Answer:
To calculate the root mean square velocity of atoms in a gas, we need to know the mass of the atoms, the temperature of the gas, and the gas constant. The root mean square velocity can be calculated using the following equation:
v_rms = sqrt((3RT)/m)
Where v_rms is the root mean square velocity, R is the gas constant, T is the temperature in kelvins, and m is the mass of the atoms in kilograms.
For nitrogen gas (N2), the mass of each atom is 14/6.022 x 10^23 = 2.34 x 10^-23 kg.
For CO2, the mass of each atom is 12/6.022 x 10^23 = 2.0 x 10^-23 kg.
For SO2, the mass of each atom is 32/6.022 x 10^23 = 5.3 x 10^-23 kg.
Plugging these values into the equation, we can calculate the root mean square velocity for each gas at 25°C:
v_rms (N2) = sqrt((38.31298)/(2.34 x 10^-23)) = 466 m/s
v_rms (CO2) = sqrt((38.31298)/(2.0 x 10^-23)) = 505 m/s
v_rms (SO2) = sqrt((38.31298)/(5.3 x 10^-23)) = 691 m/s
Therefore, the root mean square velocity of atoms in a sample of Nitrogen gas at 25°C is 466 m/s, while the root mean square velocity of atoms in a sample of CO2 at the same temperature and pressure is 505 m/s, and the root mean square velocity of atoms in a sample of SO2 at the same temperature and pressure is 691 m/s.
Step-by-step explanation:
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