How to solve this chemistry question?

Question

Q1. Decomposition of H₂O₂ is shown below

2H₂O₂ (l) ----------> 2H₂O (l) + O₂ (g)

At the end of the reaction, 0.75 L of gas was collected over water at 25 °C and the total pressure measured was 766 mm Hg. How many moles of H2O2 was consumed by the reaction?

Given: vapor pressure of water at 25 °C = 24 mm Hg

1 atm = 760. mm Hg R = 0.0821 atm ∙ L ∙ mole^-1 ∙ K^-1  H₂O₂ = 34.0158 g/mole

Answer 1

2H₂O₂ (l) ----------> 2H₂O (l) + O₂ (g) ... balanced equation

When collecting gas over water, one must subtract the vapor pressure of water from the total pressure to obtain the pressure of the gas alone.

P of gas = 766 mm - 24 mm = 742 mm x 1 atm/760 mm = 0.976 atm

V = volume = 0.75 L

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

T = temperature in Kelvin = 25 + 273 = 298 K

Ideal gas law : PV = nRT

Solve for n (moles):

n = PV/RT = (0.976 atm)(0.75 L) / (0.0821 Latm/Kmol)(298K)

n = 0.0299 moles of O₂ gas