Question

Describe how chemists use Hess's law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

Short answer

Chemists use Hess's Law by combining combustion reaction pathways to determine \(\Delta H^{\circ}_{\mathrm{f}}\) as a summation of enthalpik changes.

Step-by-step solution

Understanding Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken. This implies that enthalpy is a state function.

Identifying the Enthalpy of Combustion

The enthalpy of combustion is the heat released when one mole of a substance is burned in oxygen. It is often measured directly through calorimetry.

Preparing Hess's Law Application

To apply Hess's Law, you need the reaction equation for forming the compound from its elements in their standard states. Additionally, the enthalpies of formation or combustion of all reactants and products involved are required.

Constructing Reaction Pathways

Construct a series of hypothetical reactions that combine to give the desired reaction for forming the compound from its elements. Include the combustion reactions of the compound and its elemental forms.

Calculating \\Delta H^{\circ}_{\mathrm{f}} Using Hess's Law

By combining the enthalpies from the reaction pathways, using additivity of enthalpy changes as per Hess's Law, solve for the unknown enthalpy of formation, \(\Delta H^{\circ}_{\mathrm{f}}\), ensuring all paths sum up to give the combusted products.

Interpreting the Result

The solution from Step 5 will give the standard enthalpy of formation of the compound, \(\Delta H^{\circ}_{\mathrm{f}}\), indicating how much energy is required or released when the compound is formed from its elements in their standard states.

Key concepts

Enthalpy of Formation

Enthalpy of formation, often denoted as \( \Delta H_f^\circ \), is a crucial concept in thermochemistry. It represents the change in enthalpy when one mole of a compound is formed from its elements in their most stable forms under standard conditions (usually 1 atm pressure and 298 K). This value is important as it helps predict the stability and reactivity of a compound.

• If \( \Delta H_f^\circ \) is negative, the formation is exothermic, releasing heat, making the compound potentially more stable.
• If \( \Delta H_f^\circ \) is positive, the formation is endothermic, requiring heat input, suggesting less stability under standard conditions.

Hess’s Law enables the determination of \( \Delta H_f^\circ \) indirectly by using known enthalpies of reactions like combustion. By constructing a series of hypothetical reactions that form the compound from its elements, one can calculate \( \Delta H_f^\circ \) through the principle that enthalpy is a state function. This approach avoids direct measurement difficulties in experimental setups.

Enthalpy of Combustion

The enthalpy of combustion is an essential thermodynamic quantity that represents the heat released when one mole of a substance is completely burned in oxygen. This is typically a highly exothermic process, meaning it releases a significant amount of energy.

• This is often measured directly via calorimetry, providing reliable data.
• The enthalpy of combustion is usually a negative value, indicating heat release.

By understanding these values, we can utilize them in Hess’s Law to determine other thermodynamic values, like the enthalpy of formation. Knowing the combustion enthalpies of all reactants and products, chemists can construct reaction pathways that ultimately provide the desired \( \Delta H_f^\circ \) for a new compound.

Calorimetry

Calorimetry is a technique used by chemists to measure the amount of heat involved in a chemical reaction, change of state, or formation of a solution. This method becomes invaluable when determining energies such as enthalpies of combustion and formation.

• A calorimeter is the device used to measure these heat changes, which can be done under constant pressure or volume.
• By accurately measuring temperature changes, the heat of a reaction can be calculated using the relationship \( q = mc\Delta T \), where \( q \) represents heat, \( m \) is mass, \( c \) is the specific heat, and \( \Delta T \) is the change in temperature.

In the context of Hess's Law, calorimetry provides the necessary enthalpy data needed to calculate the enthalpy changes indirectly. The meticulous nature of calorimetry ensures reliable values that help chemists understand reaction energetics better.

State Function

A state function is a property whose value is determined solely by the state of the system, not by the path the system took to reach that state. Enthalpy is one such state function. This means that the total enthalpy change depends only on the initial and final states of a chemical process, not on the specific series of steps taken to get there.

• Because of this characteristic, state functions like enthalpy become instrumental in applying Hess’s Law.
• The use of enthalpy as a state function allows chemists to construct various reaction pathways that achieve the same final state, all yielding the same \( \Delta H \), which helps calculate unknown enthalpies like \( \Delta H_f^\circ \) efficiently.

This property is crucial for the application of Hess's Law, enabling accurate predictions and calculations in thermochemical reactions, providing a powerful tool in understanding chemical energetics.