Relation between particle numbers and collisions between gas molecules inside a closed container I'm not a physicist, nor studying physics, so this may be a dumb or a very hard question, I don’t know. I'm not sure if I used correct tags, feel free to correct them if you feel like it is necesary. Forgive me about my English aswell, it’s not my mother language.
I'd like to know if there is a known relation between the average collisions per particle with other particles (not with walls) and the total amount of particles in a given volume and temperature. I guess its somehow a stochastic mechanic though, but how high is the typical deviation?. Will proximity to walls affect the number of collisions or wall collisions will compensate particle collisions? 
My real interest is not to apply this to real particles, but with agents behaving like gas particles in a closed container, so every particle will be moving at the same speed (which if I’m not wrong solely depends on temperature in nature), and perfect elasticity can be simulated as well. I'm not taking gravity into consideration either. The "perfect simple answer" here is a formula relating volume, number of collisions per particle, temperature and amount of molecules (density?).
I’m always happy to learn, so if after a “simple answer” you want to refer me to additional documentation I’ll be happy to look further.
Thank you all.
 A: The formula for Mean Free Path for gas particles depends not only on density, but on the "size" of the particles.  As the size decreases, the chance of collision goes down.
If you have the mean free path and the average velocity, then path divided by speed will give you mean free time for collisions per particle. 
A: For an ideal gas, PV = nRT. 
Pressure is proportional to the number of collisions each gas molecule sees-- not just the collisions with walls, but the collisions with other gas molecules as well. Hence how you can have different air pressures at different altitudes even though there are no "walls."
A: Let's track a single spherical particle moving in an ideal gas of identical particles: 

Assuming our particle of interest has a diameter $d$ and a constant average velocity $\bar v_x$ because the gas is at constant temperature, then after time $t$ it will have swept out a cylindrical path of collision with volume $V$:
$$V\ =\ (\text{base of cylinder})(\text{height of cylinder})\ =\ (\pi d^2)(\bar v_x t)$$ 
To count the number of particles our particle of interest encountered i.e. the number of collisions it had in this time, we just need to multiply by the density: 
$$\small \text{number of collisions}\ =\ \text{(volume swept out by our particle)} \times \text{(the number of particles per unit volume)}$$
Substituting in the result from the first equation above and terms from the ideal gas law:
$$\large \text{number of collisions}\ =\ (\pi d^2)(\bar v_x t)\ \times\ \left( \frac{n}{V} \right)$$
Dividing both sides by $t$ and substituting the expression for the average velocity of a gas particle, $ \bar v_x = \sqrt{8k_B T/ \pi m}$ results in our final equation:
$$\large \text{number of collisions per second}\ =\ (\pi d^2) \left( \sqrt{8k_B T/ \pi m}\right) \times\ \left( \frac{n}{V} \right)$$
Or written in terms of pressure, by using the ideal gas law:
$$\large \text{number of collisions per second}\ =\ (\pi d^2) \left( \sqrt{8k_B T/ \pi m}\right) \times\ \left( \frac{P}{RT} \right)$$

Source notes: 


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*This derivation was based off of the "Collision Frequency" article on Chemistry Libretext as well as course reference documents from a Stanford Aeronautics & Astronautics class "AA210 - Fundamentals of Compressible Flow" 

*The image above is from the aforementioned "Collision Frequency" article on Chemistry Libretext


You may ask, "Why is the base of the swept-out cylinder $\pi d^2$?" It is the effective collision area taking into account the size of the "target" particles. See the below image from the HyperPhysics article on "Mean Free Path" (C.R. Nave, Georgia State University): 

