What volume is occupied by 12.5 g of argon gas at a pressure of 1.05 atm and a temperature of 322 K? Would the volume be different if the sample were 12.5 g of helium (under identical conditions)?

Verified step by step guidance

1. Identify the problem as one involving the Ideal Gas Law, which is given by the equation: \( PV = nRT \).
2. Calculate the number of moles \( n \) of argon using its molar mass. The molar mass of argon is approximately 39.95 g/mol. Use the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \).
3. Rearrange the Ideal Gas Law to solve for volume \( V \): \( V = \frac{nRT}{P} \).
4. Substitute the known values into the equation: \( n \) (calculated moles of argon), \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), \( T = 322 \text{ K} \), and \( P = 1.05 \text{ atm} \).
5. Repeat the process for helium, using its molar mass of approximately 4.00 g/mol, to determine if the volume would be different under the same conditions.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the volume occupied by a gas under specific conditions of pressure and temperature.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for using the Ideal Gas Law. For argon, the molar mass is approximately 40.00 g/mol, while for helium, it is about 4.00 g/mol, leading to different volumes when the same mass is considered.

Gas Behavior and Comparison

Gases behave differently based on their molecular characteristics, such as size and mass. Under identical conditions of pressure and temperature, lighter gases like helium will occupy a larger volume than heavier gases like argon when the same mass is used. This is due to the differences in their molar masses and the kinetic molecular theory, which explains how gas particles move and interact.