Why is it forbidden to drink beer on pesach. First of all beer isn't in the form of a solid food so it can't be "leavening". Second the only time we describe the prohibition of food with an amount is Yom Kippur, reguarding wether it's one or two cheek fulls. If beer or other fermented grains are forbidden then what is the amount to be חייב כרת.
Actually the answer to your question is implied in your question. Your are consuming fermented grains which is the definition of chametz. Just because you then dissolve the fermented grain in a liquid does not make it permissible. The "cheekful" reference is for liquid food, as is the reference to Rvi'is.
A good summary WHICH FOODS ARE CHAMETZ? is:
Beer and whisky
If barley is soaked in water under proper conditions, it ferments into beer, and since the barley sat in water for more than 18 minutes, beer is chametz (Shulchan Aruch 442:5). Beer contains approximately 5% alcohol and people who want a drink with a higher alcohol content do the following. The grain is allowed to ferment until it reaches about 12-13% and then the alcohol is separated from (some of) the water using a process called “distillation” to produce whisky which contains 30-95% alcohol. The consensus of the Poskim is that whisky produced from one of the 5 grains is considered chametz even though it went through the process of distillation (see Shulchan Aruch Y.D. 92:8 & 123:24, and Mishnah Berurah 442:4). Even if the whisky is made from corn or another kitniyot grain, there are a number of other reasons why it may be chametz:
The watery liquid that remains after distillation is called “backset” and is often used in creating another batch of whisky. Thus, even if the grain used in creating the whisky is kitniyot, the water may be from a chametz whisky.
Before the yeast ferments the grain, the grain’s starch must be broken-down into individual glucose molecules, and this is traditionally done with barley malt (discussed above). Since the chametz barley malt plays such a crucial role in the creation of the whisky (and also dramatically changes the taste of the grain before it is fermented), the barley malt is considered a davar hama’amid and one may not own such whisky on Pesach (see Shulchan Aruch 442:5 and Mishnah Berurah 442:25).
As such, all types of whisky should be treated as chametz unless they are specifically certified as kosher for Pesach.
Most beer produced today is produced from barley. The barley is soaked in water to malt. Barley is one of the 5 major grains which become Chometz by exposure to water. Regarding the amount of Chometz that is forbidden, Chometz is forbidden B'Mashehu (even a minute amount). However there are grain-free beers that are Kosher for Pesach.