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 (N2) molecule in a room, we can use the Maxwell-Boltzmann distribution.
The Maxwell-Boltzmann distribution describes the distribution of speeds (or velocities) of particles in a gas at a given temperature. It states that the distribution follows a bell-shaped curve, with most molecules having speeds around the average speed.
To calculate the typical speed, we need to know the temperature of the room. Let's assume it's around 25 degrees Celsius (298 Kelvin). The formula to calculate the most probable speed (vmp) is given by:
vmp = √((2 * k * T) / m)
Where:
- vmp is the most probable speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kilograms
For nitrogen gas (N2), the molar mass is approximately 0.028 kilograms per mole.
Plugging in the values and calculating:
vmp = √((2 * 1.38 x 10^-23 J/K * 298 K) / 0.028 kg/mol)
≈ √(8.17 x 10^-21 J / 0.028 kg)
≈ √(2.92 x 10^-19 m^2/s^2)
≈ 5.40 x 10^4 m/s
The most probable speed for a nitrogen molecule in this room is approximately 5.40 x 10^4 m/s.
Therefore, none of the options (a), (b), or (c) provided match the typical speed of a nitrogen molecule in this room.