You pipet your UNKNOWN into a reaction tube.... 4.00 mL

Question

Add a "boat" containing Manganese Dioxide, MnO2
Set up the gas collection apparatus shown on the right.
You sink the boat and allow the oxygen generated to collect in the collection flask. The water temperature is................. 29 oC
The Barometric Pressure is............... 764.9 mm Hg
Weight of the collection Flask with remaining water.... 239.39 g.
Weight of collection flask filled with water........... 295.00 g.
DensityH2O ................................. 0.996 g/cc

(c) Partial Pressure of Oxygen collected................................. ____________ mm Hg
(d) Volume of oxygen collected ...................................... ____________ mL
(e) Millimoles of oxygen gas generated.................................. ____________ mmol
(f) Molarity of Hydrogen Peroxide in UNKNOWN.......................... ____________ M

Answer 1

I don't know what's happening here except that this appears to be a standard gas (oxygen) evolution problem.
You can calculate pO2 from
Ptotal = pO2 + pH2O. pH2O is the vapor pressure H2O at the temperature of the experiment. You can find that in vapor pressure tables and I expect such a table is in your text/notes.