Bond enthalpies | Thermodynamics | AP Chemistry | Khan Academy

Bond enthalpy is the change in enthalpy, or delta H, for breaking a particular bond in one mole of a gaseous substance. If we think about the diatomic chlorine molecule, so Cl₂, down here is a little picture of Cl₂. Each of the green spheres is a chlorine atom, and they're bonded together by a single covalent bond. It would take energy to break this bond in diatomic chlorine gas and turn diatomic chlorine gas (Cl₂) into two individual chlorine atoms.

So we're going from Cl₂ in the gaseous state to 2Cl. Bond enthalpy can be symbolized by the letters Be. The bond enthalpy of the chlorine-chlorine single bond is equal to positive 242 kilojoules per mole. What this means is if we have one mole of chlorine-chlorine bonds, it takes positive 242 kilojoules of energy to break those bonds. Bond enthalpies are always positive because it takes energy to break bonds.

Another name for bond enthalpy is bond dissociation energy, so you might see this symbolized as BDE or just simply the letter D. Bond enthalpies are often found in the appendices of chemistry textbooks. For example, we just saw the chlorine-chlorine single bond; the bond enthalpy is 242 kilojoules per mole. Whereas, to break a carbon-carbon single bond takes 348 kilojoules of energy per mole of carbon-carbon single bonds. A carbon-carbon double bond has a bond enthalpy of 614 kilojoules per mole.

Since a carbon-carbon double bond is stronger than a carbon-carbon single bond, it takes more energy to break the double bond. That's why the carbon-carbon double bond has a higher bond enthalpy. So, the higher the value for the bond enthalpy, the stronger the bond. Notice that these are average bond enthalpies.

The average bond enthalpy for a carbon-carbon single bond is around 348 kilojoules per mole. You might see slightly different values for this depending on which textbook you're looking in, but they're all pretty close to the same value. The reason why these are average bond enthalpies is that if we look at two different molecules, down here this is ethane on the left and propane on the right. If we break a carbon-carbon single bond in ethane, the bond enthalpy is slightly different from breaking a carbon-carbon single bond in propane.

That's why we use average bond enthalpies. We've already seen that it takes energy to break bonds. So, to break the chlorine-chlorine single bond in diatomic chlorine gas takes positive 242 kilojoules per mole. If it takes energy to break bonds, that means energy is given off when bonds form. So when two individual chlorine gas atoms come together to form a chlorine-chlorine bond, energy is given off.

The magnitude of energy is still 242 kilojoules per mole; however, now we have this negative sign to indicate the energy is given off when bonds form. Bond enthalpies can be used to estimate enthalpies of reaction. To find the change in the enthalpy for a chemical reaction, you take the sum of the bond enthalpies of the bonds broken, and from that you subtract the sum of the bond enthalpies of the bonds formed.

The minus sign is in there because energy is given off when bonds form. A good way to remember this equation is to remember that B comes before F in the alphabet. So, B before F, therefore it's bonds broken minus bonds formed. Let's use bond enthalpies to estimate the enthalpy of reaction for the following reaction here of methane with chlorine gas to form chloromethane and hydrogen chloride gas.

It's often helpful to draw dot structures for these kinds of problems. If we look at the methane dot structure, we would need to break one carbon-hydrogen single bond in order to get to our products. We would also need to break a chlorine-chlorine single bond. Next, one of the chlorines goes over to the CH₃ to form CH₃Cl.

So, therefore, we are forming one carbon-chlorine single bond, and the other Cl goes with the hydrogen. So we also need to form one hydrogen-chlorine single bond. The next step is to sum the bond enthalpies of the bonds broken. So let's think about this. For our reactants, we're breaking bonds.

We have one mole of methane reacting with one mole of chlorine, and since we're breaking one carbon-hydrogen single bond for every one molecule of methane, since we have one mole of methane molecules, we're breaking one mole of carbon-hydrogen single bonds. Therefore, we can write down here one mole of carbon-hydrogen bonds, and the bond enthalpy for a carbon-hydrogen single bond is 413 kilojoules per mole.

Since there's one chlorine-chlorine single bond for every Cl₂ molecule, and we have one mole of chlorine molecules, we're breaking one mole of chlorine-chlorine single bonds. So to this, we're going to add one mole of chlorine-chlorine single bonds, and the bond enthalpy for a chlorine-chlorine single bond is 242 kilojoules per mole.

Moles cancel out, and we get that the sum of the bond enthalpies of the bonds broken is equal to 655 kilojoules. Next, we need to sum the bond enthalpies of the bonds formed. So, we're forming one mole of chloromethane and one mole of hydrogen chloride gas. Since we're forming one carbon-chlorine single bond for every molecule of chloromethane, since we're forming one mole of chloromethane, we're forming one mole of carbon-chlorine single bonds.

So, let's write down here we're forming one mole of carbon-chlorine bonds, and the bond enthalpy for a carbon-chlorine single bond is equal to 328 kilojoules per mole. Since we form one hydrogen-chlorine single bond for every molecule of hydrogen chloride, since we're making one mole of hydrogen chloride, we're forming one mole of hydrogen-chlorine single bonds.

So to this, we add one mole of hydrogen-chlorine single bonds, and the bond enthalpy for a hydrogen-chlorine single bond is 431 kilojoules per mole. Moles cancel, and we get that the sum of the bond enthalpies of the bonds formed is equal to 759 kilojoules. Next, we're ready to find the change in enthalpy for our chemical reaction.

The sum of the enthalpy of the bonds broken we found that was equal to 655 kilojoules, and from that, we subtract the sum of the bond enthalpies of the bonds formed, which we found was 759 kilojoules. So, 655 minus 759 gives negative 104 kilojoules. Sometimes we see kilojoules, or kilojoules per mole, or kilojoules per mole of reaction.

Kilojoules per mole of reaction just means how the balanced equation is written. Let's see how we can look at the units to get kilojoules per mole of reaction when we do the calculations. If we go back to breaking the carbon-hydrogen bond over here, we've seen there's one mole of carbon-hydrogen bonds that we need to break for how the equation is written.

Therefore, we can write a conversion factor of one mole of carbon-hydrogen bonds per one mole of reaction as it's written, and then we multiply that by the bond enthalpy of 413 kilojoules per mole for a carbon-hydrogen bond. This cancels out moles of carbon-hydrogen bonds, and this gives us kilojoules per mole of reaction as our units. So it's more time-consuming to write it this way, but we could do that for all of our different bond enthalpies to get kilojoules per mole of reaction for the units for our final answer.

When everything is under standard conditions, we need to add a superscript of not, so this would be the standard change in enthalpy for a chemical reaction. For the value we just calculated, negative 104 kilojoules per mole of reaction, this is under standard condition. So this is actually the standard change in enthalpy for this chemical reaction.

Remember that bond enthalpies are only averages, and so this value that we calculated is only an estimate for the standard change in enthalpy for this chemical reaction. A more accurate way of finding the standard change in enthalpy for a chemical reaction is to use standard enthalpies of formation. When you use standard enthalpies of formation to find the standard change in enthalpy for this particular chemical reaction, you get negative 99.8 kilojoules per mole of reaction.

So negative 104 is pretty close to negative 99.8.