Dillute solution chemical potential

[paweld]

Chemical potential of a substance i in an ideal solution is given by:
$$\mu_i = \mu_i^0 + RT \log x_i$$
(where $$\mu_i^0$$ is a chemical potential of pure substance i and
$$x_i$$ is mole fraction of i)
In nonideal solution $$x_i$$ has to be exchanged with activity coefficient $$a_i$$:
$$\mu_i = \mu_i^0 + RT \log a_i$$
We can write $$a_i = \gamma_i x_i$$. My question is why $$\gamma_i$$ always
tends to some constants (which not depend of temperature and preassure and is
typically equall 1) when $$x_i$$ tends to 1. Is it possible to prove it without usage of
statistical mechanics apparatus. It means that dillute solution of any substance is always almost ideal.

 

[Borek]

It means that dillute solution of any substance is always almost ideal.

Non ideality has its source in interactions between dissolved molecules. The less the concentration, the smaller the interactions, the closer the solution to ideal.

 

[paweld]

Thanks for answer.
I'm still looking for more formal proof.