Given the following thermochemical data at 298 K and 1 barΔH°...
Thermochemical Data
Given thermochemical data at 298 K and 1 bar:
- Hvap (CH3OH) = 38.0 kJ mol-1
- fH: H(g) = 218 kJ mol-1
- O(g) = 249 kJ mol-1
- C(g) = 715 kJ mol-1
- Bond dissociation energy:
- (CH) = 415 kJ mol-1
- (CO) = 356 kJ mol-1
- (OH) = 463 kJ mol-1
Finding the fH of Liquid Methyl Alcohol
To find the fH of liquid methyl alcohol (CH3OH), we need to consider the enthalpy changes involved in the formation of liquid methyl alcohol from its constituent elements.
The formation of liquid methyl alcohol can be represented by the following equation:
CH3OH(l) = C(g) + 2H(g) + O(g)
The enthalpy change of this reaction can be calculated by summing the enthalpies of formation of the products and subtracting the enthalpies of formation of the reactants.
The enthalpy change for the formation of liquid methyl alcohol can be expressed as:
ΔHf(CH3OH) = fH(CH3OH) - [fH(C(g)) + 2fH(H(g)) + fH(O(g))]
Substituting the given values:
ΔHf(CH3OH) = fH(CH3OH) - [715 kJ mol-1 + 2(218 kJ mol-1) + 249 kJ mol-1]
Simplifying:
ΔHf(CH3OH) = fH(CH3OH) - 1400 kJ mol-1
We are given that the enthalpy of vaporization (Hvap) of CH3OH is 38.0 kJ mol-1. The enthalpy of vaporization can be related to the enthalpy of formation as follows:
Hvap(CH3OH) = ΔHf(CH3OH) - ΔHf(g)
Where ΔHf(g) is the enthalpy of formation of gaseous CH3OH. Since we are given the enthalpy of formation of H(g), O(g), and C(g), we can calculate ΔHf(g) as follows:
ΔHf(g) = fH(CH3OH) - [2fH(H(g)) + fH(O(g)) + fH(C(g))]
Substituting the given values:
38.0 kJ mol-1 = ΔHf(CH3OH) - [2(218 kJ mol-1) + 249 kJ mol-1 + 715 kJ mol-1]
Simplifying:
38.0 kJ mol-1 = ΔHf(CH3OH) - 1400 kJ mol-1
Rearranging the equation:
ΔHf(CH3OH) = 1438 kJ mol-1
Therefore, the