Problem 42 - Chemistry: An Atoms-Focused Approach

Question

Convert the following pressures into millimeters of mercury: (a) 0.541 atm; (b) 2.8 kPa.

Step-by-Step Solution

Answer

Question: Convert the given pressures to millimeters of mercury (mmHg): (a) 0.541 atm and (b) 2.8 kPa. Answer: (a) 0.541 atm is equivalent to 411.16 mmHg. (b) 2.8 kPa is equivalent to 21.00174 mmHg.

Step 1: Identify the conversion factor for atm to mmHg

We are given the conversion factor for atm to mmHg as 1 atm = 760 mmHg.

Step 2: Convert the given pressure to mmHg

Now, use the conversion factor to convert 0.541 atm to mmHg. Multiply the given pressure (0.541 atm) by the conversion factor (760 mmHg/atm): (0.541 atm) * (760 mmHg/atm) = X mmHg Note that the "atm" units cancel out, leaving us with mmHg as the final unit.

Step 3: Calculate the resulting pressure in mmHg

After multiplying the given pressure by the conversion factor: (0.541) * (760) = 411.16 mmHg So, the pressure of 0.541 atm is equivalent to 411.16 mmHg. (b) Given pressure = 2.8 kPa

Step 1: Identify the conversion factor for kPa to mmHg

We are given the conversion factor for kPa to mmHg as 1 kPa = 7.50062 mmHg.

Step 2: Convert the given pressure to mmHg

Now, use the conversion factor to convert 2.8 kPa to mmHg. Multiply the given pressure (2.8 kPa) by the conversion factor (7.50062 mmHg/kPa): (2.8 kPa) * (7.50062 mmHg/kPa) = X mmHg Note that the "kPa" units cancel out, leaving us with mmHg as the final unit.

Step 3: Calculate the resulting pressure in mmHg

After multiplying the given pressure by the conversion factor: (2.8) * (7.50062) = 21.00174 mmHg So, the pressure of 2.8 kPa is equivalent to 21.00174 mmHg.

Key Concepts

Millimeters of Mercury

Millimeters of mercury (mmHg) is a unit of pressure that originates from the way pressure is measured using a mercury column. It is one of the oldest units of pressure still in use today. This unit is commonly used in fields like medicine, especially in the measurement of blood pressure, where values are often expressed in mmHg.

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. In terms of millimeters of mercury, one mmHg is defined as the pressure exerted by a 1 millimeter tall column of mercury at 0°C at standard gravity.

• 1 mmHg is considered equivalent to 133.322 pascals (Pa) in the International System of Units.
• It is widely accepted because it directly relates to the pressure measurement methods historically used.

To convert between different pressure units, knowing specific conversion factors is key. For example, 1 atmosphere (atm) is equivalent to 760 mmHg. This conversion factor allows easy transformation between these two commonly used units.

Atmospheres

Atmospheres (atm) is a unit of pressure originally based on the average atmospheric pressure at sea level. It is still widely used in various scientific calculations and applications, including chemistry and physics. An atmosphere is a convenient way to express ambient pressure conditions because it closely approximates the typical pressure of the Earth’s atmosphere.

In the context of conversion, the atmosphere is easy to use when dealing with gases and reactions where pressure is a critical component.

• 1 atm is defined as being precisely equal to 101,325 Pa or 101.325 kPa.
• It simplifies many scientific equations due to its direct relation to normal atmospheric conditions.
• As mentioned earlier, 1 atm is also equal to 760 mmHg, making the conversion to and from mmHg straightforward.

Just remember, if you need to convert pressures given in atmospheres to other units, such as millimeters of mercury, the conversion factor 760 mmHg per atm must be utilized, simplifying the transformation.

Kilopascals

Kilopascals (kPa) is a unit of pressure derived from the pascal (Pa), which is the SI unit of pressure. The pascal is a relatively small unit, so kilopascals, which are equal to 1,000 pascals, are often used to make numbers more manageable.

The kilopascal is widely used across the globe, particularly in countries that utilize the metric system. It is frequently seen in engineering contexts and is a commonly used unit of atmospheric pressure in meteorology.

• 1 kPa is equivalent to 7.50062 mmHg, allowing for precise conversions between these units.
• Because of its SI roots, kPa easily integrates into scientific calculations involving pressure.
• Knowing that 1 atm equals 101.325 kPa can help link kilopascals with atmospheric pressure units.

Applying this information is straightforward: when you need to convert from kPa to mmHg, multiplying by the conversion factor of 7.50062 mmHg per kPa will yield the correct pressure in mmHg, maintaining accuracy and consistency.