Are the -COOH functional groups the only acid groups on the graphene surface? If so, then titration or TPD (Temperature Programmed Desorption) is your best bet for quantification.

FTIR is great for qualifying what types of functional groups your sample possesses, but for solid samples it is difficult. A gaseous sample can be quantified if you relate the pressure of gas with the intensity of the peak. This way you can get a calibration curve.

However, a solid sample has different variables. One fairly rough way you can do the quantification is by doing a similar calibration curve, where you prepare the graphene sample with some dilution, mixing with KBr or other appropriate solid. Basically have a known amount of graphene in each dilution mix. When you run each sample with FTIR, the more dilute sample (less graphene, more KBr) should give you lower intensity, while a more concentrated sample (more graphene, less KBr) should give you higher intensity. Since you know the degree of functionalisation you have done (i.e. percentage - though more accurately obtained using TGA-DSC analysis to get mass/mol of functionalisation). You do a very rough calibration, plotting intensity vs. mass/mol of functionalisation).

I shall reiterate, it is very difficult to quantify solids well since there are a lot of variables to consider, and also very labor intensive. FTIR is great for qualifying what you have on there. However, if it is just a COOH group, then other quantification methods would be more efficient and accurate.

Why calculate it? You could easily titrate it with base and get real numbers.

Are the -COOH functional groups the only acid groups on the graphene surface? If so, then titration or TPD (Temperature Programmed Desorption) is your best bet for quantification.

FTIR is great for qualifying what types of functional groups your sample possesses, but for solid samples it is difficult. A gaseous sample can be quantified if you relate the pressure of gas with the intensity of the peak. This way you can get a calibration curve.

However, a solid sample has different variables. One fairly rough way you can do the quantification is by doing a similar calibration curve, where you prepare the graphene sample with some dilution, mixing with KBr or other appropriate solid. Basically have a known amount of graphene in each dilution mix. When you run each sample with FTIR, the more dilute sample (less graphene, more KBr) should give you lower intensity, while a more concentrated sample (more graphene, less KBr) should give you higher intensity. Since you know the degree of functionalisation you have done (i.e. percentage - though more accurately obtained using TGA-DSC analysis to get mass/mol of functionalisation). You do a very rough calibration, plotting intensity vs. mass/mol of functionalisation).

I shall reiterate, it is very difficult to quantify solids well since there are a lot of variables to consider, and also very labor intensive. FTIR is great for qualifying what you have on there. However, if it is just a COOH group, then other quantification methods would be more efficient and accurate.

I think quantitative IR measurement will be the most accurate method for determination quantity of carboxyllic groups

especially for monolayers, you could give xps a try. it may complete the picture you obtain by ftir.

 u do solid state 13C CPMAS NMR with internal reference

you can use RMN spectral and complete with chromatographic GPC/ SDM (mass spectroscopic) coupled 

There are many different method. As suggested by other, you could try FTIR, XPS, and also other spectroscopic method. You could also follow the titration method.

I can give another one suggestion. Although, it is not perfect, you can some idea easily. In this case you have to be sure that you functional group reacted only with -COOH group of GO and your functional moity is UV active If so, then first take UV-vis of the functional group containing molecule before functionalization. Do it again after functionalization. The difference of absorbance will give you the rough estimation of no of -COOH group in GO.