Hess's Law: Videos & Practice Problems

Hess's Law is a principle in thermochemistry that allows us to determine the enthalpy change (ΔH_rxn) of an overall reaction by summing the enthalpy changes of individual steps in a reaction pathway. The law states that the total enthalpy change for a reaction is the same, regardless of the number of steps or the route taken, as long as the initial and final conditions are the same. When manipulating thermochemical equations, any changes made to the coefficients or the direction of the reaction must be reflected in the enthalpy value. For instance, if a reaction is reversed, the sign of ΔH_rxn is also reversed. If coefficients are multiplied or divided by a factor, ΔH_rxn must be multiplied or divided by the same factor. By applying Hess's Law, we can cancel out intermediate species that appear on both sides of the combined reactions and derive the ΔH_rxn for the overall process, which is crucial for understanding energy changes in chemical reactions.

Hess's Law

Hess's law is a fundamental principle in thermochemistry that allows us to determine the overall enthalpy change of a reaction by rearranging thermochemical equations. A thermochemical equation is a chemical equation that includes the enthalpy of reaction, denoted as ΔH_rxn. The key concept is that any modification to the original equation will directly affect the enthalpy of reaction.

For example, consider the thermochemical equation:

2 Mg(s) + O₂(g) → 2 MgO(s) with ΔH_rxn = -1204 kJ.

There are three primary operations that can be performed on this equation, each influencing ΔH_rxn accordingly:

1. **Multiplying the Equation**: If the entire equation is multiplied by a factor, the coefficients of the reactants and products change, and the enthalpy change must also be multiplied by the same factor. For instance, if we multiply the equation by 2, it becomes:

4 Mg(s) + 2 O₂(g) → 4 MgO(s) with ΔH_rxn = -2408 kJ.

2. **Dividing the Equation**: Similarly, if the equation is divided by a number, the coefficients are halved, and the enthalpy change is divided by the same number. Dividing the original equation by 2 results in:

1 Mg(s) + 1/2 O₂(g) → 1 MgO(s) with ΔH_rxn = -602 kJ.

3. **Reversing the Equation**: When the reaction is reversed, the products become reactants and vice versa. This operation also reverses the sign of ΔH_rxn. For example, reversing the original equation gives:

2 MgO(s) → 2 Mg(s) + O₂(g) with ΔH_rxn = +1204 kJ.

In summary, Hess's law emphasizes that the enthalpy of reaction is directly proportional to the changes made to the thermochemical equation. Understanding these relationships is crucial for calculating the enthalpy changes in various chemical reactions.

Hess's Law Example 1

In the formation equation for boron trioxide, represented as:

4 B(s) + 3 O₂(g) → 2 B₂O₃(s)

the enthalpy change (ΔH) is given as -2547 kJ. To find the new enthalpy value after rearranging the equation, we need to analyze the changes made to the original reaction.

First, we observe that the reaction has been reversed, meaning that the products become reactants and vice versa. This reversal of the reaction also reverses the sign of ΔH, changing it from negative to positive. Therefore, the new ΔH will initially be +2547 kJ.

Next, we notice that the coefficients in the balanced equation have been altered. The original coefficients were 4, 3, and 2, but after rearranging, they become 8, 6, and 4 respectively. This indicates that the entire reaction has been multiplied by a factor of 2. When the coefficients of a reaction are multiplied, the ΔH must also be multiplied by the same factor.

Thus, we calculate the new ΔH as follows:

New ΔH = 2 × (+2547 kJ) = +5094 kJ.

In conclusion, the enthalpy change for the rearranged equation is +5094 kJ. This demonstrates that reversing a reaction changes the sign of ΔH, while multiplying the coefficients requires the same multiplication of the ΔH value.

Calculate the∆Hrxnfor the following thermochemical equation:

When given the following:

• A. -296.8 kJ
• B. -148.4 kJ
• C. 148.4 kJ
• D. 296.8 kJ

Answer: (B)

Hess's Law

In chemical thermodynamics, many reactions occur through a series of steps rather than a single process. Hess's law is a fundamental principle that states the total enthalpy change of a reaction is equal to the sum of the enthalpy changes of its individual steps. This means that regardless of the pathway taken, the overall enthalpy change remains constant.

To illustrate this, consider two partial reactions that combine to form an overall reaction. For example, if xenon difluoride (XeF₂) is a reactant, it will participate in the reaction, while fluorine (F₂), which may appear as both a product and a reactant, will cancel out in the process. This cancellation is crucial as it highlights the concept of reaction intermediates, which are species that appear in the steps of a reaction but do not appear in the final balanced equation.

When determining the overall enthalpy change (ΔH) for the reaction, one must sum the standard enthalpy values of the individual steps. For instance, if the standard enthalpy values of the partial reactions are +123 kJ and -262 kJ, the overall enthalpy change can be calculated as follows:

ΔH = 123 kJ - 262 kJ = -139 kJ

This negative value indicates that the reaction is exothermic, meaning it releases energy. Hess's law thus provides a systematic approach to calculate the enthalpy change for complex reactions by utilizing simpler, known reactions, reinforcing the idea that the pathway taken does not affect the total energy change of the system.

Hess's Law Example 2

To calculate the enthalpy of a reaction using Hess's Law, we start with the overall reaction, which in this case involves carbon monoxide (CO) and nitrogen monoxide (NO) producing carbon dioxide (CO₂) and half a mole of nitrogen gas (N₂). The first step is to identify the relevant partial reactions that correspond to the compounds in the overall equation.

For the first compound, carbon monoxide, we find it in the partial reactions. However, it appears as a product in one of the reactions, so we need to reverse that reaction to make it a reactant. Reversing the reaction also changes the sign of the standard enthalpy change (ΔH) associated with that reaction.

Next, we look for nitrogen monoxide. We find it in a partial reaction, but it has a coefficient of 2, while we need only 1 mole for our overall equation. To adjust this, we divide the reaction by 2 and reverse it, which again changes the sign of ΔH and divides it by 2. This gives us the correct stoichiometry for nitrogen monoxide as a reactant.

After adjusting for both CO and NO, we confirm that we have the correct amounts of carbon dioxide and nitrogen gas as products. At this point, all compounds in the overall reaction match those in the adjusted partial reactions.

In the next step, we combine the partial reactions, ensuring to cancel out any reaction intermediates—compounds that appear as both reactants and products. In this case, half a mole of O₂ cancels out, leaving us with the desired overall reaction.

Finally, we sum the standard enthalpy values of the adjusted partial reactions to find the overall enthalpy of the reaction. By adding the enthalpy values, we find that the total enthalpy of reaction is ΔH = -373.3 kJ. This value represents the heat released during the reaction, indicating that it is exothermic.

Calculate the∆H_rxnfor

Given the following set of reactions:

• A. -494.4 kJ
• B. -692.8 kJ
• C. 494.4 kJ
• D. -346.4 kJ

Answer: (B)

Calculate the∆H_rxn for

Given the following reactions:

• A. -177.85 kJ
• B. -355.73 kJ
• C. -258.36 kJ
• D. -487.27 kJ

Answer: (A)

Here’s what students ask on this topic:

What is Hess's Law?

Hess's Law, named after Russian chemist Germain Hess, is a principle in chemistry that states the total enthalpy change for a chemical reaction is the same, no matter how many steps the reaction is carried out in. Enthalpy, denoted by H, is a measure of the total energy of a thermodynamic system, usually expressed in kilojoules per mole (kJ/mol).

In simpler terms, Hess's Law implies that if you have a series of chemical reactions leading from a specific set of reactants to a particular set of products, the total enthalpy change will be the same whether the reaction takes place in one step or through multiple steps. This is because enthalpy is a state function, which means its value depends only on the initial and final states of the system, not on the path taken to get from one to the other.

This principle is particularly useful for calculating the enthalpy changes of reactions where the direct measurement is difficult. Instead, you can sum the enthalpy changes of individual steps that are known, which together give the overall reaction's enthalpy change.

How can Hess's law be used?

Hess's Law can be used to calculate the overall change in enthalpy (ΔH) for a chemical reaction when that reaction can be expressed as the sum of multiple steps for which enthalpy changes are known. This is particularly useful when the direct measurement of the enthalpy change of a reaction is not possible or practical.

To apply Hess's Law, you would follow these steps:

1. Write down the chemical equations for all the intermediate steps of the reaction.
2. Ensure that the sum of these steps gives the overall reaction you're interested in.
3. For each step, write down the known enthalpy change.
4. If necessary, reverse or multiply the intermediate reactions to match the overall reaction; remember to also reverse or multiply the enthalpy values accordingly (reversing a reaction changes the sign of ΔH, multiplying changes the magnitude).
5. Add up all the enthalpy changes from the intermediate steps to find the total enthalpy change for the overall reaction.

Hess's Law is based on the principle that the total enthalpy change for a chemical reaction is the same, no matter how it occurs, as enthalpy is a state function. This makes it a powerful tool in the field of thermochemistry for determining the energy changes involved in chemical reactions.

How do you use Hess's law for enthalpy change?

Hess's Law states that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, as long as the initial and final conditions are the same. To use Hess's Law to calculate enthalpy change, follow these steps:

1. Write down the chemical equations for the steps of the reaction for which you know the enthalpy changes. These steps should add up to the overall reaction.
2. Ensure that the equations are balanced in terms of both mass and charge.
3. Adjust the enthalpy changes to correspond with the coefficients used in the balanced equations. If you reverse an equation, change the sign of its enthalpy change. If you multiply the coefficients in an equation by a factor, multiply the enthalpy change by that factor as well.
4. Add up the enthalpy changes for the steps. This sum will give you the overall enthalpy change for the reaction.

By following these steps, you can determine the enthalpy change of a reaction even if it does not occur in a single step or if the enthalpy change for the overall reaction is not directly measurable.

How is Hess's law applied in calculating enthalpy?

Hess's Law is a principle that states the total enthalpy change for a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. This is because enthalpy is a state function, which means its value is determined only by the initial and final states of the system, not the path taken to get from one to the other.

To apply Hess's Law in calculating enthalpy, follow these steps:

1. Write down the chemical equations for the steps of the reaction for which you know the enthalpy changes. These steps could be hypothetical or actual intermediate reactions.
2. Ensure that the equations are correctly balanced.
3. Adjust the enthalpy values for these steps if the equations are multiplied or divided to match the molar quantities of the overall reaction.
4. Add or subtract these enthalpy changes to reflect the overall process, paying attention to the stoichiometry of the reactions.
5. The sum of these enthalpy changes will give you the total enthalpy change for the overall reaction.

This method allows you to calculate the enthalpy change for a reaction that may be difficult to measure directly by using known enthalpy changes from related reactions.