalent to 760 millimeters of mercury (mm Hg)

Understanding these units helps in converting and comparing different pressure readings, which is important in many scientific and practical applications such as weather forecasting and scuba diving.

Pressure Conversion

Pressure conversion refers to the process of changing the pressure value from one unit to another, such as atm, kPa, and mm Hg. This is useful because different fields sometimes prefer different units based on convenience or tradition. The conversion process involves using precise conversion factors. Here are the necessary conversions for this exercise:

• 1 atmosphere is equal to 760 mm Hg
• 1 atmosphere is also 101.3 kPa

By multiplying a given pressure value by these conversion factors, you can seamlessly convert from one unit to another, as demonstrated by the original exercise. This practice is important for maintaining accuracy in scientific calculations and data interpretation.

kPa (Kilopascal)

The kilopascal (kPa) is a metric unit of pressure. It is widely used in various scientific and engineering fields. A kilopascal is equal to 1,000 pascals, and here's how it relates to atmospheric pressure:

• Standard atmospheric pressure is about 101.3 kPa, which provides a useful reference for many practical applications.
• In the context of the ocean depth scenario, pressures are often converted to kPa for a clearer comparison to everyday pressures experienced on land.

The conversion from atmospheres to kPa, as covered in the exercise, makes it easier to understand and communicate pressure levels in terms that are familiar to many professionals worldwide.

mm Hg (Millimeters of Mercury)

Millimeters of mercury, abbreviated as mm Hg, is a unit of measurement often used in medicine and aviation. It originates from the use of mercury in barometers, devices that measure atmospheric pressure by observing the height of mercury in a glass tube:

• Standard atmospheric pressure is defined as 760 mm Hg at sea level.
• This unit provides a historical perspective and is still popular in some areas due to its simplicity and direct measurement method.

In the exercise, converting pressure from atmospheres to mm Hg assists in aligning with these traditional measurements, ensuring consistency across different fields without losing the accuracy needed for scientific evaluations.