Question

Which of the following substances have an enthalpy of formation equal to zero? a. \(\mathrm{Cl}_{2}(g)\) b. \(\mathrm{H}_{2}(g)\) c. \(\mathrm{N}_{2}(l)\) d. \(\mathrm{Cl}(g)\)

Short answer

The substances with an enthalpy of formation equal to zero are \(\mathrm{Cl}_{2}(g)\) and \(\mathrm{H}_{2}(g)\), as they are in their standard states at 1 atm pressure and 298.15 K.

Step-by-step solution

Identify the standard states of the given substances

Identify the substances listed and determine the standard states of their constituent elements. This involves looking at periodic table or reference material to find the most stable state these elements exist in at standard conditions.

Compare the given substances to their standard states

Determine which substances are in their standard states. If a substance is in its standard state, its enthalpy of formation would be zero.

Identify the substances with enthalpy of formation equal to zero

Based on the comparison in Step 2, list the substances that have an enthalpy of formation equal to zero. Substance a. \(\mathrm{Cl}_{2}(g)\) - In its standard state, Chlorine exists as a diatomic gas. So, this is in its standard state. b. \(\mathrm{H}_{2}(g)\) - In its standard state, Hydrogen exists as a diatomic gas. So, this is in its standard state. c. \(\mathrm{N}_{2}(l)\) - In its standard state, Nitrogen exists as a diatomic gas. This is not in its standard state, as this is a liquid. d. \(\mathrm{Cl}(g)\) - In its standard state, Chlorine exists as a diatomic gas. This is not in its standard state, as this is a monoatomic gas.

Conclusion

Based on our analysis, the substances with an enthalpy of formation equal to zero are \(\mathrm{Cl}_{2}(g)\) and \(\mathrm{H}_{2}(g)\). These are the substances that are in their standard state at 1 atm pressure and 298.15 K.

Key concepts

Understanding Standard State

In chemical thermodynamics, the concept of "standard state" is crucial. For a substance, the standard state refers to a set condition of 1 atmosphere pressure and a specified temperature, typically 298.15 Kelvin (25 °C). It is the state in which the substance is most stable under these conditions. The significance of the standard state is that it provides a reference point to determine other thermodynamic quantities like enthalpy of formation.
Enthalpy of formation is a measure of the energy change when a compound forms from its elements. In the standard state, the enthalpy of formation for a pure element is defined as zero, because no energy change is involved when an element exists in its most stable form. For example:

• Oxygen forms a diatomic molecule, \( ext{O}_2(g)\), at standard conditions.
• Similarly, carbon exists as graphite in its standard state.

The observed enthalpy values of other substances can be calculated relative to these reference points.

The Role of Diatomic Gases

Many elements naturally exist as diatomic molecules in their standard states, especially at standard conditions. A diatomic gas means the molecule is composed of two atoms. This is a significant concept in chemistry because these gases exhibit specific properties.
Common examples of elements forming diatomic gases include:

• Hydrogen, \( ext{H}_2(g)\)
• Nitrogen, \( ext{N}_2(g)\)
• Oxygen, \( ext{O}_2(g)\)
• Chlorine, \( ext{Cl}_2(g)\)

Understanding that these elements exist naturally in pairs under standard conditions helps explain why their enthalpy of formation is zero—it’s the natural, most stable arrangement. If an element with diatomic nature is found in another form, such as a monoatomic gas, it is not in its standard state.

Basics of Chemical Thermodynamics

Chemical thermodynamics studies the interrelation of heat with chemical reactions and understanding energy transformations. Enthalpy, a core concept in thermodynamics, reflects the total heat content of a system at constant pressure.
Thermodynamic principles explain how energy changes influence chemical reactions and processes. In any chemical reaction, understanding the energy exchange, such as heat absorption or release, offers insights into reaction feasibility and direction.

• Enthalpy of formation specifically refers to the heat change when one mole of a compound forms from its elemental constituents in their standard states.
• Reaction feasibility is often dictated by these enthalpy changes, coupled with other factors like entropy.

This forms the basis for predicting the spontaneity and potential extent of chemical reactions, making thermodynamics essential in fields like physical chemistry and engineering.