Problem 36 - Chemistry The Molecular Nature of Matter

Question

Carry out the following unit conversions: (a) 0.625 atm to torr, (b) 825 torr to atm, (c) \(62 \mathrm{~mm} \mathrm{Hg}\) to torr, (d) \(1.22 \mathrm{kPa}\) to bar.

Step-by-Step Solution

Answer

a) 0.625 atm is 475 torr, b) 825 torr is approximately 1.086 atm, c) 62 mm Hg is 62 torr, d) 1.22 kPa is 0.0122 bar.

Step 1: Convert atm to torr

To convert atmospheres (atm) to millimeters of mercury (torr), use the conversion factor 1 atm = 760 torr. Multiply the given pressure in atm by the conversion factor to get the pressure in torr.

Step 2: Convert torr to atm

To convert torr to atm, use the conversion factor 1 atm = 760 torr. Divide the given pressure in torr by the conversion factor to get the pressure in atm.

Step 3: Convert mm Hg to torr

Millimeters of mercury (mm Hg) is equivalent to torr, so no conversion is necessary. 1 mm Hg equals 1 torr.

Step 4: Convert kPa to bar

To convert kilopascals (kPa) to bar, use the conversion factor 1 bar = 100 kPa. Divide the given pressure in kPa by the conversion factor to get the pressure in bar.

Key Concepts

Atmospheres to Torr Conversion

Understanding the conversion between atmospheres and torr is essential when working with pressure units in various scientific contexts. An atmosphere (atm) is a unit of pressure defined as being precisely equal to the average atmospheric pressure on Earth at sea level. Torr, on the other hand, is a unit of pressure based on an absolute scale, named after the Italian physicist Evangelista Torricelli.

To convert from atmospheres to torr, we use the direct relationship between these two units: 1 atm is equivalent to 760 torr. Therefore, simply multiplying the value in atmospheres by 760 will give you the pressure in torr. For instance, to convert 0.625 atm to torr, you would perform the following calculation:
\(0.625 \text{ atm} \times 760 \text{ torr/atm} = 475 \text{ torr}\).

It is crucial for accuracy within scientific experiments and calculations to perform these conversions correctly, ensuring measurements are consistent across various units of pressure.

Torr to Atmospheres Conversion

In the realm of pressure measurements, converting torr to atmospheres is just as common as the reverse. This process is necessary when you need to interpret pressure readings in units that are more closely related to atmospheric pressure conditions.

The conversion factor between torr and atmospheres remains the same as before, but in this case, you divide by 760 since there are 760 torr in one atmosphere: \(\frac{1 \text{ atm}}{760 \text{ torr}}\). For example, converting 825 torr to atmospheres involves dividing 825 by 760, as shown in the equation:
\(825 \text{ torr} \times \frac{1 \text{ atm}}{760 \text{ torr}} \u003dapprox 1.086 \text{ atm}\).

This conversion ensures that pressure units match those commonly used in various scientific research, weather reporting, and engineering applications.

Millimeters of Mercury to Torr Conversion

The millimeters of mercury (mm Hg) unit and the torr are often used interchangeably because they represent the same amount of pressure. One mm Hg is exactly equal to one torr; thus, the conversion is straightforward: 1 mm Hg = 1 torr. This comes from the original definition of the torr, which was based on the height of a mercury column that can be supported by a pressure differential. If you encounter a measurement in mm Hg and require it in torr, no mathematical transformation is necessary. For instance, \(62 \mathrm{~mm} \mathrm{Hg}\) is simply \(62 \text{ torr}\).

Recognizing this one-to-one correspondence between these two units is essential when making precise measurements in scientific experiments and for calibration of pressure-measuring instruments.

Kilopascals to Bar Conversion

The kilopascal (kPa) and the bar are both units of pressure, with the bar being closely aligned with atmospheric pressure, just like the atm. To convert from kilopascals to bar, the conversion factor is that 1 bar is equal to 100 kPa. This relationship means that to find the pressure in bar, you would divide the pressure in kilopascals by 100.

An example conversion from the exercise is converting \(1.22 \text{ kPa}\) to bar. This is done by dividing 1.22 by 100, which yields:
\(1.22 \text{ kPa} \times \frac{1 \text{ bar}}{100 \text{ kPa}} = 0.0122 \text{ bar}\).

Understanding this conversion is significant, especially in fields such as meteorology and engineering, where different standards might be in use and accuracy is paramount.