All that remains
Disposing of the body is a key problem for your murderer, especially one of the serial persuasion. Some real-life killers have turned to chemicals, with varying degrees of success. John Haigh, the "acid bath murderer", used sulphuric acid which didn't always work completely - a gallstone, human body fat and a piece of an identifiable denture remained from his last victims, proving fatal for Haigh. In 2016 Stefano Brizzi was convicted of murdering London PC Gordon Semple and dissolving (incompletely) his body in an unspecified acid (http://www.theguardian.com/uk-news/2016/dec/12). In fiction you may have seen the attempt, in Breaking Bad, to destroy a body with hydrofluoric acid - a horrendous chemical which would never be available in a school lab in the quantities shown. Here, the "apprentice" ignored instructions to buy a specific type of plastic bath and used the house bathtub - with catastrophic consequences. The chemical dissolved the ceramic and metal tub so the acid, liquefied corpse and bath remains cascaded through the collapsing ceiling.
Chemicals will destroy tissue and bones, at least partially. The alkali sodium hydroxide, known as caustic soda in the UK and lye in the US, will readily dissolve flesh and make bones crumbly. Strong acids such as hydrochloric (spirits of salts in the UK and muriatic acid in the US) and sulphuric can also be used. Hydrochloric acid was used to damage, although not destroy completely, a corpse in Robert Galbraith's The Silkworm.
An article in July's Chemistry World discusses chemical disposal of bodies and there is a demonstration (with meat, not a body) at www.rsc.li/2sTTWjr. Complete destruction is rarely possible - identifiable material is likely to remain - but treatment with acid or alkali can reduce a body to a more disposable state and will hamper identification. Disposing of the resulting corrosive, malodorous sludge is another issue - not everyone has access to a convenient manhole leading to a sewer, which Haigh did at one of his premises.
There could be a problem getting hold of enough chemicals to destroy a body (it takes more than a couple of bottles) but it can be done. Sodium hydroxide is sold to the public as a drain cleaner and sulphuric acid used to be until restrictions were brought in following a series of acid attacks. The video above suggest similar issues in the US. Sodium hydroxide and hydrochloric acid, however, are not tightly controlled in the UK and are widely available.
Assuming that the villain can obtain sufficient chemical, and a large enough vessel to put it and the body in, there are two practical matters to consider. Firstly, dissolving something as large as a body will take time and may need repeated changes of acid/alkali. It took two days for Haigh's first victim's body to be converted to sludge capable of being poured down a manhole. Secondly, a dreadful smell would be generated as the chemicals react with the flesh and the body falls apart - remember why even a fresh cadaver emits odours at an autopsy. In the Brizzi case above neighbours complained about a vile odour but - amazingly - were initially fobbed off with the explanation that cooking smells were responsible. In the case of hydrochloric acid part of the smell would be hydrogen chloride - a choking, toxic gas which at best would cause serious lung, throat and eye irritation and at worst prove fatal in a poorly ventilated space.
Note to scriptwriters: if you are planning to incorporate body disposal by acid in a TV or film script, specify that there should be room in the vessel to accommodate the body without the acid overflowing. I recall an old episode of Taggart where this was planned but the drum in question was almost full of acid to start with. The perpetrators, when arrested, could well have been minus their feet.