Problem 4 - Chemistry and Chemical Reactivity

Question

Put the following in order of increasing pressure: \(363 \mathrm{mm}\) \(\mathrm{Hg}, 363 \mathrm{kPa}, 0.256 \mathrm{atm},\) and \(0.523 \mathrm{bar}\)

Step-by-Step Solution

Answer

\(0.256 \mathrm{atm} < 363 \mathrm{mm} \mathrm{Hg} < 0.523 \mathrm{bar} < 363 \mathrm{kPa}\)

Step 1: Convert mm Hg to kPa

Use the conversion factor: 1 mm Hg = 0.133322 kPa. Calculate:\[ 363 \text{ mm Hg} \times 0.133322 \frac{\text{kPa}}{\text{mm Hg}} = 48.407526 \text{ kPa} \]

Step 2: Convert atm to kPa

Use the conversion factor: 1 atm = 101.325 kPa. Calculate:\[ 0.256 \text{ atm} \times 101.325 \frac{\text{kPa}}{\text{atm}} = 25.9572 \text{ kPa} \]

Step 3: Convert bar to kPa

Use the conversion factor: 1 bar = 100 kPa. Calculate:\[ 0.523 \text{ bar} \times 100 \frac{\text{kPa}}{\text{bar}} = 52.3 \text{ kPa} \]

Step 4: Compare the values

Now that we have all values in kPa: - 363 mm Hg = 48.407526 kPa - 0.256 atm = 25.9572 kPa - 0.523 bar = 52.3 kPa - 363 kPa = 363 kPa Order them from the smallest to largest: - 25.9572 kPa (0.256 atm) - 48.407526 kPa (363 mm Hg) - 52.3 kPa (0.523 bar) - 363 kPa (363 kPa)

Key Concepts

Pressure Units

Pressure is a measure of force applied over a specific area. Various units are used to express pressure, each serving its purpose in different contexts and regions. Knowing these units is crucial for understanding pressure readings. Here are some common pressure units:

• KiloPascals (kPa): A metric unit of pressure widely used across scientific and engineering communities. It is part of the International System of Units (SI), where 1 kPa is equal to 1,000 Pascals (Pa).


• Millimeters of Mercury (mm Hg): Often used in medicine and meteorology, particularly for blood pressure and barometric pressure readings. It originated from using mercury in barometers.


• Bar: A metric unit that is convenient for expressing atmospheric pressure, where 1 bar is approximately equal to atmospheric pressure at sea level.


• Atmospheres (atm): This unit is commonly used to describe atmospheric pressure relative to sea level, where 1 atm is the standard atmospheric pressure exerted at sea level.

Each unit reflects a different way of measuring and understanding pressure, catering to specific fields and applications.

Conversion Factors

Conversion factors are ratios used to express a quantity in different units while maintaining the same physical quantity. Converting between pressure units is common in various fields and typically involves using established conversion factors:

• From mm Hg to kPa: Use the conversion factor, where 1 mm Hg is equal to approximately 0.133322 kPa. For example, to convert 363 mm Hg to kPa, multiply by this conversion factor.


• From atm to kPa: The conversion factor here is 1 atm equals 101.325 kPa. This is useful when converting atmospheric readings to kPa, like converting 0.256 atm to kPa.


• From bar to kPa: The conversion is straightforward where 1 bar equals 100 kPa, simplifying conversions for industrial and scientific contexts.

Understanding these conversion factors is essential for accurately interpreting and converting pressure readings across different units. These factors ensure that the true magnitude of pressure is preserved despite the change in units.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of air in the Earth's atmosphere. It is a key concept in meteorology and various scientific studies. At sea level, standard atmospheric pressure is defined as 101.325 kPa or 1 atm. Atmospheric pressure can change with altitude and weather conditions. Some practical applications and phenomena related to atmospheric pressure include:

• Weather Predictions: Changes in atmospheric pressure can indicate upcoming weather changes. A dropping pressure generally signals stormy weather, while rising pressure can mean fair weather.


• Human Physiology: Humans are adapted to pressure levels near sea level. Rapid changes in atmospheric pressure can lead to discomfort and conditions like altitude sickness.

Understanding atmospheric pressure helps in assessing environmental conditions and their impact on daily life.

KiloPascals

The kiloPascal (symbol: kPa) is a unit of pressure that belongs to the International System of Units (SI). It is widely used in engineering, meteorology, and physics for its ease of use and conversion with other SI units. Here are some key attributes of kiloPascals:

• Universal Metric System: As part of the SI, kPa is crucial in providing a standardized measure of pressure that can be easily converted with other metric measures such as meters, kilograms, and seconds.


• Applications: KiloPascals are commonly used to measure everything from tire pressure in vehicles to barometric pressure in weather forecasting. They offer a concise way to express large pressures without resorting to very large numbers.


• Conversion Versatility: As demonstrated in exercises like converting atm, mm Hg, and bar to kPa, this unit serves as a bridge for easier understanding and comparison of pressure values in diverse contexts.

Using kPa allows for efficient communication and documentation of pressure data across various scientific and industrial fields.