Understanding the Concepts

* Average Speed of Gas Molecules: The average speed of gas molecules is related to their temperature. The higher the temperature, the faster the molecules move on average.

* Root-Mean-Square Speed: A common way to express the average speed of gas molecules is the root-mean-square speed (urms). It's calculated using the following equation:

urms = √(3RT/M)

where:

* urms = root-mean-square speed (m/s)

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

* T = temperature (K)

* M = molar mass (kg/mol)

Setting up the Problem

We want the average speeds of xenon atoms (Xe) and chlorine molecules (Cl2) to be equal:

urms (Xe) = urms (Cl2)

Calculations

1. Molar Masses:

* Xe: 131.29 g/mol = 0.13129 kg/mol

* Cl2: 70.90 g/mol = 0.07090 kg/mol

2. Set up the Equation:

√(3R * T(Xe) / M(Xe)) = √(3R * T(Cl2) / M(Cl2))

3. Simplify: Since both sides have √(3R), we can cancel them:

T(Xe) / M(Xe) = T(Cl2) / M(Cl2)

4. Solve for T(Xe):

T(Xe) = (M(Xe) / M(Cl2)) * T(Cl2)

T(Xe) = (0.13129 kg/mol / 0.07090 kg/mol) * T(Cl2)

T(Xe) ≈ 1.85 * T(Cl2)

Conclusion

Xenon atoms will have the same average speed as chlorine molecules at a temperature that is approximately 1.85 times higher than the temperature of the chlorine molecules.

Important Note: This solution assumes ideal gas behavior. In reality, deviations from ideal behavior might occur at very high temperatures or pressures.