Perform the following pressure in conversions: (a) Convert 649 torr to \(\mathrm{kPa}\). (b) Convert \(5.07 \mathrm{kPa}\) to atm. (c) Convert \(3.64 \mathrm{~atm}\) to \(\mathrm{mm} \mathrm{Hg}\). (d) Convert 803 torr to atm. (e) Convert \(1.08 \mathrm{~atm}\) to \(\mathrm{cm} \mathrm{Hg}\).

Understanding the conversion between torr and kilopascals (kPa) is essential in various fields like chemistry where pressure measurements are a routine. To grasp this concept, one should be familiar with the use of conversion factors. The direct conversion factor is: 1 torr equals 0.133322 kPa.

This means that to convert a pressure reading from torr to kPa, you simply need to multiply the number of torrs by 0.133322. For example, the textbook problem asks to convert 649 torr to kPa. Using the conversion factor:\[649 \text{{ torr}} \times 0.133322 \frac{{\text{{kPa}}}}{{\text{{torr}}}} = 86.572678 \text{{ kPa}}.\]
To enhance understanding, imagine torr as units of small pebbles and kPa as handfuls of pebbles—it takes a specific number of small pebbles (torrs) to make up one handful (kPa). Conversions are like counting out the number of small pebbles needed to ensure we have the right number of handfuls. By consistently applying the conversion factor, one can easily switch between these two units of pressure.

In situations such as reporting atmospheric pressure readings, knowledge of converting kilopascals (kPa) to atmospheres (atm) is essential. The conversion factor to remember here is that 1 atm is equal to 101.325 kPa.

So, to convert from kPa to atm, a division by this conversion factor is required. Let's consider the provided problem: converting 5.07 kPa into atm would follow the equation:\[\frac{{5.07 \text{{ kPa}}}}{{101.325 \text{{ kPa/atm}}}} = 0.050027 \text{{ atm}}.\]
Consider atmospheres as large balloons; when you are converting kPa to atm, you are determining how much of that balloon is filled by the given pressure in kilopascals. This conversion is particularly important when comparing pressures to the standard atmospheric pressure, which is a common reference in science. Utilizing this conversion factor allows students to shift between different scales of pressure seamlessly.

Moving from the atmospheric pressure unit (atm) to millimeters of mercury (mmHg) may be necessary for tasks such as calibrating blood pressure readings. The conversion factor between these two is notably simple: 1 atm equals 760 mmHg.

Therefore, to convert atm to mmHg, multiply the atm value by 760. If we take the exercise's query to convert 3.64 atm to mmHg as an illustration, the process is straightforward:\[3.64 \text{{ atm}} \times 760 \frac{{\text{{mmHg}}}}{{\text{{atm}}}} = 2764.4 \text{{ mmHg}}.\]
Imagine atm as large cups of water, and mmHg as teaspoons—it takes 760 teaspoons to fill the large cup. This analogy typifies the conversion process, where you're simply gauging how many teaspoons (mmHg) it takes to match the pressure in the cup (atm). Such conversions are vital in healthcare, laboratories and understanding weather patterns.