calculate the heat of formation of ethane at 25C.The bond enthalpies for H-H,C-C and C-H are 104.2 kcal,80 kcal and 99.5 Kcal respectively. Heat of vaporization of carbon is 171.7 kcal

To calculate the heat of formation of ethane (C2H6) at 25°C, we can utilize the bond enthalpies you provided along with the heat of vaporization of carbon. The heat of formation represents the change in enthalpy when one mole of a compound is formed from its elements in their standard states. For ethane, the reaction can be represented as:

2 C(s) + 3 H2(g) → C2H6(g)

Step-by-Step Breakdown

1. Identify the Bonds in the Reaction

In ethane (C2H6), there are:

• 6 C-H bonds
• 1 C-C bond

2. Calculate the Energy Required to Break the Bonds

Next, we need to break the bonds in the reactants to form ethane. The energy required to break the bonds is given by the bond enthalpies:

• For H-H bonds: 3 bonds × 104.2 kcal/bond = 312.6 kcal
• For C-C bonds: 1 bond × 80 kcal/bond = 80 kcal
• For C-H bonds: 6 bonds × 99.5 kcal/bond = 597 kcal

Adding these energies gives us the total energy required to break bonds in the reactants:

Total energy to break bonds = 312.6 + 80 + 597 = 989.6 kcal

3. Calculate the Energy Released by Forming Bonds in Ethane

Now, we consider the bonds formed in the products. In forming ethane, we are forming:

• 6 C-H bonds
• 1 C-C bond

The energy released when these bonds are formed is:

• For C-H bonds: 6 bonds × 99.5 kcal/bond = 597 kcal
• For C-C bonds: 1 bond × 80 kcal/bond = 80 kcal

Total energy released when forming bonds = 597 + 80 = 677 kcal

4. Determine the Heat of Formation

The heat of formation can be calculated by subtracting the energy released from the energy required to break the bonds:

Heat of formation (ΔHf) = Energy required to break bonds - Energy released when forming bonds

ΔHf = 989.6 kcal - 677 kcal = 312.6 kcal

Final Result

Therefore, the heat of formation of ethane (C2H6) at 25°C is approximately 312.6 kcal/mol.

Notes on Heat of Vaporization

The heat of vaporization of carbon, 171.7 kcal, is not directly used in this calculation since we're focusing on the formation of ethane from its elemental forms. However, it could be relevant in other contexts, such as when considering the transformation of solid carbon to gaseous carbon in different reactions.

This calculation shows how bond enthalpies can be applied to determine the thermodynamic properties of compounds, illustrating the balance between energy input and output in chemical reactions.