A 4.44 L container holds 15.4 g of oxygen at \(22.55^{\circ} \mathrm{C} .\) What is the pressure?

When studying the behavior of gases, the molar mass of a gas is often a critical piece of information, as it relates to converting the mass of a gas to the amount of substance or moles. Molar mass is defined as the mass of one mole of a substance and is typically expressed in grams per mole (g/mol).

For diatomic elements like oxygen (\(O_2\)), the molar mass is calculated by adding together the atomic masses of each atom that makes up the molecule. Since each oxygen atom has a molar mass of approximately 16.00 g/mol, the molar mass for an oxygen molecule (\(O_2\)) is therefore 32.00 g/mol because it consists of two oxygen atoms. Understanding this concept is crucial when working with the Ideal Gas Law, as it allows us to convert the given mass of a gas into moles, an essential step for further calculations.

Temperature plays a vital role in gas law calculations, affecting the kinetic energy and movement of gas particles. However, temperature needs to be in the correct unit to be used in such formulas, specifically the Kelvin scale for most gas law equations, including the Ideal Gas Law.

Converting Celsius to Kelvin is straightforward: you simply add 273.15 to the Celsius temperature to get the temperature in Kelvin. This is because 0 Kelvin (absolute zero) is -273.15 degrees Celsius, which is why we add this constant. For instance, a room temperature of around 20 degrees Celsius is approximately 293.15 Kelvin. This conversion is necessary because the Kelvin scale measures temperature with relation to absolute zero, thereby ensuring proportional changes in the kinetic energy of gas particles are accurately represented.

Gas pressure is one of the fundamental properties described in the Ideal Gas Law, where pressure (\(P\)), volume (\(V\)), number of moles (\(n\)), the gas constant (\(R\)), and temperature (\(T\)) all relate. To calculate the gas pressure, we rearrange the Ideal Gas Law formula \[P = \frac{nRT}{V}\].

Gas pressure can be thought of as the force applied by gas particles as they collide with the walls of their container. This pressure is influenced by how many particles there are (moles of gas), the volume of the container they're in, and how energetically they're moving (temperature). The gas constant (\(R\)) ties these variables together and is dependent on the units used for pressure and volume. It's worth noting that the units chosen must be consistent throughout the calculation. Once we have the moles from the molar mass calculation, temperature in Kelvin, and an understanding of the volume and the gas constant, we can then solve for the pressure exerted by the gas.