Convert each measurement to atm. (a) \(1277 \mathrm{~mm} \mathrm{Hg}\) (b) \(2.38 \times 10^{5} \mathrm{~Pa}\) (c) \(127 \mathrm{psi}\) (d) 455 torr

Conversion from millimeters of mercury (mmHg) to atmospheres (atm) is a simple yet vital process in chemistry, particularly when dealing with gas laws and pressure measurement. MmHg, also called Torricellian millimeters, is a unit of pressure defined as the extra pressure generated by a column of mercury one millimeter high. When you need to convert mmHg to atm, use the conversion factor that 1 atmosphere is equivalent to 760 mmHg.

To convert, you divide the pressure value in mmHg by 760, as shown in the example:
\[\frac{1277 \mathrm{~mmHg}}{760 \mathrm{~mmHg/atm}} = 1.6803 \mathrm{~atm}\]
This conversion is essential for standardizing measurements and for calculations involving the Ideal Gas Law or when moving between different measurement systems.

In the realm of pressure measurement, the Pascal (Pa) is the SI unit and is widely used across scientific disciplines. One Pascal is defined as one newton per square meter. On the contrary, the atm is a unit of pressure used to describe the average atmospheric pressure at sea level. To convert from Pascals to atmospheres, you utilize the conversion factor where 1 atmosphere equals to 101,325 Pascals.

The conversion is performed by dividing the given pressure in Pascals by this value:
\[\frac{2.38 \times 10^{5} \mathrm{~Pa}}{1.01325 \times 10^{5} \mathrm{~Pa/atm}} = 2.3488 \mathrm{~atm}\]
Understanding how to accurately convert between these two units is integral for scientists and engineers when comparing laboratory results with standard atmospheric conditions.

The unit pounds per square inch (psi) is commonly used in various industries, especially in the United States, to gauge the pressure of gases and liquids. One psi represents the pressure exerted by a one-pound force applied to an area of one square inch. To convert psi to atm, which is more prevalent in scientific contexts, you can use the conversion factor that 1 atm is approximately equal to 14.6959 psi.

Thus, if you have a pressure reading in psi, to convert it into atmospheres, simply divide by 14.6959:
\[\frac{127 \mathrm{~psi}}{14.6959 \mathrm{~psi/atm}} = 8.6401 \mathrm{~atm}\]
This conversion is vital for aligning the American engineering standards with scientific research parameters internationally.

The term torr is another unit of pressure, named after Evangelista Torricelli, an Italian physicist and mathematician. It is somewhat special in that 1 torr is exactly equal to 1 mmHg, both representing the pressure generated by a mercury column one millimeter in height. Since we know that 1 atmosphere is equivalent to 760 mmHg, the same conversion factor can be used for converting torr to atm.

Simplifying the conversion process:
\[\frac{455 \mathrm{~torr}}{760 \mathrm{~mmHg/atm}} = 0.5987 \mathrm{~atm}\]
It's important to be familiar with this conversion, as torr and mmHg are often used in barometric pressure measurements and vacuum systems.