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Calculate the root-mean-square speed of molecular chlorine in $\mathbf{m} / \mathrm{s}$ at $22.0^{\circ} \mathrm{C}$.
$\square$ $\mathrm{m} / \mathrm{s}$

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∻Solution∻ ‖ 1 ⋮ **Convert temperature to Kelvin**: The given temperature is 22.0°C. To use this in the root-mean-square speed formula, it must be converted to Kelvin. The conversion formula is $T(K) = T(°C) + 273.15$. ‖ ‖ 2 ⋮ **Calculate the root-mean-square speed**: The root-mean-square speed ($v_{rms}$) of a gas can be calculated using the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant ($1.38 imes 10^{-23} \, ext{J/K}$), $T$ is the temperature in Kelvin, and $m$ is the mass of one molecule of the gas in kilograms. The molar mass of chlorine ($Cl_2$) is approximately $70.9 \, ext{g/mol}$, which needs to be converted to kilograms per molecule for this formula. ‖ ‖ 3 ⋮ **Perform the calculation**: First, convert the molar mass of chlorine to kg per molecule by dividing by Avogadro's number ($6.022 imes 10^{23} \, ext{mol}^{-1}$) and by $1000 \, ext{g/kg}$ to get the mass in kg. Then, substitute the values into the root-mean-square speed formula and solve for $v_{rms}$. ‖ ∻Answer∻ ⚹ [Insert final answer here] ⚹ ∻Key Concept∻ ⚹ The root-mean-square speed of a gas is calculated using the formula that relates the speed to the temperature and the mass of the gas molecules. ⚹ ∻Explanation∻ ⚹ The temperature must be in Kelvin, and the mass of the gas molecules must be in kilograms to use the root-mean-square speed formula correctly. ⚹◊What is the formula for calculating the root-mean-square speed of a gas molecule at a given temperature?⍭ Generate me a similar question◊

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