Problem 20 - Chemistry The Central Science

Question

Perform the following conversions: \((\mathbf{a})\) 0.912 atm to torr, \((\mathbf{b})\) 0.685 bar to kilopascals, \((\mathbf{c})\) 655 \(\mathrm{mm}\) Hg to atmospheres, \((\mathbf{d})\) \(1.323 \times 10^{5}\) Pa to atmospheres, \((\mathbf{e})\) 2.50 atm to psi.

Step-by-Step Solution

Answer

The short answer for the conversions is as follows: a) \(0.912\ \text{atm} = 693.12\ \text{Torr}\) b) \(0.685\ \text{bar} = 68.5\ \text{kPa}\) c) \(655\ \text{mm}\ \text{Hg} = 0.8618\ \text{atm}\) d) \(1.323 \times 10^{5}\ \text{Pa} = 1.306\ \text{atm}\) e) \(2.50\ \text{atm} = 36.74\ \text{psi}\)

Step 1: a) Convert 0.912 atm to Torr

To convert 0.912 atm to Torr, we'll use the conversion factor 1 atm = 760 Torr: \(0.912\ \text{atm}\times \dfrac{760\ \text{Torr}}{1\ \text{atm}} = 693.12\ \text{Torr}\)

Step 2: b) Convert 0.685 bar to kilopascals

To convert 0.685 bar to kilopascals, we'll use the conversion factor 1 bar = 100 kPa: \(0.685\ \text{bar}\times \dfrac{100\ \text{kPa}}{1\ \text{bar}} = 68.5\ \text{kPa}\)

Step 3: c) Convert 655 mm Hg to atmospheres

To convert 655 mm Hg to atmospheres, we'll use the conversion factor 1 atm = 760 Torr (or mmHg): \(655\ \text{mm}\ \text{Hg}\times \dfrac{1\ \text{atm}}{760\ \text{mm}\ \text{Hg}} = 0.8618\ \text{atm}\)

Step 4: d) Convert 1.323 x 10^5 Pa to atmospheres

To convert \(1.323 \times 10^{5}\) Pa to atmospheres, we'll use the conversion factor 1 atm = 101325 Pa: \(1.323 \times 10^{5}\ \text{Pa}\times \dfrac{1\ \text{atm}}{101325\ \text{Pa}} = 1.306\ \text{atm}\)

Step 5: e) Convert 2.50 atm to psi

To convert 2.50 atm to psi, we'll use the conversion factor 1 atm = 14.696 psi: \(2.50\ \text{atm}\times \dfrac{14.696\ \text{psi}}{1\ \text{atm}} = 36.74\ \text{psi}\)

Key Concepts

Understanding Atmospheres

Atmospheres, often abbreviated as 'atm,' is a unit of pressure that measures how much force is exerted by the weight of air at sea level. One atmosphere is equivalent to the pressure of 101,325 pascals. This unit is commonly used when discussing weather, altitudes, and underwater depths. For example:

• One standard atmosphere is used to define the boiling point of water, which is 100°C (212°F) at sea level.
• At 10 meters underwater, the pressure is approximately 2 atm due to the weight of the water above.

Understanding atmospheres is important for its role in atmospheric science, diving, and aviation. It's also frequently used in chemistry for gas laws calculations.

Exploring Torr

Torr is another unit of pressure, named after the Italian physicist Evangelista Torricelli, who invented the barometer. One torr is equivalent to 1/760th of an atmosphere, or exactly one millimeter of mercury (mmHg). This makes conversion between torr and mmHg direct and simple.

Torr is commonly used in fields such as vacuum science and physics, and understanding it helps in comparing different pressure levels. For example:

• The measurement of a perfect vacuum is 0 torr.
• Standard atmospheric pressure is 760 torr.

Converting from atmospheres to torr involves multiplying by 760. For practical purposes, knowing this conversion factor can help perform quick pressure conversions.

Insights on Kilopascals

Kilopascals (kPa) are part of the metric system and represent a larger scale of pascals. One kilopascal equals 1,000 pascals. The kPa is widely accepted in scientific and engineering contexts because of its ease of communication and alignment with SI units.

• Atmospheric pressure at sea level is approximately 101.3 kPa.
• A human's blood pressure is measured in mmHg, but it can also be converted to kPa for those familiar with metric units.

Often in physics and engineering, kilopascals are used to describe pressure in various systems, such as tire pressures and weather stations. It's practical to convert between kilopascals and other units like bar or atmospheres, facilitating broader understanding across different domains.

Millimeters of Mercury (mmHg) Details

Millimeters of mercury, shortened to mmHg, is a unit that measures pressure employing the height of a column of mercury. It is mostly used in the medical field for blood pressure readings, and its value matches that of torr.

• Normal blood pressure is defined as about 120/80 mmHg.
• Weather barometers often use mmHg to measure atmospheric pressure.

Knowing that 1 atm equals 760 mmHg allows for easy conversion between these units. This is especially helpful in medicine and meteorology, where precise pressure readings are crucial for interpreting conditions and outcomes.

Psi and its Applications

Psi, standing for pounds per square inch, is a unit of pressure commonly used in the United States, especially in plumbing, car tires, and other mechanical systems. It represents the force of one pound-force applied to an area of one square inch.

• Normal car tire pressures are often in the range of 30-35 psi.
• Pressure washers may specify pressure outputs in psi for easy understanding of their power.

The conversion factor from atmospheres to psi is approximately 14.696 psi per atmosphere. Understanding this conversion helps in adjusting measurements taken in different units, ensuring accurate and useful data across various domestic and technical applications.