Calculate the C-H bond energy in methane at 25 decree celceus from data . Heat of formation of methane is -17.9 kcal ,heat of vaporization of carbon is171.1cal and heat of formation of hydrogen atom is 52.1kcal/mol.

To calculate the C-H bond energy in methane (CH₄) at 25 degrees Celsius, we can use the given thermodynamic data. The bond energy can be derived from the heat of formation of methane and the heats of formation of its constituent elements. Let's break this down step by step.

Understanding the Components

First, we need to clarify the data provided:

• Heat of formation of methane (ΔH_f CH₄) = -17.9 kcal/mol
• Heat of vaporization of carbon (ΔH_vap C) = 171.1 cal/g
• Heat of formation of hydrogen atom (ΔH_f H) = 52.1 kcal/mol

The Reaction for Formation of Methane

The formation of methane from its elements can be represented by the following reaction:

C(s) + 2 H₂(g) → CH₄(g)

Using Hess's Law

According to Hess's Law, 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 of methane in terms of the bond energies:

ΔH_f CH₄ = ΔH_f C + 2ΔH_f H - 4 * (C-H bond energy)

Calculating the Required Values

We need to convert the heat of vaporization of carbon from cal to kcal for consistency:

ΔH_vap C = 171.1 cal/g = 0.1711 kcal/g

Now, we can substitute the values into the equation:

ΔH_f CH₄ = 0 + 2(-52.1 kcal/mol) - 4 * (C-H bond energy)

Setting Up the Equation

Substituting the known values:

-17.9 kcal/mol = 0 - 104.2 kcal/mol - 4 * (C-H bond energy)

Solving for C-H Bond Energy

Rearranging the equation gives:

4 * (C-H bond energy) = -104.2 kcal/mol + 17.9 kcal/mol

4 * (C-H bond energy) = -86.3 kcal/mol

C-H bond energy = -86.3 kcal/mol / 4

C-H bond energy = -21.575 kcal/mol

Final Result

Thus, the C-H bond energy in methane at 25 degrees Celsius is approximately 21.6 kcal/mol. This value indicates the energy required to break one mole of C-H bonds in methane, reflecting the stability of the molecule due to these strong bonds.

In summary, by applying Hess's Law and using the provided thermodynamic data, we can effectively calculate the bond energy of C-H in methane, illustrating the relationship between bond energies and heat of formation.