The balanced equation shows that 2 moles of C2H5OH react with 9 moles of O2 to produce 6 moles of CO2. This means that for every 9 moles of O2, 6 moles of CO2 are produced.
To find out how many liters of CO2 will be produced from 10 liters of O2, we need to use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Assuming that the pressure, temperature, and volume are constant, we can rearrange the ideal gas law to solve for n:
n = PV/RT
Since we know the volume (10 L) and number of moles of O2 (nO2 = 10 L/22.4 L/mol = 0.4464 mol), we can use the mole ratio from the balanced equation to find the number of moles of CO2 produced:
nCO2 = (6/9) * nO2 = 0.2976 mol
Finally, we can use the ideal gas law again to find the volume of CO2 produced:
VCO2 = nCO2 * RT/P
Assuming the same temperature and pressure conditions, we can use the same values for R and P:
VCO2 = (0.2976 mol) * (0.0821 L·atm/mol·K) * (298 K) / (1 atm)
VCO2 ≈ 7.3 L
Therefore, approximately 7.3 liters of CO2 will be produced from 10 liters of O2.