Final answer:
To calculate the volume of oxygen produced by the decomposition of BaO₂, we use the ideal gas law equation and the given values of temperature and pressure. We first calculate the number of moles of oxygen produced by the decomposition using the molar mass and given mass of BaO₂. Then, we use the ideal gas law equation to find the volume of oxygen produced. The final volume can be calculated using the number of moles of oxygen and the given temperature and pressure.
Step-by-step explanation:
To solve this problem, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
- P is the pressure in atm
- V is the volume in liters
- n is the number of moles
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin
First, we need to calculate the number of moles of oxygen produced by the decomposition of BaO₂. To do this, we can use the molar mass of BaO₂ and the given mass:
129.7 g BaO₂ * (1 mol BaO₂ / molar mass of BaO₂) = x mol BaO₂
Next, we use the balanced chemical equation to determine the ratio of moles of oxygen to moles of BaO₂:
1 mol BaO₂ → 1 mol O₂
Therefore, the number of moles of O₂ produced is also x.
Now, we can use the ideal gas law equation to calculate the volume of O₂:
(127.4 kPa * 1 atm/101.3 kPa) * V = x mol O₂ * (0.0821 L·atm/mol·K) * (423.0 K)
Simplifying the equation, we can solve for V:
V = x * (0.0821 L·atm/mol·K) * (423.0 K) / (127.4 kPa * 1 atm/101.3 kPa)
Plugging in the value of x (the number of moles of O₂), we can calculate the volume of O₂ produced:
V = x * (0.0821 L·atm/mol·K) * (423.0 K) / (127.4 kPa * 1 atm/101.3 kPa)
This simplified equation will give us the final answer, which should be one of the multiple-choice options given.