What is a typical speed for a N2 molecule in this room?
a) 50 m/s
b) 500m/s
c) 1500 m/s
To determine the typical speed of a nitrogen molecule (N2) in a room, we can use the concept of the root mean square (rms) speed. The rms speed of a gas molecule is given by the equation:
v = sqrt(3RT/M)
Where:
v is the rms speed of the gas molecule,
R is the gas constant,
T is the temperature in Kelvin,
M is the molar mass of the gas molecule.
For nitrogen gas (N2), the molar mass (M) is approximately 28 g/mol. The temperature in the room may vary, but let's assume it is around 25 degrees Celsius, which is equivalent to 298 Kelvin.
Using these values, we can calculate the typical speed of a nitrogen molecule in the room:
v = sqrt(3 * R * T / M)
v = sqrt(3 * 8.314 J/mol*K * 298 K / 28 g/mol)
v = sqrt(6226.616 J/(mol*g))
Converting J/(mol*g) to m/s by using the conversion factor 1 J/(mol*g) = 1 kg*m^2/s^2 (since 1 Joule = 1 kg*m^2/s^2), we get:
v = sqrt(6226.616 kg*m^2/(g*s^2))
v = sqrt(6226.616) m/s
v ≈ 78.9 m/s
Therefore, the typical speed of a nitrogen molecule (N2) in this room is roughly 78.9 m/s.
None of the given options (a) 50 m/s, b) 500 m/s, c) 1500 m/s) match the calculated value.