Professor Pi's writeup was very good (I have never seen the stuff on reaction rate yields before and I'm midway through my 2nd year in a Masters in Chemistry) but I would like to add more on the percentage yield of batch products.

Usually, the most useful yield calculation for batch reactions is the percentage yield. The reasons for this should be obvious, assume one person is running a crappy reaction, say an aldol reaction on the kilogram scale of an aldehyde with a hindered ketone and looking for the aldehyde-ketone product. The aldehyde will self-condense and there will be minimal aldehyde-ketone formation, maybe 3g. Another chemist, who has thought about what they are doing, runs an aldol reaction on a milligram scale which can only go in one direction and isolates 0.3g. On the pure yields, the crappy aldol reaction is more succesful. However, the percentage yield cancels out the inequalities between the amounts of starting materials.

It can be defined crudely as:

 

Amount of product obtainedx 100

Theoretical maximum product

 

While it is usually worked out in moles (chemical measure of number of molecules) the logic remains the same. If the reaction you are doing should double the size of your starting material, starting with a kilo should give 2 kilos of product. Obtaining 1.8 kilos would be a 90% yield etc.

It should be noted that yields of >100% are well known and yields of up to 250% have been seen in undergraduate laboratories. This is because the sample is contaminated, either with solvent or reaction byproducts. It is impossible to get >100%yield of a pure compound.

Typically, unless a very simple reaction is being used batch processes will be utilised. In organic synthesis this is very important as the final yield is found by multiplying all the steps together eg. a 5 step synthesis, each step having a %yield of 80% (incidentally,a reasonably good yield for an organic reaction)

Total yield = 0.8*0.8*0.8*0.8*0.8*0.8= 0.327% or for every 100g you put in the first reaction, 33 come out as your finished product

 

Incidentally, a low %yield does not necessarily mean a process will be expensive. The Haber process (the major source of ammonia for fertilisers) fuses nitrogen and hydrogen to make ammonia. It is ridiculously inefficient, most plants operating at around 10-20% efficiency, mostly due to nitrogen's and hydrogen's unreactivity. However, the reactants can be easily recycled and so the low efficiency is a moot point.

 

(before anyone downvotes this because I said hydrogen was unreactive, it is. the stability of water drives it's aerobic combustion, it is still bloody difficult to get it to react. for example, alkenes (carbon-carbon double bonds) add to bromine in water. To get the same reaction with hydrogen, several atmospheres pressure and a palladium catalyst are required. For a metaphorical version, its the difference between asking politely to open the door and smashing it open with a sledgehammer)