Question

Convert the following pressures into \(\mathrm{mm} \mathrm{Hg}\). a. 0.903 atm b. \(2.1240 \times 10^{6} \mathrm{~Pa}\) c. 445 kPa d. 342 torr

Short answer

a. 686.28 mmHg b. 15954 mmHg c. 3340.28 mmHg d. 342 mmHg

Step-by-step solution

a. 0.903 atm

To convert 0.903 atm to mmHg, multiply by the conversion factor: mmHg = 0.903 atm × 760 mmHg/atm mmHg = 686.28 So, 0.903 atm is equal to 686.28 mmHg.

b. \(2.1240 \times 10^{6} \mathrm{~Pa}\)

To convert \(2.1240\times10^6\) Pa to mmHg, multiply by the conversion factor: mmHg = \(2.1240\times10^6\) Pa × 0.00750062 mmHg/Pa mmHg ≈ 15954 So, \(2.1240\times10^6\) Pa is approximately equal to 15954 mmHg.

c. 445 kPa

To convert 445 kPa to mmHg, multiply by the conversion factor: mmHg = 445 kPa × 7.50062 mmHg/kPa mmHg ≈ 3340.28 So, 445 kPa is approximately equal to 3340.28 mmHg.

d. 342 torr

Since torr and mmHg are equivalent units, no conversion is necessary. 342 torr = 342 mmHg So, 342 torr is equal to 342 mmHg.

Key concepts

Atmospheric Pressure

Understanding atmospheric pressure is essential when delving into the topic of pressure conversion in chemistry. Atmospheric pressure is the force exerted by the weight of the air above us. At sea level, it is commonly accepted that the atmospheric pressure is about 101,325 Pascals (Pa), or 1 atmosphere (atm), which also equates to 760 millimeters of mercury (mmHg). This standard measurement originates from the use of a mercury barometer, where the atmospheric pressure supports a column of mercury, which rises to a height measured in millimeters. This concept is vital for students to grasp, as it sets the foundation for understanding how pressure is measured and converted in different units.

Pascal to mmHg Conversion

When faced with the need to convert units from Pascals (Pa) to millimeters of mercury (mmHg), a conversion factor is vital. Pascal is the SI unit of pressure and is defined as one newton per square meter. To convert Pascals to mmHg, a student should use the conversion factor \(1 \text{mmHg} = 133.322 \text{Pa}\). Therefore, the equation \( \text{mmHg} = \text{Pa} \times \frac{1 \text{mmHg}}{133.322 \text{Pa}} \) simplifies the process. For example, to convert \(2.1240 \times 10^{6} \text{Pa}\) to mmHg:

Step 1: Multiply the value in Pascals by the conversion factor.
\( \text{mmHg} = 2.1240 \times 10^{6} \text{Pa} \times \frac{1 \text{mmHg}}{133.322 \text{Pa}} \)
Step 2: Calculate to get the pressure in mmHg.
In practice, knowing this conversion factor can help students switch between SI and non-SI units, which is often required in various scientific calculations.

kPa to mmHg Conversion

When converting from kilopascals (kPa) to millimeters of mercury (mmHg), it helps to know that 1 kPa equals 1,000 Pascals. Thus, the conversion factor for kPa to mmHg is the same as for Pa to mmHg, but adjusted for the difference in magnitude:

\(1 \text{mmHg} = \frac{1,000 \text{Pa}}{133.322 \text{Pa}} = 7.50062 \text{mmHg/kPa}\)

So, the conversion equation becomes \( \text{mmHg} = \text{kPa} \times 7.50062 \text{mmHg/kPa} \). Converting 445 kPa to mmHg, for instance, involves simply multiplying 445 by the conversion factor of 7.50062. This step simplifies the understanding and application of pressure conversions in a real-world context, thereby enhancing problem-solving skills in chemistry.

Torr and mmHg Equivalence

The torr is another unit of pressure commonly used in scientific measurements. It is defined as \(1/760\) of an atmosphere, and this originates from the millimeters of mercury (mmHg) measurement. That means, 1 torr is essentially equivalent to 1 mmHg, which simplifies conversions between these two units to a direct one-to-one relationship.

If a student is tasked with converting torr to mmHg, there is no need for a conversion factor or complex calculations. For example, 342 torr directly translates to 342 mmHg. This equivalence is useful when working with vacuum pressures or barometric pressure readings in meteorology, where mmHg and torr can be used interchangeably. Understanding this equivalence allows students to confidently navigate between different pressure units without confusion.