given relative permitivity of water, how much energy (kj/mol) is required to break the hydrogen bond in water? (Er=80.0)
To calculate the energy required to break the hydrogen bond in water, we need to use the equation:
E = (1/2) * k * (q1 * q2) / r
Where:
E is the energy required (in joules)
k is the electrostatic constant (8.99 × 10^9 N m^2/C^2)
q1 and q2 are the charges involved (in coulombs)
r is the distance between the charges (in meters)
Since we are dealing with the hydrogen bond in water, the charges involved are the partial positive charge on the hydrogen atom (q1) and the partial negative charge on the oxygen atom (q2). These charges are caused by the difference in electronegativity between hydrogen and oxygen.
The distance (r) between these charges is approximately 0.0957 nm (or 0.0957 × 10^-9 meters).
Now, let's calculate the energy required by substituting the values into the equation:
E = (1/2) * (8.99 × 10^9 N m^2/C^2) * (q1 * q2) / r
The relative permittivity of water is given as Er = 80.0. The relationship between relative permittivity and vacuum permittivity (E0) is Er = E / E0. Rearranging this equation, we get E = Er * E0.
The vacuum permittivity (E0) is 8.854 × 10^-12 C^2 / N m^2.
Substituting the values, we have:
E = (80.0) * (8.854 × 10^-12 C^2 / N m^2) * (1/2) * (q1 * q2) / r
The charges for q1 and q2 cancel each other out in the water molecule, so the magnitude of each charge is the same. Therefore, we can rewrite the equation as:
E = (80.0) * (8.854 × 10^-12 C^2 / N m^2) * (1/2) * (q^2) / r
Since we are dealing with the energy per mole, we need to convert the energy from joules to kilojoules by dividing the result by 1000.
Finally, we need to recall the value of the charge of an electron (e), which is approximately 1.6 × 10^-19 Coulombs. Substituting this value in the equation:
E = (80.0) * (8.854 × 10^-12 C^2 / N m^2) * (1/2) * ((1.6 × 10^-19 C)^2) / (0.0957 × 10^-9 m)
Simplifying this equation will give us the energy required to break the hydrogen bond in water in kilojoules per mole (kJ/mol).