Name: calculating reaction heat with hess's law
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 40 s
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Hess's Law

Hydrogen gas leaking from electric cars can react with the ozone layer in the atmosphere and produce water. For reactions like this, directly measuring the enthalpy change in a laboratory setting is difficult.

However, this reaction can be carried out in the lab in two steps to measure the enthalpy of each step.

In step 1, oxygen gas is converted to ozone gas, and &#916;H1 = +285.4 kJ. In step 2, hydrogen and oxygen gases combine to produce water vapor, and &#916;H2 = &#8722;483.6 kJ.

As enthalpy is a state function, the enthalpy change of a reaction depends only on the initial state of the system, hydrogen and ozone, and the final state, water, regardless of the intermediate steps.

Hess&#8217;s Law of constant heat summation states that if a chemical equation can be written in multiple steps, then the net enthalpy change for the equation can be written as a sum of enthalpies associated with each step.

Often, thermochemical reactions must be manipulated in order to make the reactions sum to a given reaction. The stoichiometric quantities and the direction of the reaction can be changed and a new enthalpy of each manipulated reaction can be determined.

In this example, the two steps with known changes in enthalpy cannot directly be added to find the unknown enthalpy of reaction. 

This is because the first equation has ozone as a product, while the reaction of interest has ozone as a reactant.

To account for this, the first equation, an endothermic reaction, must be converted into the reverse exothermic reaction where ozone decomposes into oxygen and releases 285.4 kJ. The new &#916;H has the same value but the opposite sign. 

Still, adding the reverse of step 1 and step 2 does not yield the 3 moles of water as in the conversion of ozone to water because the stoichiometric coefficients are different.

To account for this, the stoichiometric coefficients of each of the reactions and their associated enthalpy changes must be multiplied by factors that allow the coefficient to match the reaction of interest or cancel out. Because enthalpy change depends on the amounts of reactants and products, the ratio between the coefficients and the enthalpy change remains constant.

To obtain 3 moles of water, step 2 must be multiplied by 3 over 2 giving a new &#916;H2 of &#8722;725.4 kJ. 

To consume 1 mole of ozone, the reverse of step 1 must be multiplied by 1 over 2, giving a new &#916;H1 of &#8722;142.7 J.

Summing the modified thermochemical equation and canceling all compounds that appear in both reactants and products, yields the reaction of interest. When the new &#916;H1 and &#916;H2 are added, the enthalpy change for the reaction between hydrogen and ozone is &#8722;868.1 kJ.

hess's law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.

This type of calculation usually involves the use of Hess&#8217;s law, which states: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps. Hess&#8217;s law is valid because enthalpy is a state function: Enthalpy changes depend only on where a chemical process starts and ends, but not on the path it takes from start to finish. For example, the reaction of carbon with oxygen to form carbon dioxide occurs either directly or by a two-step process. The direct process is written as:

<img alt="Combustion reaction equation, C(s) + O2(g) &#8594; CO2(g), &#916;H = -394 kJ, thermochemistry concept." src="/files/core/CDNSource/lessons/800/800_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

In the two-step process, first carbon monoxide is formed:

<img alt="Chemical reaction equation: C(s) + 1/2 O2(g) &#8594; CO(g), &#916;H1=-111 kJ; thermodynamic diagram." src="/files/core/CDNSource/lessons/800/800_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq2" />

Then, carbon monoxide reacts further to form carbon dioxide:

<img alt="Exothermic reaction; CO(g) + 1/2 O&#8322;(g) &#8594; CO&#8322;(g) with &#916;H&#8322; = -283 kJ; chemical equation." src="/files/core/CDNSource/lessons/800/800_Equations-03.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq3" />

The equation describing the overall reaction is the sum of these two chemical changes:

<img alt="Chemical reaction equation for carbon monoxide and dioxide formation, combustion process diagram." src="/files/core/CDNSource/lessons/800/800_Equations-04.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq4" />

Because the CO produced in Step 1 is consumed in Step 2, the net change is:

<img alt="Carbon combustion reaction equation, carbon plus oxygen forms carbon dioxide." src="/files/core/CDNSource/lessons/800/800_Equations-05.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq5" />

According to Hess&#8217;s law, the enthalpy change of the reaction will equal the sum of the enthalpy changes of the steps.

<img alt="&#916;H calculation equation; thermodynamics concept; entropy change; formula analysis; chemistry." src="/files/core/CDNSource/lessons/800/800_Equations-06.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq6" />

&#916;H of the overall reaction is the same, regardless of whether it occurs in one step or two. This finding (overall &#916;H for the reaction = sum of &#916;H values for reaction &#8220;steps&#8221; in the overall reaction) is true in general for chemical and physical processes.

There are two important features of &#916;H that prove useful while solving problems using Hess&#8217;s law. This is based on the fact that &#916;H is directly proportional to the quantities of reactants or products, and changing the reaction (or the thermochemical equation) in well-defined ways changes the &#916;H accordingly.

For example, the enthalpy change for the reaction forming 1 mole of NO2 (g) is +33.2 kJ:

<img alt="Chemical reaction equation; nitrogen and oxygen form nitrogen dioxide; enthalpy change &#916;H=+33.2kJ." src="/files/core/CDNSource/lessons/800/800_Equations-07.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq7" />

When 2 moles of NO2 (twice as much) are formed, the &#916;H is twice as large:

<img alt="Nitrogen reaction equation, N2 + O2 &#8594; 2NO2, &#916;H=+66.4 kJ, exothermic process." src="/files/core/CDNSource/lessons/800/800_Equations-08.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq8" />

In general, if multiplying or dividing a chemical equation, the change in enthalpy should also be multiplied or divided by the same number.

&#916;H for a reaction in one direction is equal in magnitude and opposite in sign to &#916;H for the reaction in the reverse direction. For example:

<img alt="Chemical reaction, \( \text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g) \), exothermic, \( \Delta H = -184.6 \) kJ." src="/files/core/CDNSource/lessons/800/800_Equations-09.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq9" />

Then, for the reverse reaction, the enthalpy change is also reversed:

<img alt="Chemical reaction equation with enthalpy change, 2HCl(g) &#8594; H&#8322;(g) + Cl&#8322;(g), &#916;H=+184.6 kJ." src="/files/core/CDNSource/lessons/800/800_Equations-10.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq10" />

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy">Openstax, Chemistry 2e, Section 5.3: Enthalpy.</a>

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally ...

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KEY TERMS AND CONCEPTS

calculating reaction heat with hess's law

Calculating reaction heat with Hess's law lets chemists find enthalpy changes without measuring every reaction directly. Some reactions are hard or impossible to test in the lab. Even when a reaction can be measured, it is often easier to calculate the heat change from other known enthalpy values.

Hess's law says that if a process can be written as the sum of several stepwise processes, the enthalpy change for the total process equals the sum of the enthalpy changes for the steps. This works because enthalpy is a state function. That means the enthalpy change depends on the starting and ending points of a chemical process, not on the path taken between them.

A useful example is the formation of carbon dioxide from carbon and oxygen. The reaction can happen directly, or it can happen in two steps. In the two-step route, carbon monoxide forms first, and then carbon monoxide reacts again to make carbon dioxide. When the steps are added, the overall reaction is the same as the direct one, so the overall enthalpy change equals the sum of the step enthalpy changes.

Two features of enthalpy help when solving Hess's law problems. First, enthalpy change is directly proportional to the amount of reactants or products, so changing the size of a thermochemical equation changes the enthalpy change by the same factor. For example, if a reaction forms 1 mole of NO2 with a change of +33.2 kJ, forming 2 moles gives twice that enthalpy change.

Second, reversing a reaction reverses the sign of ΔH. The enthalpy change for the forward reaction and the reverse reaction are equal in size but opposite in sign. These rules make it possible to build an overall enthalpy change from known reaction steps.

Calculating Reaction Heat with Hess's Law

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Calculating reaction heat with Hess's law lets chemists find enthalpy changes without measuring every reaction directly. Some reactions are hard or impossible to test in the lab. Even when a reaction can be measured, it is often easier to calculate the heat change from other known enthalpy values. Hess's law says that if a process can be written as the sum of several stepwise processes, the enthalpy change for the total process equals the sum of the enthalpy changes for the steps. This works...

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Calculating Reaction Heat with Hess's Law

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