The first law of therodynamics state that ae = q - w . is this also a statement of the principle of a conservative of energy ?

The first law of thermodynamics is concerned with the conservation of energy. The key concept in this law is that the change in internal energy is equal to the heat that flows into the system minus the work done. This is the same as saying that if we apply heat to the system, the system may store it as internal energy or use it to perform the work.

2h2o2--> 2h2o + o2

this reaction is of the spontaneous decomposition of hydrogen peroxide down into water and oxygen.

add 2 molecules of hydrogen peroxide and 2 molecules of water. since oxygen is naturally diatomic, the total number of atoms of each element is now the same on both sides of the equation so it is balanced.

this may not be entirely correct but let me know.