Math  /  Algebra

QuestionCalculate the root-mean-square speed of the air pollutant gas SO2\mathrm{SO}_{2} at 25C25^{\circ} \mathrm{C} \square m/s\mathrm{m} / \mathrm{s}

Studdy Solution
Use the root-mean-square speed formula to find vrmsv_{\text{rms}}.
vrms=3kTm v_{\text{rms}} = \sqrt{\frac{3kT}{m}}
Substitute the known values: k=1.38×1023J/K k = 1.38 \times 10^{-23} \, \mathrm{J/K} T=298.15K T = 298.15 \, \mathrm{K} m=64.07×103kg/mol m = 64.07 \times 10^{-3} \, \mathrm{kg/mol}
vrms=3×1.38×1023×298.1564.07×103/6.022×1023 v_{\text{rms}} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 298.15}{64.07 \times 10^{-3} / 6.022 \times 10^{23}}}
Note: The molar mass mm should be divided by Avogadro's number (6.022×1023mol16.022 \times 10^{23} \, \mathrm{mol}^{-1}) to convert to mass per molecule.
Calculate: vrms=3×1.38×1023×298.151.064×1025 v_{\text{rms}} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 298.15}{1.064 \times 10^{-25}}}
vrms215m/s v_{\text{rms}} \approx 215 \, \mathrm{m/s}

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