Final answer:
The volume of oxygen produced by the decomposition of BaO₂ can be calculated by first determining the moles of BaO₂ decomposed, then using stoichiometry to find the moles of O₂, and finally applying the ideal gas law with the given temperature and pressure.
Step-by-step explanation:
Calculating the Volume of Oxygen Produced by Decomposition
To determine the volume of oxygen gas produced by the decomposition of barium peroxide (BaO₂), we first need to find the number of moles of BaO₂ that decomposed. The molar mass of BaO₂ is given as 169.33 g/mol. Using the mass given in the problem, we can calculate the moles of BaO₂:
moles of BaO₂ = mass / molar mass = 134.0 g / 169.33 g/mol
Next, the balanced equation for the decomposition of BaO₂ to BaO and O₂ is:
2 BaO₂(s) → 2 BaO(s) + O₂(g)
From the stoichiometry of the equation, we see that 2 moles of BaO₂ produce 1 mole of O₂, thus:
moles of O₂ = moles of BaO₂ / 2
Now, we use the ideal gas law to calculate the volume of O₂ produced:
PV = nRT
Where:
- P is the pressure in atmospheres (atm)
- V is the volume in liters (L)
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L·atm/K·mol)
- T is the absolute temperature in kelvins (K)
V = (nRT) / P
After calculating the moles of O₂, insert the values into the ideal gas law equation along with R = 0.0821 L·atm/K·mol, T = 439.0 K, and P = 1.00 atm to find the volume of oxygen.