The heat of formation of gaseous octane (C8H18(g)) is -49.79 kcal/mole. (a) Calculate the energy required to form one mole of gaseous octane, (b) Estimate the heat of formation of gaseous octane, and (c) compare your estimation with the actual enthalpy of formation of the gaseous octane and explain your observation.
To calculate the energy required to form one mole of gaseous octane (C8H18(g)), we can use the concept of the heat of formation (ΔHf). The heat of formation is the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states.
(a) To calculate the energy required to form one mole of gaseous octane, we need to analyze the chemical equation for the formation of octane:
8C (graphite) + 9H2 (g) → C8H18 (g)
The heat of formation is given as -49.79 kcal/mole, which means that 49.79 kcal of energy is released when one mole of octane is formed.
Since there are 8 moles of carbon (C) and 9 moles of hydrogen (H2) required to form one mole of octane, we can calculate the energy required using the following equation:
Energy required = 8 * ΔHf(C) + 9 * ΔHf(H2)
Given that the standard heat of formation of carbon (ΔHf(C)) is 0 kcal/mole and the standard heat of formation of hydrogen gas (ΔHf(H2)) is 0 kcal/mole, the energy required would be:
Energy required = 8 * 0 kcal/mole + 9 * 0 kcal/mole
= 0 kcal/mole
Therefore, the energy required to form one mole of gaseous octane is 0 kcal/mole.
(b) To estimate the heat of formation of gaseous octane, we can calculate it based on the energy required to form one mole of octane. Since the energy required is 0 kcal/mole, we can estimate the heat of formation to be 0 kcal/mole.
(c) Comparing our estimation with the actual enthalpy of formation, we observe that our estimated heat of formation of gaseous octane (0 kcal/mole) is different from the given value of -49.79 kcal/mole.
This discrepancy could arise due to several reasons. One possibility is that the given value of -49.79 kcal/mole may not be accurate or may be based on a different reference state. Another possibility is that the estimation assumes the formation of octane under standard conditions, but in reality, the reaction conditions may differ. Additionally, the estimation assumes ideal behavior, whereas in practice, there could be deviations from ideal conditions.
In conclusion, the observed difference between our estimation and the actual enthalpy of formation highlights the complexity of thermodynamic calculations and the influence of various factors on the real-world values.