Problem 13 - Chemistry A Molecular Approach

Question

Define molar volume and list its value for a gas at STP.

Step-by-Step Solution

Answer

The molar volume of a gas is the volume occupied by one mole of the gas. At STP (273.15 K and 1 atm), it is 22.414 L/mol.

Step 1: Definition of Molar Volume

Molar volume is defined as the volume occupied by one mole of a substance (element or compound) at a given temperature and pressure. It is expressed in units of liters per mole (L/mol).

Step 2: Molar Volume at Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 273.15 K (0 degrees Celsius) and a pressure of 1 atmosphere (atm). For an ideal gas at STP, the molar volume is a constant value.

Step 3: Value of Molar Volume at STP for a Gas

The molar volume of an ideal gas at STP is 22.414 liters per mole. This is derived from the ideal gas law when n=1 mole, P=1 atm, T=273.15 K, and R is the ideal gas constant.

Key Concepts

Standard Temperature and Pressure (STP)

Understanding Standard Temperature and Pressure (STP) is essential when studying the properties of gases. It is a reference point used by chemists and physicists to compare different sets of experimental data. At STP, the temperature is set to 273.15 Kelvin (0 degrees Celsius), and the pressure is 1 atmosphere (atm). This simplifies many calculations involving gases because it provides a common baseline.

In the context of the molar volume, which refers to the volume one mole of a gas occupies under specific conditions, STP allows for consistency across measurements and calculations. Since temperature and pressure affect the behavior of gases, STP ensures that the specified conditions are uniform, making it easier to predict and understand gas behavior under these controlled conditions.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry and physics that relates the pressure (P), volume (V), temperature (T), and amount (n) of an ideal gas. It is represented by the equation
\[ PV = nRT \]
where 'R' is the ideal gas constant. This law assumes that the particles of a gas behave ideally, meaning they have no volume and do not interact with each other, which is an approximation of the behavior of real gases under certain conditions.

The ideal gas law can be used to derive the molar volume of a gas at STP. By setting n=1 mole, P=1 atm, and T=273.15 K in the equation and solving for V, you get the molar volume of the gas under those conditions. This relationship is vital for the calculation of various gas-related exercises and it allows students to see the direct connection between the theoretical principles and their practical applications.

Liters per Mole

The unit 'liters per mole' is crucial when dealing with the molar volume of gases. It indicates how much space one mole of a gas will occupy. At STP, this volume is approximately 22.414 liters per mole for an ideal gas.

This measurement allows chemists to convert between amounts in moles and the volume a gas would occupy, facilitating the comparison of gases. It's a standard unit that provides a clear and precise method for discussing and comparing the properties of gases. If you know the molar volume of a gas, you can determine how many moles there are in a given volume or, conversely, how much volume a known number of moles will take up.