The cabin pressure has just dropped on a fighter jet. The pressure gauge says 631 torr. Anytime the cabin pressure drops below \(0.850 \mathrm{~atm}\), the pilot is required to put on an oxygen mask. (a) Calculate the pressure in atm. (b) Calculate the pressure in psi. (c) Calculate the pressure in \(\mathrm{kPa}\). (d) Does the pilot need to put on an oxygen mask?

Understanding the conversion between different pressure units is fundamental in various fields of science, especially in chemistry where reactions often occur under specific pressure conditions. A common task is converting from torr to atm. The unit 'torr' is named after Evangelista Torricelli, an Italian physicist and mathematician, who was the first to create a sustained vacuum and discover the principle of the barometer. The 'atm' or atmosphere is a unit of pressure defined as the pressure exerted by the weight of the Earth's atmosphere at sea level.

To convert torr to atm, we must use the conversion factor that states 1 atm is equivalent to 760 torr. The conversion formula is as follows: \[ \text{Pressure in atm} = \frac{\text{Pressure in torr}}{760} \].

This formula is crucial because it allows us to easily switch between units depending on what is required for the problem at hand or which units are more convenient for a particular calculation. For example, when dealing with gas laws and calculations, it’s often necessary to use atm instead of torr, as the former is more commonly used in standard equations and scientific literature.

In chemistry, pressure measurement is paramount, particularly in gas laws and the study of reaction kinetics and equilibrium. Several units are commonly used to measure pressure: atmospheres (atm), torr, pascal (Pa), and pounds per square inch (psi), to name a few.

Each of these units has a specific conversion factor relative to the others. The atmosphere (atm) is widely used in chemistry because many experiments are conducted under standard atmospheric conditions. However, the pascal (Pa) is the SI unit of pressure, and it is used extensively in physics. In many countries, pressure is also commonly given in psi, especially in industrial and automotive applications.

It's essential to be comfortable with converting between these different units:

• To convert atm to kPa, multiply by 101.325 (since 1 atm = 101.325 kPa).
• To convert atm to psi, multiply by 14.696 (since 1 atm = 14.696 psi).

These conversions are not only necessary for solving textbook problems but also for practical applications where the standard units of measurements might differ.

Gas laws are fundamental principles in chemistry that describe how the pressure, volume, and temperature of a gas relate to each other. Boyle's Law, Charles's Law, and Gay-Lussac's Law are among the simplest gas laws, each holding a specific variable constant (volume, pressure, and temperature, respectively). Avogadro's Law introduces the amount of gas into the equation, and the combined gas law brings these relationships together. The most comprehensive gas law, ideal gas law, incorporates all these variables into one formula: \[ PV = nRT \].

In this equation, P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. For pressure calculations, it’s essential to ensure that the pressure is expressed in the correct units that correspond with the ideal gas constant being used. Usually, in the ideal gas equation, pressure is expressed in atmospheres (atm) because the commonly used value for R is 0.0821 L·atm/mol·K.

Real gas behavior, which deviates from the ideal, can be accounted for using the Van der Waals equation. However, for many practical purposes and conditions, the ideal gas law suffices. Correctly performing pressure conversions before applying gas laws is critical as this ensures the accuracy of the calculations and, therefore, the reliability of the results obtained from these equations.