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 \((1 \mathrm{~atm}=14.7 \mathrm{psi})\). a. \(\mathrm{mm} \mathrm{Hg}\) c. \(\mathrm{Pa}\) b. torr d. \(\mathrm{psi}\)

Short answer

a. The pressure in mm Hg is \(3648\, \text{mm Hg}\). c. The pressure in Pa is \(486360\, \text{Pa}\). b. The pressure in torr is \(3648\, \text{torr}\). d. The pressure in psi is \(70.56\, \text{psi}\).

Step-by-step solution

(Step 1: Conversion to mm Hg)

To convert 4.8 atm to mm Hg, we use the conversion factor 1 atm = 760 mm Hg. \(4.8\,\text{atm} \times\frac{760\,\text{mm Hg}}{1\, \text{atm}}=3648\, \text{mm Hg}\) a. The pressure in mm Hg is \(3648\, \text{mm Hg}\).

(Step 2: Conversion to Pa)

To convert 4.8 atm to Pa, we use the conversion factor 1 atm = 101325 Pa. \(4.8\, \text{atm} \times \frac{101325\, \text{Pa}}{1\, \text{atm}} = 486360\, \text{Pa}\) c. The pressure in Pa is \(486360\, \text{Pa}\).

(Step 3: Conversion to torr)

Since 1 atm is equal to 760 torr, the conversion to torr will be the same as the one for mm Hg: b. The pressure in torr is \(3648\, \text{torr}\).

(Step 4: Conversion to psi)

To convert 4.8 atm to psi, we use the conversion factor 1 atm = 14.7 psi. \(4.8\, \text{atm} \times \frac{14.7\, \text{psi}}{1\, \text{atm}} = 70.56\, \text{psi}\) d. The pressure in psi is \(70.56\, \text{psi}\).

Key concepts

Atmospheres (atm)

Atmospheres, commonly abbreviated as atm, are a standard unit of pressure used widely in chemistry and physics.
One atmosphere is defined as being equivalent to the average air pressure at sea level. Understanding atm is crucial since it's a basic measurement often seen in gas law equations.
In practical terms, when dealing with problems involving pressures, scientists and engineers frequently use atmospheres because this unit provides a nice benchmark relative to Earth’s atmospheric conditions. For example, the problem here uses 4.8 atm, indicating a pressure much greater than what we typically experience in daily life, which is 1 atm at sea level.

Pressure Units

Pressure units are various measurements used to express pressure levels. Pressure is essentially the force exerted per unit area, and its units can vary depending on the context of its application.
Some of the common pressure units include:

• Millimeters of Mercury (mm Hg): Often used in medicine and meteorology. It comes from measurement using a mercury column.
• Torr: Practically similar to mm Hg. Directly related since 1 torr = 1 mm Hg.
• Pascal (Pa): The SI unit of pressure, used widely in science and engineering. It defines 1 Pa as 1 Newton per square meter.
• Pounds per square inch (psi): Predominantly used in the United States, commonly seen in tire pressure readings.

Each of these units can be converted into others with known conversion factors, vital for students aiming to solve problems that require unit conversion.

Conversion Factors

Conversion factors are essential tools in converting quantities from one unit to another. For pressure conversions, knowing the right conversion factor is key to accurate results.

Important Conversion Factors for Pressure

• 1 atm = 760 mm Hg = 760 torr
• 1 atm = 101325 Pa
• 1 atm = 14.7 psi

To convert between different pressure units, simply multiply the given value in atmospheres by the appropriate conversion factor for the target unit. This process simplifies calculations and reduces errors when switching units. Having these factors at your fingertips enables quick and efficient problem-solving.

Refrigerants

Refrigerants, such as Freon-12 mentioned in the problem, are substances used in cooling systems to transfer heat.
These chemicals are critical for systems like air conditioners, refrigerators, and freezers. Freon-12, or dichlorodifluoromethane (\(\mathrm{CF}_{2} \mathrm{Cl}_{2}\)), was once widely used because of its effective cooling properties.

Understanding Refrigerants in Pressure Problems

When working with refrigerants, pressure is a crucial factor to monitor. The efficiency and performance of cooling systems heavily depend on maintaining the correct pressure levels.
Improper pressures can lead to insufficient cooling or even damage to the system. Therefore, accurately converting and understanding pressure units is not just academic—it has real-world applications in ensuring that cooling systems work efficiently and safely.