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Chapter 7: Problem 19

Standard enthalpies of formation are relative values. What are \(\Delta H_{\mathrm{f}}^{\circ}\) values relative to?

Short Answer

Expert verified
The \(\Delta H_{\mathrm{f}}^{\circ}\) values are relative to the enthalpy of the constituent elements in their most stable forms (reference state) at standard conditions (1 atm and 298.15 K, or 25掳C). For example, the reference state for hydrogen is H鈧� gas, while for carbon, it is solid graphite.

Step by step solution

01

Defining standard enthalpy of formation

Standard enthalpy of formation, denoted by \(\Delta H_{\mathrm{f}}^{\circ}\), is the change in enthalpy during the formation of one mole of a substance at standard conditions (1 atm and 298.15 K, or 25掳C) from its constituent elements in their most stable forms (reference state). It is an essential concept in thermodynamics to calculate the enthalpy changes in various chemical reactions.
02

Reference state of constituent elements

The \(\Delta H_{\mathrm{f}}^{\circ}\) values are relative to the enthalpy of the constituent elements in their most stable forms (reference state) at standard conditions. For example, the reference state for hydrogen is H2 gas, while for carbon it is solid graphite. Since these reference states are assigned an enthalpy value of zero, the standard enthalpy of formation measures the enthalpy change from these reference states to the formation of the compound. In conclusion, the \(\Delta H_{\mathrm{f}}^{\circ}\) values are relative to the enthalpy of the constituent elements in their most stable forms at standard conditions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is a fundamental branch of physics that deals with heat, work, and the transformation of energy. It plays a crucial role in understanding how substances interact and change, especially during chemical reactions.

One of the key concepts of thermodynamics is enthalpy (\(H\)), which is a measure of total heat content of a system. While energy can neither be created nor destroyed, it can change forms, and in chemical processes, enthalpy helps us track these energy transformations. Enthalpy changes can tell us how much heat is absorbed or released during a reaction, which is vital for predicting reaction behavior and determining reaction feasibility.
Enthalpy Change
Enthalpy change, denoted by \(\Delta H\), refers to the difference in enthalpy between the products and reactants during a chemical reaction. It's a crucial indicator used to determine whether a reaction is exothermic or endothermic.

For instance, when \(\Delta H\ < 0\), the reaction is exothermic, meaning it releases heat to the surroundings. Conversely, if \(\Delta H\ > 0\), the reaction absorbs heat, making it endothermic. The standard enthalpy of formation, \(\Delta H_{\mathrm{f}}^{\circ}\), is a specific type of enthalpy change that occurs when one mole of a compound forms from its elements in their standard states.
Chemical Reactions
Chemical reactions are processes in which substances, called reactants, transform into different substances, known as products. Each reaction comes with an associated enthalpy change that determines how energy is exchanged within the system.

In a reaction, the breaking of bonds within reactants (which requires energy) and the formation of new bonds in products (which releases energy) contribute to the overall enthalpy change. By using the standard enthalpies of formation for each compound involved, we can calculate the total enthalpy change for any given chemical reaction.
Reference State
The reference state is a predefined standard condition used as a basis for comparison in thermodynamics. For substances involved in chemical reactions, the reference state is often the most stable physical form of the element at 1 atmosphere of pressure and a temperature of 298.15 K (25掳C).

When discussing enthalpy changes, particularly \(\Delta H_{\mathrm{f}}^{\circ}\), this concept ensures that all calculations start from a common ground. Assigning a value of zero enthalpy to elements in their reference state simplifies the calculation of enthalpy changes in compounds, effectively providing a 'zero point' from which all formation reactions are measured.

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Most popular questions from this chapter

In a coffee-cup calorimeter, \(150.0 \mathrm{mL}\) of \(0.50 \mathrm{M}\) HCl is added to \(50.0 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{NaOH}\) to make \(200.0 \mathrm{g}\) solution at an initial temperature of \(48.2^{\circ} \mathrm{C}\). If the enthalpy of neutralization for the reaction between a strong acid and a strong base is \(-56 \mathrm{kJ} / \mathrm{mol},\) calculate the final temperature of the calorimeter contents. Assume the specific heat capacity of the solution is \(4.184 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) and assume no heat loss to the surroundings.

Consider the following reaction: $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-891 \mathrm{kJ}$$ Calculate the enthalpy change for each of the following cases: a. \(1.00 \mathrm{g}\) methane is burned in excess oxygen. b. \(1.00 \times 10^{3} \mathrm{L}\) methane gas at \(740 .\) torr and \(25^{\circ} \mathrm{C}\) are burned in excess oxygen. The density of \(\mathrm{CH}_{4}(g)\) at these conditions is \(0.639 \mathrm{g} / \mathrm{L}\).

A \(110 .-\mathrm{g}\) sample of copper (specific heat capacity \(=\) the \(0.20 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\)) is heated to \(82.4^{\circ} \mathrm{C}\) and then placed in a container of water at \(22.3^{\circ} \mathrm{C} .\) The final temperature of the water and copper is \(24.9^{\circ} \mathrm{C} .\) What is the mass of the water in the container, assuming that all the heat lost by the copper is gained by the water?

The reaction $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ is the last step in the commercial production of sulfuric acid. The enthalpy change for this reaction is \(-227 \mathrm{kJ}\). In designing a sulfuric acid plant, is it necessary to provide for heating or cooling of the reaction mixture? Explain.

One of the components of polluted air is NO. It is formed in the high- temperature environment of internal combustion engines by the following reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H=180 \mathrm{kJ}$$ Why are high temperatures needed to convert \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) to NO?
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