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As a general rule, consult a copy of Perrin (Purification of Laboratory Chemicals, 4th Ed; http://books.google.com/books?id=SYzm1tx2z3QC) for further details on how to purify your solvents. These days many laboratories will use a commercially available solvent purification system, others will distil solvents using more traditional techniques.
Tetrahydrofuran, dichloromethane, dimethylformamide, chloroform, acetonitrile, methanol, diethyl ether and toluene are all commonly used solvents, and in many cases they are required in anhydrous form. In some cases there are multiple ways to dry a given solvent. Here are some suggestions:
As a general precaution ethers can produce explosive peroxides, making distillation of these solvents hazardous. If one is available, use a blast guard (really thick piece of pyrex? attached to a stand), and do not use stills once they have passed their use-by date. The process of distillation also removes the stabilisers that are added to the ethers, consquently distilled ethers should not be stored for long periods of time. For directions on handling sodium etc. consult 'reagant specific hazards'.
Stills that use metals (THF) should be quenched by pouring any excess solvent into a large container fileld with isopropanol or tert-butanol. The reaction may become exothermic, so addition of the solvent to the alcohol must be done slowly. The remaining metal in the still can be quenched like normal.
You can reuse 4A molecular sieves from most applications, though you should discard those used in the perperation of DMF. Sieves can be regenerated by heating at 350° C for 24 hours or under vacuum. The seives should cool in a desicator or they will become saturated with moisture again.
This material is based upon work supported by the National Science Foundation under Grant Number 1246120