### Video Transcript

4.6 grams of a fuel is found to
produce negative 3,965 joules of heat energy. If the ๐ ๐ of the fuel is 46
grams per mole, what is the molar enthalpy change?

First of all, enthalpy is the
energy content of a system. During a chemical reaction, the
enthalpy of a system can change. We can therefore measure the change
in enthalpy that occurs during a reaction. It is possible to measure the
change in enthalpy for any amount of substance. However, itโs common for the
enthalpy change of a reaction to be given in units of kilojoules per mole of
substance. This quantity is known as the molar
enthalpy change.

In this question, we are told that
4.6 grams of a particular fuel produces negative 3,965 joules of energy. The negative sign tells us that the
reaction in which the fuel is burned is exothermic. This means energy is released to
the surroundings. Using the information given, we
need to determine the molar enthalpy change for this reaction. We know that the molar enthalpy
change is expressed per mole of substance, not per gram of substance. Therefore, we can begin by
converting 4.6 grams of fuel to an amount in moles.

Letโs make use of the following
equation. To calculate the number of moles of
fuel, we should divide the mass of the fuel, which is 4.6 grams, by the molar mass
of the fuel provided in the problem, which is 46 grams per mole. After dividing, the units of grams
cancel, and the result is 0.1 moles.

Now, we know that the molar
enthalpy change typically uses kilojoules to express the amount of energy. So, we need to convert the amount
of energy from joules to kilojoules. We can do this by taking the given
value of energy produced, which was negative 3,965 joules, and multiplying by the
conversion factor one kilojoule per 1,000 joules. The units of joules cancel, and the
result is negative 3.965 kilojoules.

Finally, to determine the molar
enthalpy change in kilojoules per mole, we must divide the energy in kilojoules by
the number of moles. We should divide negative 3.965
kilojoules by 0.1 moles. We get the answer negative 39.65
kilojoules per mole.

In conclusion, the molar enthalpy
change of the fuel in this problem is negative 39.65 kilojoules per mole.