Question

Make the indicated pressure conversions. a. \(45.2 \mathrm{kPa}\) to atmospheres b. \(755 \mathrm{~mm} \mathrm{Hg}\) to atmospheres c. 802 torr to kilopascals d. 1.04 atm to millimeters of mercury

Short answer

a. $45.2 \mathrm{kPa}$ is approximately \(0.446 \mathrm{atm}\). b. $755 \mathrm{~mm} \mathrm{Hg}$ is approximately \(0.993 \mathrm{atm}\). c. 802 torr is approximately \(107.2 \mathrm{kPa}\). d. 1.04 atm is approximately \(790.4 \mathrm{mm~Hg}\).

Step-by-step solution

Calculate the conversion factor between kPa and atm

To convert kPa to atm, we should divide by the conversion factor: 1 atm = 101.3 kPa. So the conversion factor is: \[1 \mathrm{atm} = \frac{1}{101.3} \mathrm{kPa}\]

Convert 45.2 kPa to atm

Now we can convert 45.2 kPa to atm by multiplying it with the conversion factor: \[45.2 \mathrm{kPa} \times \frac{1 \mathrm{atm}}{101.3 \mathrm{kPa}} = 0.446 \mathrm{atm}\] Answer: 45.2 kPa is approximately \(0.446 \mathrm{atm}\). #b. Convert 755 mm Hg to atmospheres#

Calculate the conversion factor between mm Hg and atm

To convert mm Hg to atm, we should divide by the conversion factor: 1 atm = 760 mm Hg. So the conversion factor is: \[1 \mathrm{atm} = \frac{1}{760} \mathrm{mm~Hg}\]

Convert 755 mm Hg to atm

Now we can convert 755 mm Hg to atm by multiplying it with the conversion factor: \[755 \mathrm{mm~Hg} \times \frac{1 \mathrm{atm}}{760 \mathrm{mm~Hg}} = 0.993 \mathrm{atm}\] Answer: 755 mm Hg is approximately \(0.993 \mathrm{atm}\). #c. Convert 802 torr to kilopascals#

Calculate the conversion factor between torr and kPa

To convert torr to kPa, we should first convert torr to atm by using the conversion factor: 1 atm = 760 torr, and then convert atm to kPa using the conversion factor: 1 atm = 101.3 kPa. So the conversion factor is: \[1 \mathrm{kPa} = \frac{1 \mathrm{atm}}{760 \mathrm{torr}} \times 101.3 \mathrm{kPa}\]

Convert 802 torr to kPa

Now we can convert 802 torr to kPa by multiplying it with the conversion factor: \[802 \mathrm{torr} \times \frac{1 \mathrm{atm}}{760 \mathrm{torr}} \times 101.3 \mathrm{kPa} = 107.2 \mathrm{kPa}\] Answer: 802 torr is approximately \(107.2 \mathrm{kPa}\). #d. Convert 1.04 atm to millimeters of mercury#

Calculate the conversion factor between atm and mm Hg

To convert atm to mm Hg, we should multiply by the conversion factor: 1 atm = 760 mm Hg. So the conversion factor is: \[1 \mathrm{mm~Hg} = 760 \mathrm{atm}\]

Convert 1.04 atm to mm Hg

Now we can convert 1.04 atm to mm Hg by multiplying it with the conversion factor: \[1.04 \mathrm{atm} \times 760 \mathrm{mm~Hg} = 790.4 \mathrm{mm~Hg}\] Answer: 1.04 atm is approximately \(790.4 \mathrm{mm~Hg}\).

Key concepts

Unit Conversion

Unit conversion is an essential skill in scientific calculations. It allows us to transform one unit of measurement into another, making data easier to understand across different scales or systems. For pressure conversions, this process helps compare measurements like kilopascals (kPa), atmospheres (atm), millimeters of mercury (mm Hg), and torr.
To convert, you need to know the conversion factors, which act like bridges between units. For example:

• 1 atm = 101.3 kPa
• 1 atm = 760 mm Hg or 760 torr

These factors help us perform calculations by either multiplying or dividing the number of units we have. Remembering these core relationships makes the conversion straightforward.

Pressure Units

Pressure units serve different purposes, depending on the context in which they are used. Let's explore some common pressure units:
- **Atmosphere (atm):** This is a standard unit of pressure defined as being precisely equal to 101,325 Pa (pascals). It is often used in meteorology and scuba diving. - **Kilopascal (kPa):** This is a metric unit, part of the International System of Units (SI). It's commonly used in engineering and scientific fields. - **Millimeters of Mercury (mm Hg):** This unit originates from how mercury levels respond to atmospheric pressure. It remains used in medical contexts, like blood pressure readings. - **Torr:** Named after Evangelista Torricelli, this unit is largely equivalent to mm Hg and is frequently used in vacuum readings.

Scientific Calculations

Scientific calculations involving pressure conversions require a solid understanding of units and meticulous mathematical processes.
Step-by-step calculations ensure precision:

• Identify the units you are starting with and the units you need to convert to.
• Use the correct conversion factor, ensuring you align your units properly to cancel them out.
• Perform the multiplication or division as needed, paying careful attention to significant figures for accuracy.

By following these systematic steps, you can confidently convert any pressure unit with ease. Practice these calculations regularly to build proficiency in scientific conversions.