Gavin Howe
Hess's Law, named after Russian chemist Germain Hess, states that the enthalpy of a given chemical reaction is constant, regardless of whether the reaction occurs in one step or many steps. This is because enthalpy is a state function, and therefore, the overall change in enthalpy can be calculated by summing up the changes at each step. Since enthalpy is a state function, it does not depend on a specific pathway, and any coefficients can be used as long as the enthalpy is changed consistently. Thus, fractional coefficients are permissible in Hess's Law reactions, as they allow for the balancing of equations without altering the overall reaction and enthalpy change.
| Characteristics | Values |
|---|---|
| Hess' Law | The total heat of reaction along the "path" connecting reactants to products is equal to the heat of reaction along an alternative "path" |
| Named after | Germain Henri Hess, a Russian chemist and doctor |
| Publication year | 1840 |
| Calculation | Overall change in enthalpy is calculated by summing up the changes for each step of the way until the product is formed |
| Enthalpy | Enthalpy is a state function, and hence it is pathway independent |
| Use of fractions | Fractional coefficients are permissible in Hess' Law since the equation refers to moles, not molecules |
| Use of coefficients | Any coefficients can be used as long as the enthalpy is consistently changed along with it |
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What You'll Learn
- Hess' Law allows for fractions as coefficients when referring to moles, not molecules
- Fractional coefficients are used to avoid multiplying products and changing the reaction
- Hess' Law is due to enthalpy being a state function
- Elevation gain is independent of the path taken, like enthalpy
- Hess' Law can be used to calculate other state functions like changes in Gibbs' Energy and Entropy
Hess' Law allows for fractions as coefficients when referring to moles, not molecules
Hess's Law, named after Russian chemist and doctor Germain Hess, is a fundamental principle in thermochemistry. It states that the total heat of reaction between reactants and products is independent of the path taken, as long as the initial and final conditions are the same. This is because enthalpy is a state function, and changes in enthalpy depend only on the initial and final states of a system, not on the specific path taken.
This law allows chemists to calculate the overall change in enthalpy by summing up the changes at each step of a reaction, even if the reaction occurs in multiple steps. An example of a two-step reaction is the combustion of carbon:
Step 1:
\[ \text{C} (s) + \frac{1}{2} \text{O}_{2} (g) \rightarrow \text{C} \text{O} (g) ~~~~~~~~~~~~~ \Delta H_{m} = –110.5 \text{kJ} = \Delta H_{1} \]
In this step, one mole of carbon reacts with half a mole of oxygen gas to produce one mole of carbon monoxide. The change in enthalpy (\(\Delta H_m\)) for this step is \(-110.5\) kJ.
Step 2:
\[ \text{C} \text{O} (g) + \frac{1}{2} \text{O}_{2} (g) \rightarrow \text{C} \text{O}_{2} (g) ~~~~~~~~~~~~~ \Delta H_{m} = –283.0 \text{ kJ} = \Delta H_{2} \]
In the second step, the carbon monoxide produced in step 1 reacts with another half mole of oxygen gas to form one mole of carbon dioxide. The change in enthalpy for this step is \(-283.0\) kJ.
The fractional coefficient of \(\frac{1}{2}\) is used to represent half a mole of oxygen gas in both steps. These fractions are permissible in Hess's Law because the equations refer to moles, not molecules.
By summing the \(\Delta H_m\) values from both steps, we can calculate the overall change in enthalpy for the reaction:
\[ \Delta H_{\text{total}} = \Delta H_{1} + \Delta H_{2} = –110.5 \text{ kJ} + (–283.0 \text{ kJ}) = –393.5 \text{ kJ} \]
So, the total change in enthalpy for the combustion of one mole of carbon to produce one mole of carbon dioxide is \(-393.5\) kJ. This calculation demonstrates how Hess's Law allows for fractions as coefficients when referring to moles, providing a powerful tool for understanding and predicting chemical reactions.
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Fractional coefficients are used to avoid multiplying products and changing the reaction
In chemistry, fractional coefficients are used to balance chemical equations and maintain the law of conservation of mass. This law dictates that the number of atoms of each element must be the same on both sides of the equation. For example, consider the reaction:
C (s) + 1/2 O2 (g) → CO (g)
Here, the fractional coefficient of 1/2 indicates that only half a mole of oxygen is reacting. This is necessary to balance the equation and ensure that the number of oxygen atoms on both sides is consistent.
Fractional coefficients are also used to avoid multiplying products and changing the reaction. For instance, in the reaction:
2H2 + O2 → 2H2O
If we balance it as:
2H2 + O2 → 2*2H2O
We multiply the products (H2O) by 2. Since reaction enthalpies given next to Hess's law reactions represent the change in enthalpy per mole of the product, multiplying a coefficient to the product would change the reaction and the enthalpy. Using fractional coefficients elsewhere in the equation is a way to avoid this issue.
In Hess's law, we calculate the overall enthalpy change. Enthalpy, as a state function, is not pathway-dependent. Therefore, it doesn't matter which pathway is taken, and any coefficients can be used as long as the enthalpy is adjusted consistently.
While fractional coefficients may seem mathematically unconventional, they hold scientific significance. They indicate that only a fraction of a molecule is involved in the reaction. For example, a coefficient of 1/2 before oxygen (O2) means that only half a molecule of oxygen is reacting. This is important for stoichiometry, as it ensures that the number of atoms of each element remains balanced in the equation.
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Hess' Law is due to enthalpy being a state function
Hess's Law, also known as Hess's Law of Constant Heat Summation, is a relationship in physical chemistry and thermodynamics. It was formulated by Russian chemist and doctor Germain Hess, who published it in 1840. The law states that the total enthalpy change during a chemical reaction is independent of the sequence of steps taken. In other words, the overall enthalpy change is the sum of all the individual changes, regardless of the number of steps or stages.
Hess's Law is based on the fact that enthalpy is a state function. A state function is a property that depends only on the current state of a system, regardless of how that state was reached. For a thermodynamic system, the state is defined by its pressure, temperature, volume, and number of moles of components. Enthalpy, as a state function, is independent of the path taken and is only dependent on the initial and final states of a reaction. This means that the enthalpy change for a reaction will be the same regardless of the intermediate steps, as long as the initial and final conditions are the same. This is analogous to the difference in elevation between the first and third floors of a building, which remains the same regardless of the path taken to ascend the floors.
The concept of Hess's Law can be applied to other state functions, such as changes in Gibbs' Energy and Entropy. For example, the Bordwell thermodynamic cycle uses Hess's Law to determine experimentally inaccessible Gibbs free energy values. Enthalpy changes are additive, and the standard enthalpy of reaction can be calculated by summing the standard enthalpies of formation of products and reactants. This allows for the prediction of enthalpy changes in complex synthesis by compiling standard enthalpies of formation.
The use of fractions in Hess's Law arises from the fact that enthalpy is a state function and is independent of the pathway. In a chemical reaction, the reaction enthalpies are typically given per mole of product. When balancing chemical equations, using fractions as coefficients ensures that the overall enthalpy change remains consistent, even when the amount of product changes. This flexibility in using coefficients allows for the convenient manipulation of chemical equations while still adhering to the principles of Hess's Law.
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Elevation gain is independent of the path taken, like enthalpy
The concept of elevation gain in hiking and enthalpy in chemistry may seem unrelated, but they share an intriguing similarity. When it comes to hiking trails, the method used to calculate elevation gain can vary. Some hikers simply consider the net elevation gain, which is the difference between the starting and ending elevations. However, this method doesn't capture the complexity of the trail, which may involve numerous ascents and descents. A more comprehensive approach involves counting the number of contour intervals crossed or touched along the route, providing a better understanding of the terrain's undulations.
Now, let's delve into the concept of enthalpy in chemistry and its connection to Hess's Law. Enthalpy represents the total heat energy of a system, and it changes when a chemical reaction occurs. Hess's Law states that the total enthalpy change for a chemical reaction is independent of the specific pathway taken. In other words, it only depends on the initial and final states of the system, regardless of the intermediate steps. This is analogous to the concept of elevation gain being independent of the path taken during a hike. Just as hikers can reach the same peak via different trails, chemical reactions can achieve the same overall enthalpy change through various reaction pathways.
The key principle underlying this similarity is the law of conservation of energy. Energy cannot be created or destroyed; it can only change forms or be transferred. In the context of hiking, the total elevation gain represents the energy expended during the journey, regardless of the specific path taken. Similarly, in chemistry, the total enthalpy change represents the energy change in a reaction, irrespective of the intermediate steps. This concept is particularly useful when dealing with reactions that are challenging to perform in a laboratory setting, as it allows for the calculation of enthalpy changes by combining multiple reactions.
The use of fractions in Hess's Law further emphasizes the independence of the pathway. In chemical equations, fractional coefficients are often used to balance reactions without altering the overall enthalpy change. For example, consider the reaction between hydrogen and oxygen to form water. By using fractions, we can balance the equation without affecting the enthalpy, ensuring that the overall energy change remains constant regardless of the specific coefficients used. This flexibility in coefficient usage reflects the principle that the total energy change is independent of the pathway, just like the elevation gain in hiking remains constant regardless of the chosen trail.
In summary, the concept of elevation gain in hiking and enthalpy in chemistry share a common thread: they are both independent of the path taken. Whether it's a hiker ascending a mountain or a chemical reaction progressing through different pathways, the total elevation gain and the total enthalpy change, respectively, remain unchanged. This similarity underscores the fundamental principle of energy conservation, highlighting the interconnected nature of scientific principles across seemingly unrelated disciplines.
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Hess' Law can be used to calculate other state functions like changes in Gibbs' Energy and Entropy
Hess's Law is a consequence of the concept of state functions, which are fundamental in thermodynamics. A state function is defined as a property of a system that depends only on its current state, rather than the path taken to reach that state. In other words, the change in a state function is determined solely by the initial and final states of the system.
Hess's Law, named after Russian chemist Germain Hess, is specifically linked to the state function of enthalpy. Enthalpy is a measure of the total energy exchanged in a chemical reaction. Hess's Law demonstrates that the change in enthalpy for a chemical reaction is independent of the pathway taken, and depends only on the initial and final states of the reactants and products. This is because enthalpy is a state function, and its value depends only on the state of the materials, specifically their temperature, pressure, and composition.
The concepts of Hess's Law can be extended beyond enthalpy changes to other state functions, such as changes in Gibbs' Energy and Entropy. This is because, like enthalpy, these state functions are also independent of the path taken and can be calculated using Hess's Law. For example, the Bordwell thermodynamic cycle combines ΔG values with ΔH values from Hess's Law to determine experimentally inaccessible Gibbs free energy values. Similarly, entropy values that have not been directly measured can be calculated using alternative paths through Hess's Law.
Furthermore, Hess's Law aids in visualizing energy changes in complex reaction series, enhancing our understanding of thermodynamic stability. By manipulating individual reaction steps, chemists can optimize conditions for desired products. Hess's Law simplifies complex reactions by allowing chemists to focus on the initial and final states, making it a valuable tool in chemical analysis and reaction optimization.
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Frequently asked questions
Hess's Law states that the total heat of reaction is independent of the path connecting the reactant to the product. This is because enthalpy is a state function, and therefore it does not matter which way it was calculated. As long as the enthalpy is changed consistently, it is fine to use fractions as coefficients.
Consider the reaction of 1 mol C(s) and 0.5 mol O2(g) to form 1 mol CO(g). The fractional coefficient of 0.5 for O2(g) is permissible because the equation refers to moles, not molecules.
A state function is a property that is independent of the path taken to reach a certain state. For example, your elevation when standing on the third floor of a building is independent of how you got there. Similarly, in Hess's Law, the heat of reaction is a state function, and it can be calculated by summing up the changes at each step of the reaction.
