Calculate the root mean square velocity and kinetic energy of F₂, Cl₂, and Br₂ at 298 K. Rank these three halogens with respect to their rate of effusion.

Key Concepts

Root Mean Square Velocity

The root mean square (RMS) velocity is a measure of the average speed of particles in a gas. It is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. This concept is crucial for understanding how the speed of gas molecules relates to their mass and temperature.

Kinetic Energy of Gases

The kinetic energy of gas molecules is directly related to their temperature and can be expressed using the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the gas particles. At a constant temperature, the average kinetic energy of gas molecules is the same, which allows for comparisons between different gases based on their molar masses.

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases effuse faster than heavier gases. Understanding this law is essential for ranking the rates of effusion of F2, Cl2, and Br2, as it allows us to predict which gas will effuse more quickly based on their respective molar masses.