Step-by-step explanation:
To solve this problem, we need to use the ideal gas law to calculate the volume of gas produced, and then convert it to liters. The ideal gas law is given by:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to calculate the number of moles of oxygen produced in the decomposition of 408.70 moles of KCIO3. From the balanced chemical equation, we see that 2 moles of KCIO3 produces 3 moles of O2. Therefore, 408.70 moles of KCIO3 will produce:
(408.70 mol KCIO3) x (3 mol O2 / 2 mol KCIO3) = 613.05 mol O2
Next, we need to convert the temperature from Celsius to Kelvin:
T = 66.00°C + 273.15 = 339.15 K
Now we can use the ideal gas law to calculate the volume of gas produced:
PV = nRT
V = nRT/P
V = (613.05 mol) x (0.08206 L·atm/K·mol) x (339.15 K) / (2.80 kPa x 101.325 kPa/atm)
V = 16,508.89 L
Finally, we need to round the answer to two decimal places, as requested:
V ≈ 16,508.89 L ≈ 16,508.90 L (rounded to two decimal places)
Therefore, approximately 16,508.90 liters of O2 will be produced at 66.00°C and 2.80 kPa pressure in the decomposition of 408.70 moles KCIO3.