How many grams of carbon dioxide are contained in 1.000 L of the gas, at \(25.0^{\circ} \mathrm{C}\) and 101.325 \(\mathrm{kPa}\) ? What is the density of the gas at these conditions? What would the density of oxygen be at these conditions?

Understanding how to convert Celsius to Kelvin is vital when working with the Ideal Gas Law. The Kelvin scale is the standard unit of temperature in physical sciences, so it's essential to convert any other temperature measurements to Kelvin. To accomplish this, you can simply add 273.15 to the Celsius temperature. This specific number accounts for the difference between the freezing point of water on both scales. For example, a room temperature of about 25°C would be equivalent to 298.15 K. Always ensure the accuracy of your conversion before proceeding with gas law calculations.

When given a temperature like in our original problem, which is 25.0°C, the formula to convert to Kelvin becomes \( K = ^{\circ}C + 273.15 \), leading to a converted temperature of \( 25.0 + 273.15 = 298.15 K \). This step serves as the foundation for correctly applying the Ideal Gas Law.

Pressure units often require conversion to atmospheres (atm) when using the Ideal Gas Law. Commonly, pressure can be measured in pascals (Pa), kilopascals (kPa), millimeters of mercury (mmHg), or torr. The conversion factor from kilopascals to atmospheres is important to remember: \(1 atm = 101.325 kPa\).

For our task, we have a pressure of 101.325 kPa which we convert to atm using this ratio: \(101.325 kPa = 101.325 / 101.325 = 1 atm\). This helps normalize the pressure into a unit compatible with the Ideal Gas Law, which ensures the calculation is consistent and accurate.

The molar mass of a substance is the weight of one mole of that substance and is typically expressed in grams per mole (g/mol). To find the molar mass of a molecule, sum the weights of each constituent atom, which are found on the periodic table.

For instance, in carbon dioxide ( CO2), there is one carbon atom and two oxygen atoms. Using the atomic weights: carbon (approximately 12.01 g/mol) and oxygen (approximately 16.00 g/mol), the molar mass calculation would be \(12.01 g/mol + 2 \times 16.00 g/mol = 44.01 g/mol\). Knowing the molar mass is essential for converting moles to grams, which is a crucial step in many chemistry problems involving the Ideal Gas Law.

The density of a gas is typically expressed as grams per liter (g/L). It's calculated by dividing the mass of the gas in grams by its volume in liters. The formula \(Density = \frac{Mass}{Volume}\) is simple yet powerful for finding the density of a gas under specified conditions, as required by the Ideal Gas Law.

From the given problem, once we determine the mass of the carbon dioxide in grams, we can find the density by using the formula with a known volume of 1.000 L. Similarly, to find the density of oxygen or any other gas, use the same process with the appropriate molar mass. Remember, for the Ideal Gas Law, accurate density calculation is only possible when the mass and volume are in compatible units.