BET surface area is measured by specific surface area of the adsorbent. BET surface area is measured by using non-corrosive gases like N2, CO2, Ar etc. BET surface area depends on size and number of gas molecules adsorbed. Langmuir surface area depends on adsorption capacity of the adsorbent. 

But still  why langmuir is more in compare to BET? it's always been taught that BET is multilayer adsorption and Langmuir is monolayer. By sense I feel BET must be more because first monolayer generated than multilayer so I think BET must be more. But experience shows vice versa results always

BET isotherm is determined from the monolayer formation of gas molecules adsorbed on the surface of adsorbent, multilayer formation not taken into account for calculating the surface area. that is the volume of gas required to form monolayer is taken for calculating surface area. BET surface area is inversely proportional to the molar volume of adsorbate gas and amount of adsorbent used. Langmuir surface area is inversely proportional to the molecular mass of the adsorbate only.

Both the Langmuir equation and the Brunauer Emmett Teller (BET) equation model the adsorption behavior of a gas (on the surface of a solid) in terms of the monolayer capacity (and hence both can be used for surface area measurement based on that assumption).

However, the Langmuir equation is derived around the monolayer being the limit of adsorption (and thus cannot be exceeded - which we know to be untrue in real physisorption systems with a freely accessible surface), whereas the BET equation models partial and multilayer adsorption in terms of the monolayer (at least up to a point).  Therefore, when applying the Langmuir equation to data which is not strictly limited to a monolayer, e.g. "type II" or "IV" isotherm - and not a "type I" (here I am using the IUPAC nomenclature) it is not surprising that the Langmuir can over-estimate the surface area! This is often very evident by lack of linearity in the Langmuir plot if using the same calculation range as BET. Yet for many materials one can find reasonable agreement if the relative pressure (P/Po) points used for the Langmuir are taken at much lower P/Po than for the BET (i.e. corresponding to P/Po before the so-called "knee" of the isotherm).

One can perhaps appreciate the difference between the two approaches from the equations themselves. At first they do not appear to be so different since both are of the form

A = B + D, or more exactly

A = 1/kQm + (k'/Qm)(P/Po)

where A = (P/Po)/Q (Langmuir) or 1/Q((Po/P)-1) (BET)... i.e. simple expression of the data pairs Q (amount adsorbed) and P/Po.

When we turn our attention to the right side of the equation, the term B is effectively the same, being proportional to 1/Qm, Qm being the monolayer quantity, k being related to the heat of adsorption. However, the second term on the right, 'D' is where the difference lies. In the Langmuir equation k' = 1, but in the BET equation k' = (k-1)/k. In the BET equation k is usually given the symbol C.

Tough to follow I know, so to clarify... the Langmuir equation only considers the heat of adsorption in the B term not in both B and D, and that's basically the difference between monolayer (Langmuir) and monolayer+multilayer (BET) models.

Note: both Langmuir and BET can yield surface area values grossly in error when applied to microporous materials, even though the isotherm might be of type I which exhibits a very obvious plateau (limiting value of amount adsorbed). This is simply due to the fact that in physisorption of gases in a purely microporous solid, the limiting value is not due to the formation of a monolayer (all adsorbate molecules in kinetic (adsdes) equilibrium with adsorptive (in this sense adsorbate = immobilized molecules on the surface and adsorptive = mobile gas phase above the surface). Rather, the plateau is due to micropore volume filling... which has a limiting value when the micropores are filled!

Probably time to stop here rather than continue with a full length thesis. For further reading I would direct those interested to books by Rouquerol & Sing, or by Lowell et al.

Really a good answer sir, more justification I got through this. thank you so much

 Since it is already explained technically, let me explain it logically. This is just for understanding. Keep in mind that the surface area is measured as a function of the amount of adsorbate adsorbed (Q in Mr. Thomas's answer).

Say we have 100 marbles (equivalent to molecules in this case). The base area (nothing but the surface area of adsorbent) required to arrange them in monolayer (Langmuir) is larger than the base area required to arrange them in multilayers (BET theory). Remember that surface area of adsorbent is being calculated and therefore, after the first layer in BET theory, gas molecules are being adsorbed (or condensed) on other adsorbate molecules and on the same initial adsorbent surface. In essence, it is a simple mass balance: molecules in Langmuir monolayer are placed in BET multilayers, thereby decreasing the BET's first layer surface area.

which data to be reported langmuir or BET??

Bharat,

BET is to be preferred over Langmuir (and "DFT" is to be preferred over BET). But whenever reporting "surface area" always be sure to report it as "XXX surface area", where XXX = single point BET (in which case cite the P/Po at which it was calculated, or XXX = Multipoint BET (preferably with P./Po range given, plus C-constant (if C constant is negative, go back and recalculate with different P/Po range that gives +ve value), or XXX = Langmuir (with P/Po range), or XXX = DFT (NLDFT/QSDFT, together with specific "kernel" used).

I attached a useful document.

To more clearly answer this is I think a picture is in order:

Lets say you know that 5 molecules have adsorbed onto the surface of a material: (1) (2) (3) (4) (5). And you are trying to use that amount of adsorption to determine the surface area.

Langmuir theory limits this adsorption to a monolayer of surface coverage. I.e., adsorption can only be one layer deep, so the molecules must be spread over a wide area.

(1)(2)(3)(4)(5)

|----------------------|

^^^^ total Langmuir area

BET theory allows for the molecules to be adsorbed in multilayers. I.e., moleculers can be stacked on top of one another and therefore compacted into a smaller area.

(1)(2)

(3)(4)(5)

|-------------|

^^^^Total BET area

that is a good question Mihir Belani

Thanks Mazin Fadhil Khudhair