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At 25 °C, which of the following gases has molecules with the greatest average molecular speed?
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7. Gases
Root Mean Square Speed
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At what temperature does neon (m = 20 u) have a root mean square (rms) speed of 750 m/s?
A
680 K
B
220 K
C
1200 K
D
340 K
Guida verificata passo dopo passo1
Recall the formula for the root mean square (rms) speed of a gas molecule: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(v_{rms}\) is the rms speed, \(R\) is the ideal gas constant, \(T\) is the temperature in kelvin, and \(M\) is the molar mass in kilograms per mole.
Convert the given atomic mass of neon from atomic mass units (u) to kilograms per mole. Since 1 u = \(1.6605 \times 10^{-27}\) kg, and molar mass \(M\) in kg/mol is the atomic mass in grams per mole divided by 1000, use \(M = 20 \times 10^{-3}\) kg/mol.
Rearrange the rms speed formula to solve for temperature \(T\): \(T = \frac{M v_{rms}^2}{3R}\).
Substitute the known values into the rearranged formula: use \(M = 0.020\) kg/mol, \(v_{rms} = 750\) m/s, and \(R = 8.314\) J/(mol·K).
Calculate the temperature \(T\) using the substituted values to find the temperature at which neon has the given rms speed.
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