Problem 37 - Chemistry An Atoms First Approach

Question

Freon-12 \(\left(\mathrm{CF}_{2} \mathrm{Cl}_{2}\right)\) is commonly used as the refrigerant in central home air conditioners. The system is initially charged to a pressure of 4.8 atm. Express this pressure in each of the following units ( 1 atm \(=14.7\) psi). a. \(\mathrm{mm} \mathrm{Hg}\) b. \(torr\) c. \(Pa\) d. \(psi\)

Step-by-Step Solution

Answer

The given pressure of 4.8 atm is equivalent to: a. 3648 mmHg b. 3648 torr c. 486360 Pa d. 70.56 psi

Step 1: Conversion to millimeters of mercury (mmHg)

To convert the pressure from atm to mmHg, use the conversion factor 1 atm = 760 mmHg. The given pressure is 4.8 atm. \(4.8 \ \mathrm{atm} \times \frac{760 \ \mathrm{mmHg}}{1 \ \mathrm{atm}} = 3648 \ \mathrm{mmHg}\) Therefore, the pressure is 3648 mmHg.

Step 2: Conversion to torr

To convert the pressure from atm to torr, use the conversion factor 1 atm = 760 torr. The given pressure is 4.8 atm. \(4.8 \ \mathrm{atm} \times \frac{760 \ \mathrm{torr}}{1 \ \mathrm{atm}} = 3648 \ \mathrm{torr}\) Therefore, the pressure is 3648 torr.

Step 3: Conversion to Pascals (Pa)

To convert the pressure from atm to Pa, use the conversion factor 1 atm = 101325 Pa. The given pressure is 4.8 atm. \(4.8 \ \mathrm{atm} \times \frac{101325 \ \mathrm{Pa}}{1 \ \mathrm{atm}} = 486360 \ \mathrm{Pa}\) Therefore, the pressure is 486360 Pa.

Step 4: Conversion to pounds per square inch (psi)

To convert the pressure from atm to psi, use the given conversion factor 1 atm = 14.7 psi. The given pressure is 4.8 atm. \(4.8 \ \mathrm{atm} \times \frac{14.7 \ \mathrm{psi}}{1 \ \mathrm{atm}} = 70.56 \ \mathrm{psi}\) Therefore, the pressure is 70.56 psi. So, the given pressure of 4.8 atm is equivalent to: a. 3648 mmHg b. 3648 torr c. 486360 Pa d. 70.56 psi

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us on Earth's surface. It's a fundamental concept in meteorology and is crucial for understanding pressure changes in various conditions, such as weather systems. Atmospheric pressure at sea level is taken as a standard for measuring pressure, which is approximately 1 atmosphere (atm). This is due to the weight of the column of air above a specific area.
Typical atmospheric pressure can vary with altitude and weather conditions, but standard atmospheric pressure is defined as exactly 101,325 Pascals (Pa) or 760 millimeters of mercury (mmHg). This standard also allows us to make precise conversions between different units of pressure.

Millimeters of Mercury (mmHg)

Millimeters of Mercury, abbreviated as mmHg, is a unit of pressure used in medical and scientific fields to measure blood pressure and other pressures where high precision is required.
The term originates from the height of a mercury column a specific pressure can support. For example, 1 atm of pressure is equivalent to 760 mmHg. Therefore, when converting from atmospheres to mmHg, you multiply the number of atmospheres by 760.

• 1 atm = 760 mmHg
• Example: To convert 4.8 atm to mmHg:
  4.8 atm × 760 mmHg/atm = 3648 mmHg

This conversion is applicable in various contexts including laboratory and clinical settings where precise pressure measurements are necessary.

Pascals (Pa)

Pascals are the SI (International System of Units) unit of pressure and are widely used in scientific and engineering applications. One Pascal is defined as one newton of force applied over an area of one square meter. This makes it a very versatile unit for measuring pressure.

• 1 atm = 101,325 Pa
• To convert from atm to Pascals:

Simply multiply the pressure in atmospheres by 101,325 Pa/atm.
For instance, a pressure of 4.8 atm is equivalent to:
4.8 atm × 101,325 Pa/atm = 486,360 Pa.
Pascals provide a useful measure in contexts where precise pressure calculations are pivotal, such as in the design of engines and atmospheric studies.

Pounds per Square Inch (psi)

Pounds per square inch (psi) is a common unit of pressure mainly used in the United States. It is especially prevalent in measuring tire pressure, hydraulic systems, and other instances where pressure needs to be measured in laudatory terms.
Psi is defined as one pound-force applied per square inch of area.

• 1 atm = 14.7 psi
• To convert atmospheres to psi, use the conversion factor: 1 atm = 14.7 psi

For a practical example, converting 4.8 atm to psi means calculating:
4.8 atm × 14.7 psi/atm = 70.56 psi.
Understanding this conversion is crucial in applications like checking tire pressures, where safety and efficiency heavily depend on maintaining correct psi levels.