Gasoline, which can be represented by the formula octane, bulk density is 704 g / l. To estimate the variation in enthalpy when burning 28.5 liters
gasoline, based on the binding energies: 0 = 0 (117 kcal); C = 0 (173 kcal); 0 h (111 kcal); C-C (83 kcal); C-H (99 kcal).
To estimate the variation in enthalpy when burning 28.5 liters of gasoline, we need to determine the total number of moles of each element in the gasoline and calculate the change in enthalpy for each reaction involved in the combustion process.
Step 1: Determine the number of moles of each element in the gasoline.
To do this, we need to know the molecular formula of gasoline. Since gasoline is mostly composed of octane (C8H18), we can assume the molecular formula of gasoline is C8H18.
Number of moles of carbon (C): The molar mass of carbon (C) is 12.01 g/mol. Since there are 8 carbon atoms in one molecule of octane, the total number of moles of carbon in 28.5 liters of gasoline is:
moles of C = (mass of C / molar mass of C) = (8 * 12.01 g/mol * 28.5 l) / (1,000 g/l) = (273.1 g) / (1,000 g/mol) = 0.2731 mol
Number of moles of hydrogen (H): The molar mass of hydrogen (H) is 1.008 g/mol. Since there are 18 hydrogen atoms in one molecule of octane, the total number of moles of hydrogen in 28.5 liters of gasoline is:
moles of H = (mass of H / molar mass of H) = (18 * 1.008 g/mol * 28.5 l) / (1,000 g/l) = (515.16 g) / (1,000 g/mol) = 0.51516 mol
Note: These calculations assume that the gasoline is pure octane and does not account for impurities or other components.
Step 2: Calculate the change in enthalpy for each reaction involved in the combustion process.
The combustion of octane involves multiple reactions, including the formation of carbon dioxide (CO2) and water (H2O). Based on the given binding energies, we can calculate the change in enthalpy for each reaction using the difference in binding energies between the products and reactants.
Reaction 1: C8H18 + 12.5O2 → 8CO2 + 9H2O
Change in enthalpy (ΔH1) = (8 * 117 kcal) + (9 * 111 kcal) - ((12.5 * 2) * 0 kcal) - (0 kcal) = 936 kcal + 999 kcal - 0 kcal - 0 kcal = 1935 kcal
Reaction 2: C8H18 → 8C + 9H2
Change in enthalpy (ΔH2) = (8 * 173 kcal) + (9 * 99 kcal) - (0 kcal) - ((8 * 12.01) + (18 * 1.008)) kcal = 1384 kcal + 891 kcal - 0 kcal - 258.37 kcal = 2016.63 kcal
Step 3: Calculate the overall change in enthalpy for the combustion of 28.5 liters of gasoline.
The overall change in enthalpy (ΔH_total) is the sum of the changes in enthalpy for each reaction.
ΔH_total = ΔH1 + ΔH2 = 1935 kcal + 2016.63 kcal = 3951.63 kcal
So, the estimated variation in enthalpy when burning 28.5 liters of gasoline is approximately 3951.63 kcal.