What volume will each of the following occupy at STP? (a) \(6.02 \times 10^{23}\) molecules of \(\mathrm{CO}_{2}\) (b) \(2.5 \mathrm{~mol} \mathrm{CH}_{4}\) (c) \(12.5\) g oxygen

Understanding Standard Temperature and Pressure (STP) is essential when calculating gas volumes in chemistry. STP refers to a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere (atm), which is the average atmospheric pressure at sea level. At STP, gases behave predictably, which allows for straightforward calculations.

One of the reasons why STP conditions are so important is that they provide a reference point for comparing different gases. Since temperature and pressure can greatly affect the volume that a gas occupies, having a standard set of conditions eliminates those variables, making it easier to study and understand the properties of gases. When we mention a gas volume at STP, it implies that the measurements were taken or are being predicted for these specific environmental parameters.

At the heart of these calculations lies Avogadro's number, which is approximately equal to \(6.02 \times 10^{23}\). This value is fundamental in chemistry because it is the number of units, such as atoms or molecules, in one mole of any substance. This number was determined through experimentation and provides a bridge between the microscopic world of atoms and the macroscopic world of grams and liters that we can measure in the lab.

For a gas at STP, Avogadro's number tells us that one mole will occupy a volume of 22.4 liters. This is because, under these conditions, the molecules of an ideal gas are spaced out in such a way that, regardless of the type of gas, this volume is consistently occupied. By using Avogadro's number as the conversion factor, we can easily switch between counting particles and working with mass and volume in a more tangible sense.

The molar volume of a gas, which is the volume one mole of a gas occupies under specified conditions, is especially simple to use at STP. As mentioned earlier, one mole of any ideal gas will occupy 22.4 liters at STP. This is a direct consequence of Avogadro's law, which states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.

This uniformity in volume, regardless of the gas identity, allows us to perform calculations with a great deal of symmetry. In practice, if we know the amount of a gas in moles, it becomes a straightforward calculation to determine its volume at STP using the molar volume. For example, if we have two moles of a gas, we can expect it to take up \(2 \times 22.4 = 44.8\) liters at STP.

Intimately connected to the aforementioned concepts is the understanding of molecular mass and moles. The molecular mass (also known as molar mass) of a substance is the weight of one mole of that substance and is expressed in grams per mole (g/mol). This measurement is an average of the mass of all isotopes of the atoms in the substance, weighted by their abundance.

The concept of moles bridges the gap between the microscopic world of atoms and the macroscopic world we interact with daily. A mole represents a specific number of particles (Avogadro's number), and knowing the molecular mass of a substance allows us to convert between grams and moles. For instance, to find how many moles are in a given mass of a substance, we divide the mass by the molecular mass. This step is critical in stoichiometric calculations and when you're trying to find a gas's volume at STP from a given mass of the substance.