### Video Transcript

It takes approximately 2.757 times
10 to the negative 18 joules of energy to break all the bonds in a single molecule
of methane, CH4. What is the average molar bond
energy for CH bonds? Give your answer to the nearest
whole number.

In this question, we are given the
amount of energy required to break all the bonds in a molecule of methane. The units of this measurement are
joules per molecule. Our goal in this question is to
find the average molar bond energy for carbon-to-hydrogen single bonds.

Molar bond energy is also known
more simply as bond energy and is defined as the average amount of energy required
to break a particular bond in one mole of gaseous particles. Therefore, the units of our answer
will be kilojoules per one mole of carbon-to-hydrogen single bonds.

In one molecule of methane, there
are four carbon-to-hydrogen single bonds. In other words, we must convert the
energy needed to break four CH bonds to the energy needed to break one mole of CH
bonds. Our answer will be much larger. Therefore, chemists often use
kilojoules to express this amount.

Let’s begin by converting the
energy in joules per one methane molecule to joules per one mole of methane
molecules. We will need to multiply 2.757
times 10 to the negative 18 joules per CH4 molecule by 6.022 times 10 to the 23rd
CH4 molecules per one mole. The conversion factor we are using
here is Avogadro’s constant, which is the number of entities per mole of
substance. When multiplying, the units CH4
molecules cancel.

Now, let’s convert our answer to
joules per one mole of CH bonds. Because one molecule of methane
contains four CH bonds, then one mole of methane contains four moles of CH
bonds. When multiplying, the units moles
of CH4 cancel.

Finally, we’re ready to convert our
answer from joules per mole to kilojoules per mole. All we need to do is multiply our
answer by the conversion factor one kilojoule per 1000 joules. When multiplying, the units joules
cancel.

Finally, after rounding to the
nearest whole number, the average molar bond energy for CH bonds is 415 kilojoules
per mole.