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SOLUTION:

Step 1: List the given values.

[tex]\begin{aligned} & T = 20^{\circ}\text{C} = \text{293.15 K} \\ & MM = \text{70.906 g/mol = 0.070906 kg/mol} \end{aligned}[/tex]

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

[tex]\begin{aligned} u_{\text{rms}} & = \sqrt{\frac{3RT}{MM}} \\ & = \sqrt{\frac{3(\text{8.3145 J/K}\cdot\text{mol})(\text{293.15 K})}{\text{0.070906 kg/mol}}} \\ & = \boxed{\text{321 m/s}} \end{aligned}[/tex]

Hence, the root-mean-square speed of molecular chlorine at 20°C is 321 m/s.

[tex]\\[/tex]

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