How to Measure Enthalpy Change Using Hess’s Law

By Peter J. Mikulecky, Chris Hren

For the chemist, Hesss law is a valuable tool for dissecting heat flow in complicated, multistep reactions. For the confused or disgruntled chemistry student, Hess’s law is a breath of fresh air. In essence, the law confirms that heat behaves the way we’d like it to behave: predictably.

Imagine that the product of one reaction serves as the reactant for another reaction. Now imagine that the product of the second reaction serves as the reactant for a third reaction. What you have is a set of coupled reactions, connected in series like the cars of a train:

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Therefore,

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You can think of these three reactions adding up to one big reaction

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What is the overall enthalpy change associated with this reaction

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Here’s the good news:

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Enthalpy changes are additive. But the good news gets even better. Imagine that you’re trying to figure out the total enthalpy change for the following multistep reaction:

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Here’s a wrinkle: For technical reasons, you can’t measure this enthalpy change

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directly but must calculate it from tabulated values for

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and

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No problem, right? You simply look up the tabulated values and add them. But here’s another wrinkle: when you look up the tabulated values, you find the following:

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Gasp! You need

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but you’re provided only

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Relax. The enthalpy change for a reaction has the same magnitude and opposite sign as the reverse reaction. So if

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then

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It really is that simple:

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Thanks be to Hess.

Try an example. Calculate the reaction enthalpy for the following reaction:

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Use the following data:

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Reaction enthalpies are given for two reactions. Your task is to manipulate and add Reactions 1 and 2 so the sum is equivalent to the target reaction. First, reverse Reactions 1 and 2 to obtain Reactions

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and

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and add the two reactions. Identical species that appear on opposite sides of the equations cancel out (as occurs with species P4 and Cl2):

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Finally, divide the sum by 4 to yield the target reaction equation:

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So, the reaction enthalpy for the reaction is 83.8 kJ.