Sign Confusion , please fast
How will not eating help you with your sign confusion?
Seriously though - we are busy people, we will help you when we can. You should know that by now. Don't ask for a fast response, it won't help get you one. It's your responsibility to do your revision in good time.
Now, it should be clear to you that if you want C to be large, and the magnitude of E
L is much smaller than that of E
1, the numbers must be positive. The true thermodynamic enthalpy of adsorption ΔH
ads is negative; E here is a positive quantity equal in magnitude to the enthalpy of adsorption. (I always distrust the symbol E and the waffly "heat" in these contexts; they often have the "wrong" signs from a strict thermodynamic viewpoint.)
If you review the derivation of the BET isotherm, you will see that C = exp(-(ΔH
ads - ΔH
L)/RT).
The Langmuir isotherm is not a parabola. It is like y = x/(1+x), not y/x = b+ax.