Problem 1 - General Chemistry: Principles and Modern Applications

Question

Convert each pressure to an equivalent pressure (a) 736 mmHg; (b) 0.776 bar; in atmospheres. (c) 892 Torr; (d) 225 kPa.

Step-by-Step Solution

Answer

(a) The equivalent of 736 mmHg in atmospheres is approximately 0.97 atm. (b) The equivalent of 0.776 bar in atmospheres is approximately 0.77 atm. (c) The equivalent of 892 torr in atmospheres is approximately 1.17 atm. (d) The equivalent of 225 kPa in atmospheres is approximately 2.22 atm.

Step 1: Convert mmHg to atm

To convert 736 mmHg to atmospheres, the conversion factor 760 mmHg = 1 atm is used. So, (736 mmHg/760) gives the equivalent in atmospheres.

Step 2: Convert bar to atm

To convert 0.776 bar to atmospheres, the conversion factor 1.01325 bar = 1 atm is used. So, (0.776 bar/1.01325) gives the equivalent in atmospheres.

Step 3: Convert Torr to atm

To convert 892 torr to atmospheres, the conversion factor 760 torr = 1 atm is used. So, (892 torr/760) gives the equivalent in atmospheres.

Step 4: Convert kPa to atm

To convert 225 kPa to atmospheres, the conversion factor 101.325 kPa = 1 atm is used. So, (225 kPa/101.325) gives the equivalent in atmospheres.

Key Concepts

Understanding Atmospheres

Pressure is a measure of force applied over a unit area. One of the most commonly used pressure units in science is the atmosphere, abbreviated as atm. It is a standard unit of pressure and is often used to describe atmospheric pressure. Usually, 1 atmosphere is defined as the pressure exerted by the weight of the air at sea level.

An atmosphere is equivalent to the pressure of 760 millimeters of mercury (mmHg) or 101,325 pascals (Pa). It's a convenient unit because it approximates the average air pressure at sea level on Earth. This makes it quite practical for experiments and calculations involving gases.

When you're converting other pressure units into atmospheres, you're essentially translating the measure of force applied per unit area into this universally recognized standard.

Exploring Different Pressure Units

In the field of science, there are numerous units of pressure. Each unit provides a different perspective on measuring the force exerted per unit area. Understanding these units is crucial for grasping how pressure works.

• Millimeters of mercury (mmHg): This unit often appears in medical contexts, especially when measuring blood pressure. It relies on the height of a mercury column in a barometer or manometer to describe pressure.
• Bar: This metric unit is commonly used in meteorology and engineering for its simplicity. One bar is slightly less than an atmosphere, with a precise relation where 1 atm = 1.01325 bar.
• Torr: This is similar to mmHg in that 1 Torr equals 1 mmHg. It's named after Evangelista Torricelli, an Italian physicist who invented the barometer.
• Pascal (Pa): This is the SI unit for pressure and measures one newton per square meter. It's used widely in scientific contexts for its consistency with other metric units.
• Kilopascal (kPa): Simply 1000 pascals, this unit offers a larger, more manageable number for atmospheric pressure definitions and calculations.

Each of these units can be used independently or converted into one another through known conversion factors to provide a better understanding of pressure across different contexts.

Mastering Conversion Factors

Conversion factors are essential tools in scientific calculations, especially when dealing with different pressure units. They serve as bridges that translate one unit into another to ensure consistency across calculations or reports.

To convert any given pressure measurement into atmospheres, you utilize specific, reliable conversion factors:

• mmHg to atm: Use the conversion 760 mmHg = 1 atm. For example, if you have 736 mmHg, the conversion would be \( \frac{736}{760} = 0.9684 \) atm.
• bar to atm: Use the conversion 1.01325 bar = 1 atm. If you have 0.776 bar, the conversion yields \( \frac{0.776}{1.01325} = 0.7655 \) atm.
• Torr to atm: Use the conversion 760 Torr = 1 atm. An 892 Torr reading becomes \( \frac{892}{760} = 1.1737 \) atm.
• kPa to atm: With 101.325 kPa equaling 1 atm, 225 kPa translates to \( \frac{225}{101.325} = 2.2199 \) atm.

Learning to apply these factors accurately is vital for translating pressures across various units. This skill is particularly handy in research and industry settings where multiple pressure units are used.