Calculate Mean Free Path at 300K, 1atm for Air

[smashing]

right this is the question. at a temperature of 300K and 1atm the density of air is 1.29kgm^-3 and the co-eff of viscosity is 1.75x10^-5Pas. Air has a molecular weight of 29 and the average speed is given by the square root of 8kt/piem.

what is their mean free path.

Homework Equations

so i have two equations main equations to use

1/(4sqrt(2)pi x n x d^2 and the other is kt/sqrt(2) x pi x d^2 x pressure

The Attempt at a Solution

so i use the equation that pv=nRT to find the volume (is that correct or could i use the density = mass/volume) when i have found the volume i then equate it to 4/3pi r^3 and re arrange for r and then multiply it by 2 to get the diameter. I then use the second equation but it doesn't come out correct (i have a list of possible answers and i just can't seem to get them though). Do you convert the weight into kg by dividing through by 1000 or can you just leave it as 29 atomic masses. (which would be 29 multiplied by 1.66x10^-27)?

any suggestions on where iv gone wrong would be greatly appreciated.


thanks



adam

 

[BigJDubs]

The mean free path of air is the average distance travelled by an air molecule before it collides with another molecule. To calculate the mean free path, you need to first calculate the number of molecules per unit volume. This can be done using the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. With the given values, you can solve for n. Once you have the number of moles, you can calculate the number of molecules per unit volume using Avogadro's number (6.02x10^23). Then divide the number of molecules per unit volume by the molecular weight of air (29) to get the number of molecules per unit volume. Finally, use the equation for mean free path, 1/(4sqrt(2)pi x n x d^2, where n is the number of molecules per unit volume and d is the diameter of an air molecule. The diameter of an air molecule can be calculated using the equation kT/sqrt(2) x pi x d^2 x pressure, where k is Boltzmann's constant (1.38x10^-23 J/K) and T is the temperature in Kelvin.