# Question Video: Calculating the Molar Enthalpy Change of a Fuel Chemistry • 10th Grade

4.6 g of a fuel is found to produce −3,965 J of heat energy. If the 𝑀_𝑟 of the fuel is 46 g/mol, what is the molar enthalpy change?

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### Video Transcript

4.6 grams of a fuel is found to produce negative 3,965 joules of heat energy. If the 𝑀 𝑟 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, it’s 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.

Let’s 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.