Calculate the average C—C bond strength in cyclopropane (in kJ/mol). Its combustion and the experimental enthalpy of reaction are:
C3H6(g) + 4.5O2(g) → 3CO2(g) + 3H2O(g) ΔHºrxn = -1,957.7 kJ/mol
Since all reactants and products are in the gaseous state, bond energies may be used to estimate the enthalpy of reaction. Do not use the standard C—C bond strength, leave the C—C bond strength as an unknown and solve for its value. For review see chapter 9 p. 392 (Tro) or chapter 13 p. 608 (Zumdahl).
To calculate the average C—C bond strength in cyclopropane, we can use the concept of bond energies and the given enthalpy of reaction.
The combustion reaction given is:
C3H6(g) + 4.5O2(g) → 3CO2(g) + 3H2O(g) ΔHºrxn = -1,957.7 kJ/mol
In this reaction, we can break the C—C bonds in cyclopropane to form CO2 and H2O. We need to determine the number of C—C bonds broken in this reaction.
Cyclopropane has 3 carbon atoms. Each carbon atom is bonded to two other carbon atoms, so there are 3 C—C bonds in cyclopropane.
Let's assume the average C—C bond strength in cyclopropane as x kJ/mol.
When breaking a bond, energy is absorbed. Therefore, breaking 3 C—C bonds would require 3x kJ/mol.
From the enthalpy of reaction, we know that the overall reaction releases energy (-1,957.7 kJ/mol). So the breaking of C—C bonds (-3x kJ/mol) must be compensated by the energy released in other steps of the reaction, such as forming CO2 and H2O bonds.
Since each CO2 molecule has two C=O bonds and each H2O molecule has one O—H bond, we can use bond energies to estimate the energy released in forming these bonds.
By consulting a reliable source, such as the textbook mentioned (chapter 9 p. 392 in Tro or chapter 13 p. 608 in Zumdahl), we can find the bond energy values for C=O, O—H, and O=O bonds.
Let's say the average bond energies are:
C=O bond energy (double bond): y kJ/mol
O—H bond energy: z kJ/mol
O=O bond energy: w kJ/mol
In the balanced chemical equation:
3CO2 contains 6 C=O bonds.
3H2O contains 6 O—H bonds.
4.5O2 contains 9 O=O bonds.
So, the energy released in forming these bonds would be:
6(y kJ/mol) for C=O bonds
6(z kJ/mol) for O—H bonds
9(w kJ/mol) for O=O bonds
Therefore, the total energy released from forming these bonds is:
6(y kJ/mol) + 6(z kJ/mol) + 9(w kJ/mol)
To find the average C—C bond strength (x kJ/mol), we can set up an equation based on the conservation of energy:
Energy released from forming bonds - Energy required to break C—C bonds = Overall energy change of the reaction
[6(y kJ/mol) + 6(z kJ/mol) + 9(w kJ/mol)] - (3x kJ/mol) = -1,957.7 kJ/mol
Now, we can substitute the given values for the bond energy values (y, z, and w) and solve for the unknown average C—C bond strength (x) to get the final answer.