We have introduced two dimensional cluster aggregation model to explain theoretically two phase coexistence phenomena such that adsorption is increased sharply discontinuous in particular pressure on the surface. And then, we have derived adsorption isotherms by applying fundamental statistical thermodynamics and Lagrange multipliers to the our model. By analyzing the our derived adsorption isotherms, we can explain well qualitatively that two phase coexistence on the surface adsorption would be a phenomena that occurs with the strong attractive forces between the adsorbed particles.