Imagine I synthesize and characterize a molecule for the first time, but for which I also do not know if it has any application. Is this, under EPC, patentable?
There is indeed a requirement in the EPC that the invention be susceptible of industrial application, see Article 57:
An invention shall be considered as susceptible of industrial application if it can be made or used in any kind of industry, including agriculture.
Note that this provision is quite broad (made or used in any kind of industry, including agriculture). However, in some cases, it might be necessary to elaborate why this requirement is met, see e.g. the Guidelines, F-II, 4.9:
The description should indicate explicitly the way in which the invention is capable of exploitation in industry, if this is not obvious from the description or from the nature of the invention. The expression "capable of exploitation in industry" means the same as "susceptible of industrial application", and indeed identical expressions are used in the French and German texts of the EPC. In view of the broad meaning given to the latter expression by Art. 57 (see G‑III, 1), it is to be expected that, in most cases, the way in which the invention can be exploited in industry will be self-evident, so that no more explicit description on this point will be required; but there may be a few instances, e.g. in relation to methods of testing, where the manner of industrial exploitation is not apparent and must therefore be explicitly indicated.
Also, in relation to certain biotechnological inventions, i.e. sequences and partial sequences of genes, the industrial application is not self-evident. The industrial application of such sequences must be disclosed in the patent application (see G‑III, 4).
So, yes, in your hypothetical situation, it would be prudent to add a few sentences in your description to clearly state how the compound is industrially applicable. However, as @George White♦ said, you might just say that the compound can be used as a herbicide!
In real life, however, usually someone will have bothered to synthesize a new compound with at least some ideas about its intended use...
EDIT: In hindsight, I fear I might have answered the wrong question. Too late to retract now I suppose.
An approach I have seen people use is to analyze the chemical properties and guess at what it might be used for. Is it aryl? Improved perfume synthesis! Does it have nitrogen next to benzene? A new way to synthesis drugs.
Brainstorming in this way can often lead you to both casting a wide net and find applications. All you need is one use case and then they explode by being inter-related.
The new process of synthesizing the chemical is patentable. You still need the useful angle, but I am sure you had that in mind when you started? (Why would you just randomly invent something that costs $100k of dollars without a purpose?)
Polymer patents also are very much based on "I set out to make a chemical with variable properties X Y and Z on range of blah blah blah by varying A B C from here to there, and this is how I make it." Suddenly you have locked out a large application area, an industrial process, and set ridiculously broad ranges that are unreasonable and block anyone else from entering. (This would theoretically apply to your process patent as well.)
As far as the scientific scrutiny part goes, the art of BS'ing and telling a good story goes a lot further than the data. The data part comes 2 years later after the initial filing. Plenty of time to, uh, tweak the results.
Now I am no lawyer, but I can tell you this is how the big companies do it.
Not in the US due the "useful" requirement. In the rest of the world they have a requirement for "industrial applicability" so I imagine the answer in the EPC is also no. I heard a patent attorney teaching a class say "pour it on the grass, it might be a herbicide or a plant growth enhancer. Or maybe it peels paint."