Applying Hess's Law: A Step-By-Step Guide To Success

Hess's Law, also known as Hess' Law of Constant Heat Summation, is a principle in physical chemistry and thermodynamics. It states that the total enthalpy change in a chemical reaction is independent of the steps taken, meaning the overall enthalpy change is the same regardless of the route taken. This law is particularly useful when the enthalpy change (ΔH) cannot be measured directly. Hess's Law is applied by performing algebraic operations based on the chemical equations of reactions, using previously determined values for the enthalpies of formation. This allows for the determination of the overall energy required for a chemical reaction, even if it is complex and needs to be divided into multiple steps.

Hess's Law can be used to calculate other state functions like changes in entropy and Gibbs' energy

Hess's Law, also known as Hess's Law of Constant Heat Summation, is a principle in physical chemistry and thermodynamics formulated by Swiss-born Russian chemist and physician Germain Hess in 1840. The law states that the total enthalpy change during a chemical reaction is independent of the sequence of steps taken, meaning that the change in enthalpy is the same whether the reaction occurs in one step or several steps. This is because enthalpy is a state function, and its value is proportional to the system size.

Hess's Law can be used to calculate other state functions like changes in entropy and Gibbs energy. The concept of Hess's Law can be extended to these other state functions because they are also state functions. The Bordwell thermodynamic cycle is an example of such an extension, using easily measured equilibria and redox potentials to determine experimentally inaccessible Gibbs free energy values.

The change in Gibbs free energy can be determined using the equation:

> ΔG = ΣGproducts − ΣGreactants

Where:

• ΔG is the change in Gibbs free energy
• G is the free energy
• ΣGproducts is the sum of the free energy of all products
• ΣGreactants is the sum of the free energy of all reactants

The sign of the values for the change in free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) can be used to determine whether the equation is spontaneous.

Hess's Law can also be used to calculate the change in entropy, as entropy is a state function that can be measured as an absolute value. Therefore, there is no need to use the entropy of formation; instead, one can use the absolute entropies for products and reactants:

> ΔS = ΣSp − ΣSr

Where:

• ΔS is the change in entropy
• ΣSp is the sum of the entropy of all products
• ΣSr is the sum of the entropy of all reactants

Hess's Law can be used to calculate the enthalpy of formation of benzene

Hess's Law, also known as the law of constant heat summation, is a principle in physical chemistry and thermodynamics formulated by Germain Hess in 1840. It states that the total enthalpy change during a chemical reaction is independent of the sequence of steps taken, provided that the initial and final states of the reactants and products are the same. In other words, the overall enthalpy change is the same regardless of whether the reaction occurs in one step or multiple steps.

Now, let's apply Hess's Law to calculate the enthalpy of formation of benzene (C6H6). The standard heat of combustion of benzene is −3271 kJ/mol, and for its products, CO2 and H2O, the values are −394 kJ/mol and −286 kJ/mol, respectively.

To calculate the standard heat of formation of benzene, we need to set up three combustion equations:

• 15/2 O2 ---> 6CO2 + 3H2O
• 6CO2 + 3H2O ---> C6H6 + ...
• C6H6 ---> 6C + 3H2

Now, we manipulate these equations as follows:

• Flip equation 1
• Multiply equation 2 by -1
• Multiply equation 3 by 6 and 2, respectively, to get 6C and 3H2 on the product side

After these manipulations, we get:

• 6CO2 + 3H2O ---> 15/2 O2
• -C6H6 ---> -6CO2 - 3H2O
• 6C + 3H2 ---> C6H6

Adding these equations together, we get:

3271 + 2364 + 858 = +49 kJ/mol

So, the standard heat of formation of benzene is +49 kJ/mol.

This calculation illustrates how Hess's Law can be used to determine the enthalpy of formation of a compound, such as benzene, by manipulating and combining multiple chemical equations and their associated enthalpy changes.

Hess's Law can be used to calculate the enthalpy of a reaction that cannot be measured directly

Hess's Law, also known as Hess's Law of Constant Heat Summation, is a principle in physical chemistry and thermodynamics formulated by Swiss-born Russian chemist and physician Germain Hess in 1840. It 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 same regardless of how the reaction proceeds, as long as the initial and final conditions are identical. This is because enthalpy is a state function, meaning its value is dependent on the system's size and the number of moles involved in the reaction.

Hess's Law is particularly useful when the enthalpy change of a reaction cannot be measured directly. In such cases, the law allows us to calculate the enthalpy change (ΔH) by performing basic algebraic operations using the chemical equations of reactions and previously determined values for the enthalpies of formation. This is achieved by breaking down the overall reaction into a series of individual reactions with known enthalpy changes and then summing up their enthalpy changes to find the enthalpy change for the overall reaction.

For example, consider the reaction of carbon with oxygen to form carbon dioxide. This can occur in a single step or through a two-step process. The direct process is:

\[ \ce{C}_{(s)}+\ce{O}_{2(g)}⟶\ce{CO}_{2(g)}\;\;\;ΔH^∘_{298}=\mathrm{−394\;kJ} \]

The two-step process involves the following reactions:

\[ \ce{C}_{(s)}+\dfrac{1}{2}\ce{O}_{2(g)}⟶\ce{CO}_{(g)}\;\;\;ΔH^∘_{289}=\mathrm{−111\;kJ} \]

\[ \ce{CO} {(g)}+\dfrac{1}{2}\ce{O2}(g)⟶\ce{CO2} {(g)}\;\;\;ΔH^∘_{298}=\mathrm{−283\;kJ} \]

By summing the enthalpy changes of these two steps, we obtain the same enthalpy change as the direct process:

\[ \ce{C}_{(s)}+\ce{O}_{2(g)}⟶\ce{CO}_{2(g)} \;\;\;ΔH^∘_{298}=\mathrm{−394\;kJ} \]

This principle can be extended to more complex reactions by manipulating and combining multiple reactions to match the desired reaction. For instance, consider the reaction:

\[ \ce{ClF}(g)+\ce{F2}(g)⟶\ce{ClF3}(g)\hspace{20px}ΔH°=\:?\]

We can use the following reactions to determine the ΔH° for this reaction:

• Ii) \(\ce{2OF2}(g)⟶\ce{O2}(g)+\ce{2F2}(g)\hspace{20px}ΔH^\circ_{(ii)}=\mathrm{−49.4\:kJ}\)
• Iii) \(\ce{2ClF}(g)+\ce{O2}(g)⟶\ce{Cl2O}(g)+\ce{OF2}(g)\hspace{20px}ΔH^\circ_{(iii)}=\mathrm{+205.6\: kJ}\)
• Iv) \(\ce{ClF3}(g)+\ce{O2}(g)⟶\frac{1}{2}\ce{Cl2O}(g)+\dfrac{3}{2}\ce{OF2}(g)\hspace{20px}ΔH^\circ_{(iv)}=\mathrm{+266.7\: kJ}]

By multiplying, reversing, and combining these reactions appropriately, we can isolate the desired reactants and products while summing their respective ΔH° values to find the ΔH° for the overall reaction.

Hess's Law is a powerful tool that allows chemists to determine the enthalpy change for reactions that are challenging or impossible to measure directly. It highlights the concept that enthalpy is a state function, and its change depends only on the initial and final states of the reactants and products, regardless of the specific reaction pathway.

Hess's Law can be used to calculate the enthalpy of combustion of butane

Hess's Law, also known as the law of constant heat summation, 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 same regardless of whether the reaction takes place in one step or several steps, as long as the initial and final states are the same. This law is based on the fact that enthalpy is a state function, meaning its value is proportional to the system size.

Hess's Law can be used to determine the enthalpy change (ΔH) for a reaction even when it cannot be measured directly. This is done by performing algebraic operations based on the chemical equations of reactions using previously determined values for the enthalpies of formation. The law is particularly useful when trying to calculate the enthalpy of reactions that are difficult or impossible to measure experimentally.

To apply Hess's Law to calculate the enthalpy of combustion of butane, we need to follow these steps:

Step 1: Write the Balanced Chemical Equation

Write the balanced chemical equation for the combustion of butane. Butane (C4H10) reacts with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). The balanced equation for this reaction is:

> C4H10(g) + 6O2(g) → 4CO2(g) + 5H2O(l)

Step 2: Determine the Enthalpy Changes for Each Substance

Look up the standard enthalpy of formation (ΔHf°) values for each substance involved in the reaction. These values represent the change in enthalpy when one mole of a substance is formed from its elements in their standard states. The values can be found in reference tables or chemistry handbooks.

Step 3: Apply Hess's Law

Use Hess's Law to calculate the enthalpy change for the combustion of butane. This involves summing the enthalpy changes for the products and subtracting the sum of the enthalpy changes for the reactants. The equation is as follows:

> ΔH°reaction = Σn × ΔH°f(products) - Σn × ΔH°f(reactants)

Where:

• ΔH°reaction is the standard enthalpy change for the combustion of butane.
• N is the stoichiometric coefficient for each substance.
• ΔH°f(products) is the standard enthalpy of formation for each product.
• ΔH°f(reactants) is the standard enthalpy of formation for each reactant.

By substituting the values from the balanced equation and the standard enthalpy of formation values, we can calculate the enthalpy change for the combustion of butane.

Step 4: Interpret the Results

The calculated enthalpy change will indicate whether the reaction is exothermic or endothermic. If the value is negative, the reaction is exothermic, meaning it releases heat. If the value is positive, the reaction is endothermic, meaning it absorbs heat.

Hess's Law is a valuable tool in thermodynamics and chemical engineering, especially when dealing with complex reactions or reactions that are challenging to measure directly. By following the steps outlined above, you can use Hess's Law to calculate the enthalpy of combustion for butane or any other substance of interest.

Hess's Law can be used to calculate the enthalpy of atomisation of diatomic molecules

Hess's Law, also known as the law of constant heat summation, is a fundamental principle in physical chemistry and thermodynamics. It was formulated by Swiss-born Russian chemist and physician Germain Hess and published in 1840. This law states that the total enthalpy change during a chemical reaction remains the same regardless of the number of steps or the route taken, as long as the initial and final states are the same. In other words, the overall enthalpy change is independent of the path taken.

Now, let's apply Hess's Law to calculate the enthalpy of atomisation of diatomic molecules. Enthalpy of atomisation is the energy required to break a substance down into individual atoms. For diatomic molecules, such as hydrogen (H2) or chlorine (Cl2), this process involves breaking the bond between the two atoms.

Let's consider the example of hydrogen gas (H2). The enthalpy of atomisation for hydrogen can be calculated using Hess's Law by considering the following two reactions:

• Reaction 1: H2(g) → 2H(g), which represents the dissociation of hydrogen gas into individual hydrogen atoms.
• Reaction 2: H2(g) → H(g) + ½H2(g), which is the same reaction as Reaction 1 but written in a different way.

According to Hess's Law, the enthalpy change for the overall process is the sum of the enthalpy changes of the individual steps. In this case, Reaction 2 can be considered as two steps:

• Step 1: H2(g) → H(g) + ½H2(g), with an enthalpy change of ΔH1.
• Step 2: ½H2(g) → H(g), with an enthalpy change of ΔH2.

Since Reaction 2 is essentially the same as Reaction 1, the enthalpy change for Reaction 1 (ΔH1) is equal to the sum of the enthalpy changes of Step 1 (ΔH1) and Step 2 (ΔH2). Therefore, we can write:

ΔH1 = ΔH1 + ΔH2

Now, let's assume we have the following enthalpy values:

• Enthalpy of formation of H2(g) = -15 kJ/mol
• Enthalpy of atomisation of H(g) = 200 kJ/mol

Using Hess's Law, we can calculate the enthalpy change for Reaction 1 as follows:

ΔH1 = [Enthalpy of atomisation of H(g)] - [Enthalpy of formation of H2(g)]

ΔH1 = (2 x Enthalpy of atomisation of H(g)) - [Enthalpy of formation of H2(g)]

ΔH1 = (2 x 200 kJ/mol) - (-15 kJ/mol)

ΔH1 = 400 kJ/mol + 15 kJ/mol

ΔH1 = 415 kJ/mol

So, the enthalpy of atomisation for hydrogen gas (H2) is 415 kJ/mol.

A similar approach can be used to calculate the enthalpy of atomisation for other diatomic molecules, such as nitrogen (N2), oxygen (O2), or chlorine (Cl2). By using Hess's Law and known enthalpy values, we can determine the energy required to break down these diatomic molecules into their individual atoms.

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