find the mean free path of the molecule of oxygen at normal pressure, if the coefficient of diffusion of oxygen at the same pressure and temperature of 0 ° C is equal to 0,19 cm ² / sec.

Question

find the mean free path of the molecule of oxygen at normal pressure, if the coefficient of diffusion of oxygen at the same pressure and temperature of 0 ° C is equal to 0,19 cm ² / sec.

найти среднюю длину свободного пробега молекулы кислорода при нормальном давлении, если коэффицент диффузии кислорода при том же давлении и температуре 0°С равен 0,19cm²/с.

Answer 1

To find the mean free path of a molecule of oxygen at normal pressure, we need to use the kinetic theory of gases. The mean free path is the average distance a molecule travels before colliding with another molecule.

The formula to calculate the mean free path is:

mean free path = (1 / (sqrt(2) * pi * d^2 * N))

Where:
- d is the diameter of the oxygen molecule
- N is the number of molecules per unit volume

To find the diameter of the oxygen molecule, we can use the kinetic theory of gases:

d = (4 * V / (pi * N * sqrt(2)))

Where:
- V is the volume occupied per molecule at normal pressure (It can be calculated using the ideal gas law: V = R * T / P, where R is the gas constant, T is the temperature in Kelvin, and P is the pressure in Pascals)

Now, let's gather the necessary information to calculate the mean free path:

Temperature (T): 0 °C = 273.15 K
Pressure (P): Normal pressure
Coefficient of diffusion (D): 0.19 cm²/s = 0.19 * 10^-4 m²/s

First, let's convert the coefficient of diffusion from cm²/s to m²/s:

D = 0.19 * 10^-4 m²/s

Now, we can calculate the volume occupied per molecule at normal pressure using the ideal gas law:

V = R * T / P

Since we are dealing with normal pressure, which is approximately 1 atmosphere, we can use the value of the ideal gas constant, R, in atmospheres:

R = 0.0821 L.atm/(mol.K)

Converting the pressure from atmospheres to Pascals:

1 atm = 101325 Pascals

Now we have all the necessary information to calculate the mean free path.

1. Calculate the volume occupied per molecule:

V = (0.0821 L.atm/(mol.K) * 273.15 K) / 101325 Pa

2. Convert V from liters to cubic meters:

V = V * 0.001 m³/L

3. Calculate the diameter of the oxygen molecule:

d = (4 * V / (pi * N * sqrt(2)))

4. Calculate the number of molecules per unit volume:

N = P / (R * T)

5. Calculate the mean free path:

mean free path = (1 / (sqrt(2) * pi * d^2 * N))

Now, you can plug in the values in these equations to obtain the mean free path of a molecule of oxygen at normal pressure.