Calculate collision density of air


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> Caluculate the collision density between $\ce{O2}$ and $\ce{N2}$ in air at $T = \pu{10 ^\circ C}$. Assume that the air is an ideal gas and that the molecules are spheres with diameters $\pu{0.36 nm}$ for $\ce{O2}$ and $\pu{0.37 nm}$ for $\ce{N2}$. 
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This is what I have done so far, the collision density equation is:


$$ Z\_{AB} = \frac{N\_A}{V} \frac{N\_B}{V} π d^2\_{AB} c\_A$$ 


And since we assume that air is an ideal gas, we can use:


$$\frac{N\_A}{V} = \frac{N\_B}{V} = \frac {p}{kT}$$


$$\frac {p}{kT} = \frac {1.01325 \cdot 10^5}{(1.38 \cdot 10^{-23}) \cdot 283} =2.6 \cdot 10^{25}$$


The collision cross-section can also be calculated:


$$ \sigma = \pi d^2\_{AB} = \pi \left((3.6 \cdot 10^{-10})+(3.7 \cdot 10^{-10})\right)^2 = 1.67 \cdot 10^{-18} m^2 $$


But to calculate the average speed I need the mass of the molecules, which I don't have and I am not sure if I can determine it from the information given either. I thought about calculating the volume of each molecule and then looking up the density of oxygen and nitrogen to get the mass, however I am not sure if this is the correct way that the problem should be solved. Is there a specific assumption I need to take in order to determine the masses? 


