Problem 20 - Chemistry The Central Science In Si Units

Question

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

Step-by-Step Solution

Answer

(a) 692.32 torr, (b) 68.5 kPa, (c) 0.8618 atm, (d) 1.306 atm, (e) 36.74 psi.

Step 1: Convert atm to torr

To convert atmospheres to torr, we use the conversion factor: 1 atm = 760 torr. For (a) 0.912 atm, we calculate: \(0.912 ext{ atm} \times 760 ext{ torr/atm} = 692.32 ext{ torr}\).

Step 2: Convert bar to kilopascals

To convert bar to kilopascals, use the conversion factor: 1 bar = 100 kPa. For (b) 0.685 bar, we calculate: \(0.685 ext{ bar} \times 100 ext{ kPa/bar} = 68.5 ext{ kPa}\).

Step 3: Convert mm Hg to atmospheres

To convert mm Hg to atmospheres, use the conversion factor: 760 mm Hg = 1 atm. For (c) 655 mm Hg, we calculate: \(\frac{655 ext{ mm Hg}}{760 ext{ mm Hg/atm}} = 0.8618 ext{ atm}\).

Step 4: Convert Pa to atmospheres

To convert pascals to atmospheres, use the conversion factor: 1 atm = 101325 Pa. For (d) \(1.323 \times 10^{5} ext{ Pa}\), we calculate: \(\frac{1.323 \times 10^{5} ext{ Pa}}{101325 ext{ Pa/atm}} = 1.306 ext{ atm}\).

Step 5: Convert atm to psi

To convert atmospheres to pounds per square inch (psi), use the conversion factor: 1 atm = 14.696 psi. For (e) 2.50 atm, we calculate: \(2.50 ext{ atm} \times 14.696 ext{ psi/atm} = 36.74 ext{ psi}\).

Key Concepts

Atmospheres

Atmospheres, often abbreviated as atm, is a unit of pressure that represents the average atmospheric pressure at sea level on Earth. It’s a widely used unit in chemistry and physics to express pressures, especially when dealing with gas laws and calculations.

• 1 atm is the pressure exerted by a 760 mm column of mercury.
• Equivalent to 1013.25 millibars or 101,325 Pascal.
• Commonly used as a reference for standard conditions and conversions.

Understanding atmospheres is essential because it's commonly a starting point for converting into more specialized or smaller units like torr or psi. Knowing that 1 atm equals 760 torr helps in quick mental calculations for laboratory settings.

Torr

The torr is another pressure unit derived from the millimeter of mercury (mm Hg), often used in vacuum measurements and situations where precise pressure readings are necessary. It’s named after Evangelista Torricelli, an Italian physicist.

• 760 torr is equal to 1 atmosphere of pressure.
• Equivalent to approximately 133.322 Pascal.
• Commonly used in physics and engineering, especially when dealing with low pressure.

This unit plays a critical role in various scientific applications, enabling the conversion of atmospheric measurements to smaller scales where detail and precision are required.

Pascals

Pascals, abbreviated as Pa, are part of the International System of Units (SI) and represent one of the most standard methods of measuring pressure. Named after Blaise Pascal, a French mathematician, it is defined as one newton per square meter.

• 1 Pa equals 1 N/m² (Newton per square meter).
• Ideal for scientific applications due to its SI foundation.
• Commonly used in engineering, physics, and meteorology.

Due to their small size, pressures are often measured in kilopascals (1 kPa = 1000 Pa) in practical settings. Engineers and scientists convert between atmospheres and pascals to develop accurate models and designs for structures and weather forecasting.

Kilopascals

Kilopascals (kPa) are a scaled-up version of pascals, providing a more practical size for measuring everyday pressures.

• 1 kPa is equivalent to 1000 Pa.
• Widely used in meteorology to describe atmospheric pressure (e.g., 100 kPa is approximately the pressure at sea level).
• Convenient for expressing moderate pressures, from tire inflation to internal pressures of closed systems.

Kilopascals bridge the gap between delicate laboratory measurements in pascals and everyday pressures, providing a unit that is neither too small nor too large for most practical applications.

Pounds per Square Inch

Pounds per square inch, or psi, is a widely recognized unit of pressure in various fields, notably within the United States. Its practicality and ease of use make it popular for understanding pressure in terms that relate to physical weight per unit area.

• 1 psi is the pressure resulting from a force of one pound-force applied to an area of one square inch.
• Commonly used in automotive industries, tire pressures, and air compressors.
• 1 atm is approximately 14.696 psi.

Psi is essential in fields where pressure needs to be communicated effectively to a broader audience, as people often find it to be an intuitive and accessible unit.