A25.0-g sample of barium reacted completely with water. what is the equation for the reaction? how many milliliters of dry h2 evolved from 21c and 748mmhg?

Ba+H↓2O⇒BaO+H↓2O
You'll have to divide 25.0g by the formula mass of barium and then compare the mole ratio in your formula.
PV=nRT    Rearranged is:  V=nRT/P
V=volume=? n=moles of H2  P=pressure 748mmhg
R=universal gas constant (62.3638L×mmHg/K×mol)  
T =temperature(21+273.15=)294.15K
L=1000ml
25.0g divided by 137.3g (formula mass of barium) = moles for barium
1 mole of barium = 1 mole of H2
H2 moles times 62.3638 L*mmHg/K*mol (these cancel out to L) times 294.15K over 748mmHg
Divide your answer which should be in L to ml by multiplying it by 1000.  
(25/137.3)(62.3638×294.15)/748=answer×1000
I got 4.47x10∧3 but depending on how your teacher calls each number significant change your sig figs to the lowest number.  Should look pretty similar.  Good luck!

Mgo2 is the oxidation state of manganese oxide

Your question is not clear but if you can explain yourself i would be glad to .  just trying to : ))