If you want chemical analysis you can do XPS (Xray Photospectroscopy), XPS gives you chemical oxidation states and chemical composition. Standard SEM machines also have EDX (Energy dispersive X-ray spectroscopy) and gives you chemical composition.
There is a suite of characterisation techniques that you can use depending on what you want from the results. XPS and SEM-EDX deal with a small portion of the sample which might not be representative of the bulk of the sample, and therefore huge errors are very probable. I would suggest XRD and XRF as non destructive techniques which would provide valuable insight into the composition of the sample. Comparing the adsorbed sample with the original adsorbent will give you an idea of how much an entity is adsorbed. Other techniques are ICP-OES, ICP-MS and AAS which are destructive techniques and involve the dissolution of a known sample weight in preferably nitric acid (HCl is a dirty acid and is not preferred) and making it up to a known volume. Running the adsorbed sample as well as the pristine adsorbent will determine how much an entity has been adsorbed. For these methods, matrix matching, operational standards, internal standards, quality assurance standards and replicates are mandatory in order to get a good result.