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青州's Question
Chemistry
Posted 2 months ago

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Calculate the root-mean-square speed of molecular chlorine in m/s\mathbf{m} / \mathrm{s} at 22.0C22.0^{\circ} \mathrm{C}.
\square m/s\mathrm{m} / \mathrm{s}
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Answer from Sia
Posted 2 months ago
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)+273.15T(K) = T(°C) + 273.15
2
Calculate the root-mean-square speed: The root-mean-square speed (vrmsv_{rms}) of a gas can be calculated using the formula vrms=3kTmv_{rms} = \sqrt{\frac{3kT}{m}}, where kk is the Boltzmann constant (1.38×1023J/K1.38 \times 10^{-23} \, \text{J/K}), TT is the temperature in Kelvin, and mm is the mass of one molecule of the gas in kilograms. The molar mass of chlorine (Cl2Cl_2) is approximately 70.9g/mol70.9 \, \text{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 (6.022×1023mol16.022 \times 10^{23} \, \text{mol}^{-1}) and by 1000g/kg1000 \, \text{g/kg} to get the mass in kg. Then, substitute the values into the root-mean-square speed formula and solve for vrmsv_{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.

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