How to find the electronegativity of carbon?

The electronegativity of carbon can be determined using several methods, including Pauling's equation and experimental data.

Using Pauling's Equation and Bond Energies

Pauling's equation relates the electronegativity difference between two atoms to the excess bond energy of the bond they form. This excess bond energy is calculated from the actual bond energy and the geometric mean of the homonuclear bond energies.

Steps:

1. Gather Data: You need the following bond energies:

   • E_(C-H): Bond energy of a carbon-hydrogen bond.
   • E_(C-C): Bond energy of a carbon-carbon bond.
   • E_(H-H): Bond energy of a hydrogen-hydrogen bond.
   • X_H: Electronegativity of hydrogen (approximately 2.20 on the Pauling scale - differing sources may list slightly different values such as 2.1).

2. Apply Pauling's Equation (modified): A common form of the equation is:

   |X_C - X_H| = 0.208 √[E_(C-H) - √(E_(C-C) E_(H-H))]

   • Where:
     • X_C is the electronegativity of carbon.
     • X_H is the electronegativity of hydrogen.
     • E represents the bond energies in kcal/mol. The constant 0.208 arises when using kcal/mol. If using kJ/mol, a different constant is needed (0.102).

3. Solve for X_C:

   • Plug in the known values into the equation.
   • Calculate the electronegativity difference.
   • Solve for X_C, keeping in mind that electronegativity values are generally positive. Therefore, choose the solution that yields a positive value.

Example:

Using the data provided in the reference (note: the provided data in the reference has E_H-H, represented as E, while it should be E_H-H for a valid calculation. Assuming E is E_H-H):
E_(H-H) = 104.2 kcal/mol, E_(C-C) = 83.1 kcal/mol, E_(C-H) = 98.8 kcal/mol, X_H = 2.1

|X_C - 2.1| = 0.208 √[98.8 - √(83.1 104.2)]
|X_C - 2.1| = 0.208 √[98.8 - √8658.42]
|X_C - 2.1| = 0.208 √[98.8 - 93.05]
|X_C - 2.1| = 0.208 √5.75
|X_C - 2.1| = 0.208 2.4
|X_C - 2.1| = 0.5

X_C - 2.1 = ± 0.5

Therefore:

• X_C = 2.1 + 0.5 = 2.6
• X_C = 2.1 - 0.5 = 1.6

Since carbon is known to be more electronegative than hydrogen, a value of 2.6 is more plausible in this calculated example. Note: The exact value depends on the accuracy of the provided bond energies. The generally accepted value for the electronegativity of carbon is 2.55.

Accepted Electronegativity Values

The accepted electronegativity of carbon is approximately 2.55 on the Pauling scale. You can often find this value in chemistry textbooks and online databases. This is the standard value most commonly used.

In summary, you can calculate carbon's electronegativity using Pauling's equation with bond energies, or you can use the generally accepted value of 2.55.