Equal volumes of oxygen gas and a second gas weigh \(1.00\) and \(2.375\) grams respectively under the same experimental conditions. Which of the following is the unknown gas? (a) \(\mathrm{NO}\) (b) \(\mathrm{SO}_{2}\) (c) \(\mathrm{CS}_{2}\) (d) \(\mathrm{CO}\)

Avogadro's Law is a fundamental principle in physical chemistry which states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This concept is vital when comparing different gases as it allows scientists and students to predict how gases will behave under similar conditions.

When we use Avogadro's Law for calculations, what we are essentially saying is that the volume of a gas is directly proportional to the number of moles (a measure of quantity in chemistry) present, as long as the temperature and pressure remain constant. To put it into a simple equation form, we could write it as \( V \propto n \), where \( V \) represents the volume and \( n \) represents the number of moles.

Applying this to our textbook problem simplifies our task: since the volumes of oxygen and the unknown gas are equal and under the same conditions, they must contain the same number of moles. This insight is crucial in solving for the molar mass of the unknown gas, leading us to identify the gas itself.

Molar mass is the weight of one mole of a given substance and is expressed in grams per mole (g/mol). It is a bridge between the macroscopic world we can measure and the microscopic atomic world. The molar mass of an element can be found on the periodic table as it is equivalent to the atomic weight of the element.

To calculate the molar mass of a compound, we sum up the molar masses of all the atoms that make up the compound. For diatomic oxygen (O2), this involves adding the molar masses of two oxygen atoms. Since the atomic weight of oxygen is approximately 16.00 g/mol, diatomic oxygen has a molar mass of \( 16.00 \, g/mol \times 2 = 32.00 \, g/mol \).

Using the molar mass, we can convert between mass and moles, allowing us to perform a diverse array of chemical calculations. This is displayed in the solution where, after determining the moles of oxygen based on its mass, we used Avogadro's Law and the mass of the unknown gas to find its molar mass.

Gases on a Balanced Scale

Comparing gases is a common task in physical chemistry, often required for reactions involving gaseous reactants or products. When comparing gases, we need to look at their molar masses and understand how they relate to their behaviors under the same conditions of temperature and pressure.

Role of Molar Mass in Identifying Gases

In situations like our exercise, once we know the molar mass of an unknown gas, we can use it to determine the gas's identity by comparing it with known values. It's like being a detective, where the molar mass is a clue that leads us to the name of the gas.

In our exercise, with the molar mass of the mystery gas at hand, we compared it to the molar masses of potential candidates. This comparison, much like a lineup, enabled us to pinpoint the correct gas with a molar mass that matched our calculated value.