(a) A \(350.0-\mathrm{mL}\) flask contains \(0.1500 \mathrm{~mol}\) Ar at \(24^{\circ} \mathrm{C}\). What is the pressure of the gas in kilopascals? (b) You are told that \(23.9 \mathrm{mg}\) of bromine trifluoride exerts a pressure of \(10.0\) Torr at \(100 .{ }^{\circ} \mathrm{C}\). What is the volume of the container in milliliters? (c) A \(100.0\)-mL flask contains sulfur dioxide at \(0.77 \mathrm{~atm}\) and \(30 .{ }^{\circ} \mathrm{C}\). What mass of gas is present? (d) A storage tank of volume \(6.00 \times 10^{3} \mathrm{~m}^{3}\) contains methane at \(129 \mathrm{kPa}\) and \(14^{\circ} \mathrm{C}\). How many moles of \(\mathrm{CH}_{4}\) are present? (e) A \(1.0-\mu \mathrm{L}\) ampoule of helium has a pressure of \(2.00 \mathrm{kPa}\) at \(-115^{\circ} \mathrm{C}\). How many He atoms are present?

Understanding gas pressure calculation is central to working with the ideal gas law, which is expressed as PV = nRT. In this equation, pressure (P) is directly proportional to the number of moles (n), the universal gas constant (R), and temperature (T), inversely proportional to volume (V). To calculate the gas pressure, you can rearrange the formula to P = (nRT)/V. Remember to use the correct units: temperature in Kelvin, volume in liters, and the value for R that matches the pressure units you are calculating, which is generally 8.314 kPa*L/mol*K when calculating pressure in kilopascals.

For example, when a flask contains argon gas, and we know the amount of substance, temperature, and volume, we can easily determine the pressure. Always ensure your temperature is converted from degrees Celsius to Kelvin by adding 273.15, and your volume is in liters by dividing milliliters by 1000. This will give you consistent and accurate results for the pressure of the gas.

Determining molar mass is a key step in many problems involving the ideal gas law. The molar mass is the mass per mole of a substance, typically expressed in grams per mole (g/mol). It is an intrinsic property of each chemical species and can be calculated by summing the atomic masses of all the atoms in a molecule.

To find the molar mass for a compound like bromine trifluoride (BrF3), look up the atomic masses on the periodic table for bromine and fluorine, multiply them by their respective number of atoms in the molecule, and add those values together. This will give you the molar mass of the substance, which is crucial when you need to convert from grams to moles or vice versa, using the relationship: number of moles = mass / molar mass. Accurate molar mass is essential for subsequent calculations, such as determining the volume of a container for a given mass of that substance.

The volume of a gas container can be calculated by rearranging the ideal gas law to V = (nRT)/P. This formula is useful when you have a fixed amount of gas under known pressure and temperature conditions and need to find the volume it occupies. Volume calculations are an essential part of many laboratory and industrial applications, as they enable you to predict how gases will behave when manipulated under various conditions.

For instance, when working with bromine trifluoride in a container at known pressure and temperature, after determining the moles, the ideal gas law allows you to solve for the volume. Always ensure to convert your pressure and temperature to the appropriate units, kilopascals for pressure and Kelvin for temperature. This helps maintain the integrity of your calculations and produces reliable results.

Converting moles to mass is frequently required to complete problems dealing with gas laws. Once the number of moles has been calculated through other parts of the ideal gas law, you can convert this number to mass using the substance's molar mass. The formula for this conversion is mass = moles × molar mass.

For example, if you have determined the number of moles of sulfur dioxide (SO2) in a flask, multiplying this by the molar mass of SO2 will yield the mass of the gas in the flask. Keeping track of your units and ensuring the correctness of the molar mass are crucial for obtaining the correct mass. This kind of calculation is pivotal for anyone working with chemical reactions or processes where precise quantities of substances are required.

Avogadro's number, approximately 6.022 x 10^23, is the number of atoms, ions, or molecules in one mole of a substance. It's a fundamental component in chemistry, bridging the gap between the atomic scale and the macroscopic scale. When using the ideal gas law to find the number of moles of a gas, you can multiply the result by Avogadro's number to determine the total number of particles within that gas volume.

This conversion is particularly useful when working with extremely small or precise measurements of gases, such as in the case of helium in a micro-liter ampoule. After figuring out the moles of helium using the ideal gas law, one can then obtain the exact count of helium atoms present by leveraging Avogadro's number. This concept is crucial in both theoretical calculations and practical applications involving quantities of substances at the molecular level.