heat of formation of propene is -21kcal/mol. heat of sublimation of c(graphite)is 170 kcal.bond energies of c-h,h-h and c-c bonds are 99,104,80 respectively.calculate bond energy of c=c in propene.

To find the bond energy of the C=C bond in propene, we can use the concept of heat of formation and the bond energies of the other bonds present in the molecule. Propene (C3H6) has a double bond between two carbon atoms, and we need to account for the energy changes associated with forming this molecule from its elements in their standard states.

Understanding the Components

First, let's break down the information we have:

• Heat of formation of propene (C3H6) = -21 kcal/mol
• Heat of sublimation of carbon (graphite) = 170 kcal/mol
• Bond energies:
  • C-H bond = 99 kcal/mol
  • H-H bond = 104 kcal/mol
  • C-C bond = 80 kcal/mol

Formation Reaction of Propene

The formation of propene from its elements can be represented as follows:

3C (graphite) + 3H2 (g) → C3H6

Calculating the Energy Changes

To find the bond energy of the C=C bond, we can apply Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps. We can express the heat of formation in terms of bond energies:

The total energy required to break all the bonds in the reactants (3C and 3H2) minus the energy released when forming the bonds in the products (C3H6) gives us the heat of formation.

Breaking Bonds

When we break the bonds in the reactants:

• 3 C (graphite) → 3 × 170 kcal = 510 kcal (sublimation)
• 3 H2 → 3 × 104 kcal = 312 kcal (breaking H-H bonds)

Total energy to break bonds = 510 + 312 = 822 kcal

Forming Bonds in Propene

Now, let's consider the bonds formed in propene:

• 3 C-H bonds = 3 × 99 kcal = 297 kcal
• 1 C-C bond = 80 kcal
• 1 C=C bond = ? (this is what we need to find)

Thus, the total energy released when forming the bonds in propene is:

Total energy released = 297 + 80 + (bond energy of C=C)

Setting Up the Equation

According to Hess's law, we can set up the equation:

Heat of formation = Energy to break bonds - Energy released from forming bonds

-21 kcal = 822 kcal - (297 + 80 + bond energy of C=C)

Solving for the Bond Energy of C=C

Now, let's simplify and solve for the bond energy of the C=C bond:

-21 = 822 - (297 + 80 + bond energy of C=C)

-21 = 822 - 377 - bond energy of C=C

-21 = 445 - bond energy of C=C

Rearranging gives us:

bond energy of C=C = 445 + 21 = 466 kcal

Final Result

The bond energy of the C=C bond in propene is approximately 466 kcal/mol.

This calculation illustrates how we can use bond energies and heats of formation to deduce unknown bond energies in organic molecules. Understanding these relationships is crucial for predicting the stability and reactivity of different compounds.