Hess's Law: Videos & Practice Problems

Hess's law states that the overall enthalpy change (ΔH) of a reaction is the sum of the enthalpy changes of its individual steps. Rearranging thermochemical equations affects ΔH proportionally; multiplying or dividing coefficients alters ΔH similarly, while reversing the reaction changes the sign of ΔH. This principle allows for the calculation of enthalpy in complex reactions by combining partial reactions and canceling intermediates. Understanding these concepts is crucial for mastering thermodynamics and reaction mechanisms in chemistry.

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:

1. **Multiplying the Equation**: If we multiply the entire equation by a factor, say 2, the coefficients change accordingly:

4 Mg(s) + 2 O₂(g) → 4 MgO(s)

In this case, the enthalpy change also doubles:

ΔH_rxn = 2 × (-1204 kJ) = -2408 kJ.

2. **Dividing the Equation**: Conversely, if we divide the equation by 2, the coefficients adjust to:

1 Mg(s) + 1/2 O₂(g) → 1 MgO(s)

Here, the enthalpy change is halved:

ΔH_rxn = -1204 kJ / 2 = -602 kJ.

3. **Reversing the Reaction**: If we reverse the reaction, the products become reactants and vice versa:

2 MgO(s) → 2 Mg(s) + O₂(g)

When the reaction is reversed, the sign of ΔH_rxn also changes:

ΔH_rxn = +1204 kJ.

In summary, Hess's law emphasizes that the enthalpy of reaction is directly proportional to the coefficients in the thermochemical equation. Any changes made to the equation—whether multiplying, dividing, or reversing—must be reflected in the corresponding enthalpy value, allowing for the calculation of overall enthalpy changes in complex reactions.

Hess's Law Example 1

In the context of thermodynamics, the enthalpy change (ΔH) of a reaction is crucial for understanding energy transformations. For the formation of boron trioxide (B₂O₃), the original reaction can be represented as:

4 B (s) + 3 O₂ (g) → 2 B₂O₃ (s) with an enthalpy change of ΔH = -2547 kJ.

When the reaction is reversed, the products become reactants and vice versa. This reversal changes the sign of the enthalpy change, resulting in a positive value. Additionally, if the coefficients in the balanced equation are altered, the enthalpy change must also be adjusted accordingly. In this case, the coefficients are doubled: the 2 moles of B₂O₃ become 4, the 4 moles of B become 8, and the 3 moles of O₂ become 6.

Thus, the new reaction can be expressed as:

2 B₂O₃ (s) → 8 B (s) + 6 O₂ (g).

To find the new enthalpy change, we first reverse the sign of the original ΔH, making it positive 2547 kJ. Then, since the entire reaction is multiplied by 2, we multiply the enthalpy change by 2:

ΔH = 2 × 2547 kJ = 5094 kJ.

Therefore, the new enthalpy value for the rearranged reaction is ΔH = +5094 kJ. This illustrates the principle that reversing a reaction changes the sign of ΔH, while multiplying the coefficients requires the same multiplication of the enthalpy value.

Calculate the ∆H_rxn for the following thermochemical equation:
S (s) + $\frac{3}{2}$ O₂ (g) → SO₃ (s) ΔH_rxn = ?
When given the following:
2 S (s) + 3 O₂ (g) → 2 SO₃ (s) ΔH_rxn = −296.8 kJ

• 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 the individual steps, regardless of the pathway taken. This means that if you know the enthalpy changes for each step, you can calculate the overall enthalpy change for the complete reaction.

Consider a scenario involving two partial reactions. When combining these reactions, it is essential to identify and cancel out any reaction intermediates—substances that appear in both the reactants and products. For instance, if xenon difluoride (XeF₂) is a reactant in one step and a product in another, it will cancel out, as it cannot exist on both sides of the equation simultaneously. This cancellation process helps simplify the overall reaction.

To calculate the overall enthalpy change (ΔH) for the reaction, you sum the standard enthalpy values of the individual steps. For example, if one step has an enthalpy of +123 kJ and another has -262 kJ, the overall ΔH can be determined by adding these values: ΔH = 123 kJ - 262 kJ, resulting in ΔH = -139 kJ. This negative value indicates that the reaction is exothermic, meaning it releases energy.

In summary, Hess's law provides a systematic approach to determine the enthalpy change of complex reactions by utilizing the enthalpy changes of simpler, individual steps, allowing chemists to predict the energy changes associated with chemical processes.

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.

Begin by locating the first compound, carbon monoxide, in the set of partial reactions. Since CO is a product in one of the partial reactions, we need to reverse that reaction to make it a reactant. Reversing the reaction also requires us to change the sign of the standard enthalpy change (ΔH) associated with that reaction.

Next, we look for nitrogen monoxide. The partial reaction for NO has a coefficient of 2, but we need it to be 1 to match the overall equation. Therefore, 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 NO as a reactant.

Now, we check the products. We need 1 mole of CO₂ and half a mole of N₂, both of which are present in the partial reactions. At this point, all compounds in the overall equation match the corresponding 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 appears as both a reactant and a product, so we can eliminate it from the equation.

Finally, we sum the standard enthalpy values of the partial reactions to find the overall enthalpy of the reaction. For this example, adding the enthalpy values gives us:

ΔH = -283 kJ (for CO) + (-90.3 kJ / 2) (for NO) = -373.3 kJ.

This result represents the total enthalpy change for the overall reaction, demonstrating how Hess's Law allows us to calculate the enthalpy of a reaction by using known enthalpy changes from related reactions.

Calculate the ∆H_rxn for
S (s) + $\frac32$ O₂ (g) → SO₃ (g) ΔH_rxn = ?
Given the following set of reactions:
$\frac12$ S (s) + $\frac12$ O₂ (g) → $\frac12$ SO₂ (g) ΔH° = −296.8 kJ
2 SO₃ (g) → 2 SO₂ (g) + O₂ (g) ΔH° = 198.4 kJ

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

Answer: (B)

Calculate the ∆H_rxn for
ClF (g) + F₂ (g) → ClF₃ (g) ΔH_rxn = ?
Given the following reactions:
Cl₂O (g) + F₂O (g) → 2 ClF (g) + O₂ (g) ΔH° = −167.4 kJ
4 ClF₃ (g) + 4 O₂ (g) → 2 Cl₂O (g) + 6 F₂O (g) ΔH° = 682.8 kJ
2 F₂ (g) + O₂ (g) → 2 F₂O (g) ΔH_rxn = −181.7 kJ

• 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 and how is it used in thermochemistry?

Hess's Law states that the total enthalpy change (ΔH) of a reaction is the sum of the enthalpy changes of its individual steps. This principle is crucial in thermochemistry because it allows us to determine the overall enthalpy change for complex reactions by breaking them down into simpler steps. By rearranging thermochemical equations—multiplying, dividing, or reversing them—we can calculate the ΔH for each step and sum them to find the overall ΔH. This method is particularly useful when a reaction cannot be carried out in a single step.

How does multiplying or dividing a thermochemical equation affect the enthalpy change (ΔH)?

When you multiply or divide a thermochemical equation by a coefficient, the enthalpy change (ΔH) is affected proportionally. For example, if you multiply the entire equation by 2, you must also multiply the ΔH by 2. Conversely, if you divide the equation by 2, you must divide the ΔH by 2. This is because the enthalpy change is directly proportional to the quantities of reactants and products involved in the reaction.

What happens to the enthalpy change (ΔH) when a reaction is reversed?

When a thermochemical reaction is reversed, the sign of the enthalpy change (ΔH) is also reversed. For instance, if the ΔH of the forward reaction is -1204 kJ, then the ΔH of the reverse reaction will be +1204 kJ. This is because reversing the reaction changes the direction of heat flow, converting an exothermic process into an endothermic one, or vice versa.

How do you use Hess's Law to find the enthalpy change of an overall reaction from multiple steps?

To use Hess's Law to find the enthalpy change (ΔH) of an overall reaction, you sum the enthalpy changes of the individual steps. First, write down the partial reactions and their respective ΔH values. Next, rearrange and combine these reactions so that intermediates cancel out, leaving you with the overall reaction. Finally, add the ΔH values of the partial reactions to obtain the ΔH for the overall reaction. This method allows you to calculate the enthalpy change for complex reactions that occur in multiple steps.

What are reaction intermediates and how do they affect the application of Hess's Law?

Reaction intermediates are species that appear in the steps of a reaction mechanism but not in the overall balanced equation. When applying Hess's Law, these intermediates must cancel out. This is done by ensuring that intermediates appearing as reactants in one step are also present as products in another step. By canceling out intermediates, you can combine the partial reactions to form the overall reaction, allowing you to sum their enthalpy changes (ΔH) to find the total ΔH for the overall reaction.