Question

The average kinetic energy of the molecules in a gas sample depends only on the temperature, . However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule, as shown in the equation for rms speed

rms speed=3ℳ⎯⎯⎯⎯⎯⎯⎯⎯⎯√

where =8.314 J/(mol⋅K) and ℳ is molar mass in kilograms per mole. Note that a joule is the same as a kilogram‑meter squared per second squared (kg·m2/s2).

What is the rms speed of Cl2 molecules at 413 K?

Answer 1

12.1 m/s

Step-by-step explanation:

Step 1: Given data

• Molar mass of chlorine (M): 70.9 g/mol

• Ideal gas constant (R): 8.314 J/(mol⋅K)

• Absolute temperature (T): 413 K

Step 2: Calculate the root-mean-square speed of chlorine molecules

We will use the following expression.

rms-speed = √(3 × R × T/ M)

rms-speed = √(3 × 8.314 J/(mol⋅K) × 413 K/ 70.9 g/mol)

rms-speed = 12.1 m/s