Question

Convert the following pressures into units of \(m m H g\). a. 822 torr c. 1.14 atm b. \(121.4 \mathrm{kPa}\) d. 9.75 psi

Short answer

a. 822 mmHg c. 865.6 mmHg b. 910.27 mmHg d. 504.17 mmHg

Step-by-step solution

a. Convert from torr to mmHg

The pressure is already given in torr, and since 1 torr equals 1 mmHg, the pressure value remains the same: \(822 \: \text{mmHg}\).

c. Convert from atm to mmHg

To convert the pressure value from atmospheres to mmHg, multiply by the conversion factor: \(1.14 \: \text{atm} * 760 \frac{\text{mmHg}}{\text{atm}} = 865.6 \: \text{mmHg}\).

b. Convert from kPa to mmHg

To convert the pressure value from kilopascals to mmHg, multiply by the conversion factor: \(121.4 \: \text{kPa} * 7.5006 \frac{\text{mmHg}}{\text{kPa}} = 910.27 \: \text{mmHg}\).

d. Convert from psi to mmHg

Finally, to convert the pressure value from psi to mmHg, multiply by the conversion factor: \(9.75 \: \text{psi} * 51.71 \frac{\text{mmHg}}{\text{psi}} \approx 504.17 \: \text{mmHg}\). The final converted pressure values are: a. 822 mmHg c. 865.6 mmHg b. 910.27 mmHg d. 504.17 mmHg

Key concepts

Torr to mmHg Conversion

Converting torr to millimeters of mercury (mmHg) is one of the simplest tasks in pressure conversion because they are directly interchangeable units. A torr was historically defined as the pressure exerted by a column of mercury one millimeter high. Therefore, the conversion factor between torr and mmHg is simply 1.

This means that any pressure value you have in torr is equal to the same value in mmHg. For example, 822 torr, when converted into mmHg, remains 822 mmHg. This direct conversion makes it much easier for students to relate to real-world applications, such as when dealing with barometric pressure readings in weather forecasts.

Atm to mmHg Conversion

To convert from atmospheres (atm) to millimeters of mercury (mmHg), it is essential to use the conversion factor based on the relationship between these two pressure units. One atmosphere is defined as the pressure that supports a column of mercury 760 mm high at 0°C under standard gravity.

Therefore, when converting from atm to mmHg, you multiply the number of atmospheres by 760. For example, to convert 1.14 atm to mmHg, you would perform the following calculation: \(1.14 \text{ atm} \times 760 \frac{\text{mmHg}}{\text{atm}} = 865.6 \text{ mmHg}\). Understanding this direct relationship helps clarify concepts about atmospheric pressure and its equivalence to the historic mercury column method.

kPa to mmHg Conversion

Kilopascals (kPa) to millimeters of mercury (mmHg) conversion requires using the precise conversion factor of 7.5006. This factor is a result of the definition of pascal as the SI unit for pressure and the traditional use of mercury columns to measure pressure. Since there are 1000 pascals in a kilopascal and the old standard of mercury's density and gravity are factored in, this specific number is used for conversion purposes.

To convert a value from kilopascals to millimeters of mercury, multiply the kPa value by 7.5006. For example, the conversion for 121.4 kPa to mmHg is calculated as follows: \(121.4 \text{ kPa} \times 7.5006 \frac{\text{mmHg}}{\text{kPa}} = 910.27 \text{ mmHg}\). This is a critical conversion in chemistry and physics where SI units are standard, but mmHg might be required for certain applications or comparisons.

Psi to mmHg Conversion

Converting from pounds per square inch (psi) to millimeters of mercury (mmHg) involves a conversion factor reflecting the relationship between these two units. The relevant conversion factor is 51.71 because 1 psi is the pressure resulting from one pound-force applied to an area of one square inch, while mmHg measures pressure as a height of mercury in a column.

To convert psi to mmHg, you multiply the pressure value in psi by 51.71. For instance, to convert 9.75 psi into mmHg, you would use the formula: \(9.75 \text{ psi} \times 51.71 \frac{\text{mmHg}}{\text{psi}} \approx 504.17 \text{ mmHg}\). This type of conversion is particularly useful in various scientific fields and industries where pressure needs to be represented in different units for regulatory or measurement standards.