[iamvts]

I have attached the graph. Please help me understand it. Thank you in advance.

[Corribus]

What about it don't you understand?

[iamvts]

Thanks for willing to help. My question is why at the bond length the potential energy is negative?

[Borek]

What is the convention of sign for exo- and endothermic reactions?

[Corribus]

Potential energy is always expressed relative to a frame of reference. The choice is arbitrary. We could easily set potential minimum to zero and scale everything accordingly. There are reasons why that's not the preferred way to do it, but ultimately the energy differences (such as how much energy it takes to break the bond) wouldn't be any different.

[iamvts]

"We could easily set potential minimum to zero and scale everything accordingly."

Changing frame of reference is making me more confused. Can you provide me  some graph with potential energy set to zero. Or can you please elaborate on it.

[Orcio_87]

My question is why at the bond length the potential energy is negative?

In quantum chemistry positive potential energy means repulsion and negative energy means attraction.

[iamvts]

My question is why at the bond length the potential energy is negative?

In quantum chemistry positive potential energy means repulsion and negative energy means attraction.

If it is the case then shouldn't zero be the least energy point (as both repulsion and attraction would have been balanced at that point) and if not then shouldn't the energy be minimum where the Net force = 0 (as F=-dU/dr, where F is force, U is potential energy and r is interatomic distance).

[Orcio_87]

If it is the case then shouldn't zero be the least energy point (as both repulsion and attraction would have been balanced at that point)

Zero energy (repulsion balances attraction) means zero interaction between the atoms (no bonding).

and if not then shouldn't the energy be minimum where the Net force = 0 (as F=-dU/dr, where F is force, U is potential energy and r is interatomic distance).

Yes it is, as moving atoms closer or further each other (from 74 pm balance point) will always increase potential energy (increase repulsion in the first or decrease attraction in second case).

[Corribus]

Changing frame of reference is making me more confused. Can you provide me  some graph with potential energy set to zero. Or can you please elaborate on it.

It is exactly the same concept as temperature scale or elevation. When we say that the elevation of Mt Everest is 29,000 feet, that number doesn't mean anything by itself. What we mean is that the elevation is 29,000 feet above sea level. Sea level is given a value of zero. It is a frame of reference. Just so, the Dead Aea has an elevation of -1400 feet or thereabouts relative to the frame of reference (sea level).

You could use anything as a frame of reference, but the optimum choice may change from situation to situation. When you say how tall you are, your frame of reference is the ground directly under your feet, which you set to zero intuitively. My height is roughly six feet above the ground. I live in Chicago which has an elevation of 600 feet above seal level. I could easily say my height is 606 feet above sea level, using sea level as a frame of reference for my height instead of the ground under my feet. But it would get really confusing to compare the height of people who live in different places if they all used sea level as their frame of reference. So we choose sea level as a frame of reference for geography and the local ground as a frame of reference for our personal heights. Now, you could just as well use the Dead Sea as the frame of reference for geography. In that case, Mt Everest would have an elevation of 30,400 feet (29,000 ft above sea level, which itself is 1400 feet above the Dead Sea - 29,000 + 1400 = 30,400). Choosing a different frame of reference does not alter the differences in elevation between any two places, as long as all the elevations are expressed relative to the same frame of reference.

In your example, your frame of reference (your sea level) is two completely separated atoms, which we set to zero potential energy (O kJ/mol). The bottom of the well (the dead sea) is therefore some negative number (call it -X kJ/mol). The bond dissociation energy is the difference in energy between the energy of the two separated atoms and the bottom of the well, or X kJ/mol (0-(-X)=X). But we could call the bottom of the well zero kJ/mol, in which case the potential energy of the two separated atoms would be +X (just as the elevation of sea level would be +1400 feet if we called the dead sea 0 feet in elevation). Reassigning the bottom of the well does not change the bond dissociation energy, which is just the difference between the two points on the y-axis. It's still equal to X kJ/mol.

As you can imagine, there are some reasons why we usually assign the lone atoms to be zero rather than the bottom of the well. Maybe you can think of what those reasons might be.

Make sense?

[iamvts]

If it is the case then shouldn't zero be the least energy point (as both repulsion and attraction would have been balanced at that point)

Zero energy (repulsion balances attraction) means zero interaction between the atoms (no bonding).

and if not then shouldn't the energy be minimum where the Net force = 0 (as F=-dU/dr, where F is force, U is potential energy and r is interatomic distance).

Yes it is, as moving atoms closer or further each other (from 74 pm balance point) will always increase potential energy (increase repulsion in the first or decrease attraction in second case).

At 74 pm, the slope of the graph is zero, meaning there is no net force (Force of Attraction = Force of Repulsion) but still the bond is forming and is forming at exactly that length. Could you clarify me more on it.

[Orcio_87]

the energy be minimum where the Net force = 0 (as F=-dU/dr, where F is force, U is potential energy and r is interatomic distance).

dU/dr is the change of the energy in therm of moving atoms closer or further.

Bond between the atoms is forming because the attraction energy is stronger than repulsion energy.

At 74 pm net force = 0, so there is no force to change place of atoms.

[iamvts]

Changing frame of reference is making me more confused. Can you provide me  some graph with potential energy set to zero. Or can you please elaborate on it.

It is exactly the same concept as temperature scale or elevation. When we say that the elevation of Mt Everest is 29,000 feet, that number doesn't mean anything by itself. What we mean is that the elevation is 29,000 feet above sea level. Sea level is given a value of zero. It is a frame of reference. Just so, the Dead Aea has an elevation of -1400 feet or thereabouts relative to the frame of reference (sea level).

You could use anything as a frame of reference, but the optimum choice may change from situation to situation. When you say how tall you are, your frame of reference is the ground directly under your feet, which you set to zero intuitively. My height is roughly six feet above the ground. I live in Chicago which has an elevation of 600 feet above seal level. I could easily say my height is 606 feet above sea level, using sea level as a frame of reference for my height instead of the ground under my feet. But it would get really confusing to compare the height of people who live in different places if they all used sea level as their frame of reference. So we choose sea level as a frame of reference for geography and the local ground as a frame of reference for our personal heights. Now, you could just as well use the Dead Sea as the frame of reference for geography. In that case, Mt Everest would have an elevation of 30,400 feet (29,000 ft above sea level, which itself is 1400 feet above the Dead Sea - 29,000 + 1400 = 30,400). Choosing a different frame of reference does not alter the differences in elevation between any two places, as long as all the elevations are expressed relative to the same frame of reference.

In your example, your frame of reference (your sea level) is two completely separated atoms, which we set to zero potential energy (O kJ/mol). The bottom of the well (the dead sea) is therefore some negative number (call it -X kJ/mol). The bond dissociation energy is the difference in energy between the energy of the two separated atoms and the bottom of the well, or X kJ/mol (0-(-X)=X). But we could call the bottom of the well zero kJ/mol, in which case the potential energy of the two separated atoms would be +X (just as the elevation of sea level would be +1400 feet if we called the dead sea 0 feet in elevation). Reassigning the bottom of the well does not change the bond dissociation energy, which is just the difference between the two points on the y-axis. It's still equal to X kJ/mol.

As you can imagine, there are some reasons why we usually assign the lone atoms to be zero rather than the bottom of the well. Maybe you can think of what those reasons might be.

Make sense?

Thanks for such an elaborated answer. It has cleared some doubts. But still I have some such as what does it mean to have zero Potential energy at somewhere close to 25pm in the graph.

When we see the slope of the graph we find two points (74 pm and infinity) where slope is zero meaning that Net force is zero which make sense as Force of attraction = Force of Repulsion for 74 pm and no force at infinity. Similarly at infinity the Potential energy is taken to be zero (relatively) but at another point somewhere close to 25 pm we can see that the Potential energy is again zero. What does being zero at that point mean?

Thanks for your effort and time.

[iamvts]

the energy be minimum where the Net force = 0 (as F=-dU/dr, where F is force, U is potential energy and r is interatomic distance).

dU/dr is the change of the energy in therm of moving atoms closer or further.

Bond between the atoms is forming because the attraction energy is stronger than repulsion energy.

At 74 pm net force = 0, so there is no force to change place of atoms.

As you said the bond will form when the attraction energy is greater than repulsion energy. But as we know at 74 pm the net force is 0 so how is the bond forming?

[Orcio_87]

As you said the bond will form when the attraction energy is greater than repulsion energy. But as we know at 74 pm the net force is 0 so how is the bond forming?

You are very curious about the force, he ?

The bond is forming because from 0 to 74 pm force of repulsion will drive the atoms apart each other, from 74 and further - close to each other (force of attraction), and at 74 pm there is no force that will break the bond itself.