Question Video: Using Enthalpies of Formation to Calculate the Enthalpy of Combustion | Nagwa Question Video: Using Enthalpies of Formation to Calculate the Enthalpy of Combustion | Nagwa

# Question Video: Using Enthalpies of Formation to Calculate the Enthalpy of Combustion Chemistry • First Year of Secondary School

When calculating the enthalpy of combustion of ethanol using Hess’s law, what value is used for Z?

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### Video Transcript

When calculating the enthalpy of combustion of ethanol using Hess’s law, what value is used for Z? (A) Positive three multiplied by the enthalpy of formation of water. (B) Positive three multiplied by the enthalpy of combustion of hydrogen. (C) Positive one multiplied by the enthalpy of formation of water. (D) Negative three multiplied by the enthalpy of combustion of hydrogen. (E) Negative three multiplied by the enthalpy of formation of water.

In this question, we are given an enthalpy cycle diagram consisting of several chemical reactions. Let’s start by numbering the reactions that use black arrows counterclockwise. We’ll talk about the reaction labeled Z a little bit later in the video. First of all, reaction number one represents the combustion of one mole of ethanol. Let’s clear some space to write out this chemical equation.

The symbol ΔHc that appears over the reaction arrow represents the enthalpy of combustion. If one mole of ethanol burns completely in oxygen in its standard state and under standard conditions, then the enthalpy change is the standard enthalpy of combustion. Although the enthalpy of combustion of ethanol could be measured in an experiment, it can also be calculated from a series of reactions in the enthalpy cycle.

For now, in our table, let’s represent the enthalpy change of reaction one as ΔH1. Below the combustion reaction in the diagram, the elements carbon, hydrogen, and oxygen are shown in their standard states. Three different arrows connect these elements to the reactants and products of the combustion reaction. Let’s write a chemical equation to represent reaction number two.

In reaction two, ethanol and oxygen gas are formed from their constituent elements in their standard states. The enthalpy change for this type of reaction is called the standard enthalpy of formation. It’s important to note that the standard enthalpy of formation pertains to the formation of one mole of substance. In reaction two, one mole of ethanol forms, but three moles of oxygen gas form. Therefore, when writing the enthalpy change for reaction two, we multiply the enthalpy of formation of ethanol by one and the enthalpy of formation of oxygen gas by three. For now, let’s record this enthalpy change as ΔH2.

Now, we’re ready to write an equation for reaction number three. In this reaction, two moles of carbon dioxide gas and three moles of water vapor are produced. Therefore, when writing the enthalpy change for reaction three, we need to multiply the enthalpy of formation of carbon dioxide by two and the enthalpy of formation of water by three. For simplicity’s sake, for now, let’s record this enthalpy change as ΔH3. Now that we have determined the enthalpy changes for all reactions in the enthalpy cycle, we can apply Hess’s law.

Hess’s law states that the enthalpy change of a reaction is independent of the path taken. According to Hess’s law, the sum of the enthalpy changes of reactions along an alternative path is equal to the enthalpy change of the direct path. As long as our series of reactions start and end with the same substances under the same conditions, then we can apply this rule.

In the enthalpy cycle, the direct path is reaction number one. The alternative path is to move around the enthalpy cycle from ethanol and oxygen in a counterclockwise direction. Whenever we change the direction of a reaction in an enthalpy cycle, we need to change the sign of the enthalpy change. Because we have reversed the direction of reaction number two, we need to write the enthalpy change as negative ΔH2. And because we have not changed the direction of reaction number three, we do not need to change the sign.

Using Hess’s law, we can write the following equation. The enthalpy change of the direct row, or ΔH1, equals the sum of the enthalpy changes along the alternative row. These are negative ΔH2 plus ΔH3. Now we can substitute the expressions we wrote for ΔH2 and ΔH3 into our equation. Now that we have this equation, let’s determine which part of the equation represents the reaction labeled Z.

Reaction Z represents the formation of three moles of water from its constituent elements, and its enthalpy change is just a part of the enthalpy change for reaction three. When using Hess’s law to calculate the enthalpy change for the combustion of ethanol, Z is represented as three multiplied by the enthalpy of formation of gaseous water.

Now we can bring the answer choices back on screen to determine which of them is the correct answer. When calculating the enthalpy of combustion of ethanol using Hess’s law, the value used for Z is positive three multiplied by the enthalpy of formation of water or answer choice (A).

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