1. Understand the Concepts

* Average Speed of Gases: The average speed of gas molecules is related to their temperature and molar mass.

* Root-Mean-Square Speed (vrms): A common way to express the average speed of gas molecules is the root-mean-square speed. The formula is:

vrms = √(3RT/M)

where:

* R is the ideal gas constant (8.314 J/mol·K)

* T is the temperature in Kelvin

* M is the molar mass in kg/mol

2. Set up the Equation

We want the vrms of xenon (Xe) to be equal to the vrms of chlorine gas (Cl2) at 24°C. Let's call the temperature of xenon Tx:

√(3R*Tx/MXe) = √(3R*TCl2/MCl2)

3. Convert Temperatures to Kelvin

* TCl2 = 24°C + 273.15 = 297.15 K

4. Determine Molar Masses

* MXe = 131.29 g/mol = 0.13129 kg/mol

* MCl2 = 2 * 35.45 g/mol = 70.90 g/mol = 0.07090 kg/mol

5. Solve for Tx

Since the '3R' term appears on both sides, it cancels out. We can simplify the equation and solve for Tx:

√(Tx/MXe) = √(TCl2/MCl2)

Square both sides:

Tx/MXe = TCl2/MCl2

Solve for Tx:

Tx = TCl2 * (MXe/MCl2)

6. Calculate Tx

Tx = 297.15 K * (0.13129 kg/mol / 0.07090 kg/mol)

Tx ≈ 552.7 K

7. Convert Back to Celsius

Tx ≈ 552.7 K - 273.15 = 279.55 °C

Therefore, xenon atoms will have the same average speed as Cl2 molecules at 24°C when the xenon is at approximately 279.55°C.