Energy of DNA Base Pairing, II. (See Exercise 21.24 . ) Calculate the electric potential energy

Energy of DNA Base Pairing, II. (See Exercise 21.24 . )...

Key Concepts

Electric Potential Energy

This concept refers to the energy stored in a system of charged particles due to their positions relative to one another. In molecular systems, such as those involving biological molecules, this energy quantifies the work done or required when charges are brought together from an infinite separation, and is calculated using principles like Coulomb's law.

Hydrogen Bonding

Hydrogen bonding is a key non-covalent interaction that occurs when a hydrogen atom covalently bonded to an electronegative atom (such as oxygen or nitrogen) interacts with another electronegative atom. This type of bonding is crucial for the stability and specificity of molecular structures, particularly in biological macromolecules where it helps to maintain structural integrity and facilitate molecular recognition.

Coulomb's Law

Coulomb's Law provides a fundamental description of the electrostatic force and potential energy between two point charges. It is instrumental in calculating the energy contributions from charged interactions in molecules, determining how the forces scale with the magnitude of the charges and the distance separating them, and helps underpin quantitative estimates of molecular bond energies.

Electrostatic Interactions in Molecular Systems

Electrostatic interactions are central to the understanding of forces that govern the behavior and assembly of molecules. These include interactions between permanent or induced charges, dipoles, and multipoles, which collectively influence molecular conformation, binding affinities, and the overall stability of complex structures such as those found in biological systems.

Transcript

00:01 So the potential energy of the 0 minus the 4 .09 and the oh bond of cytosine is this and can be represented by the following.

00:12 So you of these of the bonds between the 0 minus and the ho is equal to coolant constant times charge 1.

00:28 I mean the charge of oxygen times a charge of hydrogen.

00:34 So the first two bonds here over the radius or the distance between the necrii of the two molecules.

00:46 And now moving on to the second bond here.

00:48 Let me write this a little bit better so we can understand.

00:53 I'll just go ahead and just write this as you.

00:58 So the potential energy of the bonds, as i stated before.

01:03 And now it's also plus the final bond, which is, again, coolants constant.

01:08 Times the charge of oxygen and times charge of the second oxygen over the radius between the two molecules, which is just two, which is the radius between the two molecules.

01:23 So now, since these are all constants, and they're the same for the types of molecules, so we can just plug it right into the equation, and we can get the potential, which is equal to 9 .8 .99 times 10 to the power 9.

01:44 And since the coolant constant is the same in both, we can just factor it out.

01:50 So this is times negative 1 .6 times 10 to the negative 19.

01:59 Negative 19 here.

02:03 And this is squared plus...

02:10 Sorry, this is actually not squared, but it's times positive 1 .6 times.

02:18 Sent to the negative 19 and this is all over the radius of oh which is equal to 0 .18 times 10 to the negative 19 and this is plus negative 1 .6 times 10 to the negative 19 and since this time it's the charge of two oxygens we can just square this and now this is again over the radius between the the nucleus of the two oxygen is equal to 0 .3 times 10 to negative 9.

03:06 And let me draw the right to 9 a little bit better.

03:11 Here we go.

03:12 So now if we compute this into a calculator we can get the potential is equal to negative 51 .09 times 10 to the negative 20 joules.

03:33 So now to find the potential energy of the nitrogen, the nitrogen minus of the cytosine and the h -positives of the quor -9.

03:44 So let me just make that clear.

03:45 So this is here.

03:49 Let's make sure that we know which potentials we're talking about, which potentials of which bond.

03:54 So this is u -n -h.

03:59 Sorry, this is o -ho.

04:03 So now if you look at the potential of the next bond, which is the nitrogen, so which is unh, and now we can set this equal to, once again, it's the same formula as up here, except we switch out the different variables for these, for these new molecules.

04:35 So now once again if you just compute it, so it's 8 .99 times into the negative, negative that times into the positive 9.

04:49 And now it's once again negative 1 .6 times 10 to the negative 19 times 1 .6...

Please give Ace some feedback