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SOLUTION:

Step 1: List the given values.

[tex]\begin{aligned} & T = 65^{\circ}\text{C} = \text{338.15 K} \\ & MM = \text{31.999 g/mol = 0.031999 kg/mol} \end{aligned}[/tex]

Step 2: Calculate the root-mean-square speed of O₂.

[tex]\begin{aligned} u_{\text{rms}} & = \sqrt{\frac{3RT}{MM}} \\ & = \sqrt{\frac{3(\text{8.3145 J/K}\cdot\text{mol})(\text{338.15 K})}{\text{0.031999 kg/mol}}} \\ & = \boxed{\text{513.4 m/s}} \end{aligned}[/tex]

Hence, the root-mean-square speed of O₂ at 65°C is 513.4 m/s.

[tex]\\[/tex]

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