Question

Balance the given chemical reaction by short-cut method:

C6H6+O2=CO2+H2O.

Answer 1

Dunno what you mean by short cut method, but I'll try to answer it the easiest I can.
Firstly, on left side we see C6H6, so there is 6C, but in right side, only one C, in CO2, so we put co efficient 6 for CO2. Similarly, we put 3 co efficient for H2O due to 6 H in left side.
Now, total oxygen on left side is 12 from 6CO2 and 3 from 3H20, which is a total of 15,so we give co efficient 15/2, on O2 in left side.

More precisely:

Element Reactants Product
C - - - - - 6 - - - - - 1
O - - - - - 2 - - - - - 3
H - - - - - 6 - - - - - 2

Based on this tabular column, if you orderly start from balancing C, H and finally O, as stated above, the reaction will be balanced as:
C6H6 + 7.5O2 - - > 6CO2 + 3H2O

If we multiply all co efficient by 2, it will remove decimal co efficients, but uses two moles of benzene.