Question

A gauge on a compressed gas cylinder reads \(2200 \mathrm{psi}\) (pounds per square inch; \(1 \mathrm{~atm}=14.7 \mathrm{psi}\) ). Express this pressure in each of the following units. a. standard atmospheres b. megapascals (MPa) c. torr

Short answer

a. \(Atmospheres = (2200 \mathrm{psi}) * (1 \mathrm{atm} / 14.7 \mathrm{psi}) = 149.66 \mathrm{atm} \) b. \(Megapascals = ((149.66 \mathrm{atm}) * (101325 \mathrm{Pa} / 1 \mathrm{atm})) / (10^6 \mathrm{Pa} / 1 \mathrm{MPa}) = 15.17 \mathrm{MPa} \) c. \(Torr = (149.66 \mathrm{atm}) * (760 \mathrm{torr} / 1 \mathrm{atm}) = 113743.6 \mathrm{torr} \)

Step-by-step solution

Convert psi to atm

Given pressure is 2200 psi. We will use the conversion factor: 1 atm = 14.7 psi. Atmospheres = (2200 psi) * (1 atm / 14.7 psi) #a. Pressure in megapascals

Convert atm to pascals

First, we need to convert the pressure in atmospheres to pascals (Pa) using the conversion factor: 1 atm = 101325 Pa. Pascals = (Atmospheres) * (101325 Pa / 1 atm)

Convert pascals to megapascals

Now, we need to convert the pressure in pascals to megapascals (MPa) using the conversion factor: 1 MPa = 10^6 Pa. Megapascals = (Pascals) / (10^6 Pa / 1 MPa) #a. Pressure in torr

Convert atm to torr

Finally, we need to convert the pressure in atmospheres to torr using the conversion factor: 1 atm = 760 torr. Torr = (Atmospheres) * (760 torr / 1 atm)

Key concepts

Understanding Pressure Units in Chemistry

In chemistry, particularly when working with gases, it's essential to understand pressure units because pressure can strongly influence the behavior of gas particles. When we talk about pressure, we are referring to the force that the particles apply per unit area on the walls of their container. One common unit of pressure is the atmosphere (atm), which originally represented the average air pressure at sea level. Another standard unit is the pound per square inch (psi), often used in various industries including automotive and hydraulics.

The problem at hand requires a conversion from psi to various other units, which showcases the diversity of pressure units used in science and engineering. For instance, the megapascal (MPa) is a unit derived from the Pascal (Pa), which is the SI unit for pressure. It illustrates just how large or intense pressures can be when dealing with gases under different conditions. Additionally, the torr is another unit of pressure that pays homage to the Italian physicist Evangelista Torricelli. One torr is equivalent to the pressure that can support a column of mercury 1 millimeter high and is nearly equal to 1 millimeter of mercury (mmHg).

It's fascinating to see how units that originated from very different sources are now interlinked and convertible in scientific practice. This not only highlights human ingenuity but allows for universal communication and understanding across scientific disciplines.

The Role of Gas Laws in Pressure Conversions

When encountering pressure conversions in chemistry, it's often within the context of studying gas laws. These laws describe how various properties of gases (pressure, volume, temperature, and amount) interact with one another. The most fundamental gas laws include Boyle's Law, Charles's Law, and Avogadro's Law, all of which lead up to the Ideal Gas Law, represented by the equation \(PV = nRT\), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

Boyle's Law and Pressure

Boyle's Law states that the pressure of a gas is inversely proportional to its volume, as long as the temperature and amount of gas remain constant. This law is crucial because when working with pressure conversions, we often assume that the other variables are held constant unless stated otherwise.

The Impact of Temperature: Charles's Law

Charles's Law, on the other hand, illustrates that a gas's volume is directly proportional to its temperature when pressure and amount are constant. This is an essential consideration, particularly when performing experiments that involve temperature changes alongside pressure measurements.

Avogadro's Law: Volume and Moles

Avogadro's Law shows that the volume of a gas is directly proportional to the number of moles, assuming constant temperature and pressure. This law helps chemists understand that the moles of a gas can also influence its pressure.

Having a solid grasp of these gas laws is integral to understanding why certain conditions are stated or assumed when dealing with pressure conversions. They provide the foundation that allows chemists to predict how gases will behave under different conditions.

Mastering Unit Conversion for Pressure in Chemistry

Unit conversion is a fundamental skill in chemistry, as it allows scientists to communicate and compare results universally. The process typically involves a 'conversion factor,' a term that allows one to convert from one unit to another. For example, to convert psi to atm as in the original exercise, we use the conversion factor \(1 \text{ atm} = 14.7 \text{ psi}\).

Step-by-Step Unit Conversion

The key to a successful unit conversion is ensuring that the units you want to cancel out are correctly aligned. For instance, when converting from psi to atm, you ensure that psi is in the denominator so that it cancels out, leaving you with atm. It's much like a fraction's cross-cancellation technique.

It's also essential to pay attention to the significant figures and rounding rules, as they ensure that converted values maintain the correct level of precision indicative of the measurement's accuracy. Once you grasp the concept of unit conversion, it becomes a powerful tool, allowing you to switch seamlessly among different scales and units of measurement such as from Pascals to megapascals or atmospheres to torr, providing flexibility in how you report and interpret data.

By mastering unit conversion, students can more readily understand the connectivity of the different ways we measure and interpret pressure in scientific contexts. This foundational skill is not only crucial in solving textbook problems but also for advancing in the field of chemistry where precision and adaptability are paramount.