Question

The correct statement amongst the following is :

• A. The term 'standard state' implies that the temperature is \( 0^\circ C \)
• B. The standard state of pure gas is the pure gas at a pressure of 1 bar and temperature 273 K
• C. \( \Delta_f H_{298}^\ominus \) is zero for O(g)
• D. \( \Delta_f H_{500}^\ominus \) is zero for \( O_2(g) \)

Hint:

Carefully distinguish between the definition of standard state (pressure is fixed at 1 bar, temperature is not) and the standard conditions often used for data tabulation (usually 298.15 K). Remember that the standard enthalpy of formation of an element in its most stable form under standard conditions is always zero.

Answer 1

The Correct Option is D

The question asks us to determine the correct statement regarding the standard state and enthalpy change of formation. Let's consider each option and evaluate the correctness based on standard chemistry principles:

1. The term 'standard state' implies that the temperature is \(0^\circ C\): ^{}\right\wing This statement is incorrect. The term 'standard state' refers to a reference state for thermodynamic calculations. While it is often assumed to be 25°C (298 K) for simplicity, the standard state itself is not defined by a specific temperature.
2. The standard state of pure gas is the pure gas at a pressure of 1 bar and temperature 273 K: This statement is partially incorrect. The standard state for a gas is defined as the pure gas at a pressure of 1 bar. However, it does not specify a fixed temperature like 273 K; instead, standard enthalpies are commonly tabulated at 298 K, not 273 K.
3. \(\Delta_f H_{298}^\ominus\) is zero for O(g): This statement is incorrect. \(\Delta_f H_{298}^\ominus\) refers to the standard enthalpy change of formation. For oxygen in its diatomic gaseous form (\(O_2(g)\)), \(\Delta_f H_{298}^\ominus\) is zero because it is the reference state. However, for monatomic oxygen (\(O(g)\)), it is not zero due to the energy required to dissociate the diatomic \(O_2\) molecule.
4. \(\Delta_f H_{500}^\ominus\) is zero for \(O_2(g)\): This statement is correct. \(\Delta_f H_{500}^\ominus\) denotes the standard enthalpy change of formation at 500 K. Since \(O_2(g)\) is the reference state for oxygen, its standard enthalpy change of formation remains zero at any temperature including 500 K.

Based on these evaluations, the correct statement is: \(\Delta_f H_{500}^\ominus\) is zero for \(O_2(g)\). This is consistent with the fact that \(O_2(g)\) is the natural standard state for elemental oxygen.

Answer 2

Step 1: Understand the definition of standard state and standard enthalpy of formation.
Standard State: The standard state of a substance is a specific set of conditions chosen as a reference point for thermodynamic properties. By international convention, the standard pressure (\( P^\ominus \)) is 1 bar (\( 10^5 \) Pa). The temperature is not specified as part of the definition of standard state, although thermodynamic data are often tabulated at a standard temperature of 298.15 K (\( 25^\circ C \)). 
For a pure gas, the standard state is the pure gas at a pressure of 1 bar behaving ideally. For a pure liquid or solid, it is the pure substance at a pressure of 1 bar. For a solute in solution, it is a solution with a molality of 1 mol/kg behaving ideally. Standard Enthalpy of Formation (\( \Delta_f H^\ominus \)): The standard enthalpy of formation of a compound is the change of enthalpy that accompanies the formation of 1 mole of the substance in its standard state from its constituent elements in their standard states. The standard enthalpy of formation of an element in its most stable allotropic form at the specified temperature (and 1 bar pressure) is zero. 
Step 2: Evaluate each statement.
(1) The term 'standard state' implies that the temperature is \( 0^\circ C \). This statement is incorrect. The standard state specifies a pressure of 1 bar, but the temperature is not fixed at \( 0^\circ C \) (273.15 K). While 273.15 K is a common reference temperature (especially in gas laws), it is not inherently part of the definition of standard state in thermodynamics. 
(2) The standard state of pure gas is the pure gas at a pressure of 1 bar and temperature 273 K. This statement is incorrect. The standard state of a pure gas is defined at a pressure of 1 bar, but the temperature is not fixed at 273 K. The temperature can be any specified value, although 298.15 K is most commonly used for tabulated thermodynamic data. 
(3) \( \Delta_f H_{298}^\ominus \) is zero for O(g). This statement is incorrect. \( O(g) \) is atomic oxygen, which is not the most stable allotropic form of the element oxygen at 298 K and 1 bar. The most stable allotropic form of oxygen under these conditions is diatomic oxygen, \( O_2(g) \).
Therefore, \( \Delta_f H_{298}^\ominus \) for \( O(g) \) is not zero; it is the enthalpy change for the formation of \( O(g) \) from \( O_2(g) \), which requires energy to break the bond in \( O_2 \). 
(4) \( \Delta_f H_{500}^\ominus \) is zero for \( O_2(g) \). This statement is correct. \( O_2(g) \) is the most stable allotropic form of the element oxygen at 500 K and 1 bar (and at any temperature under standard pressure). By definition, the standard enthalpy of formation of an element in its most stable allotropic form at the specified temperature and standard pressure is zero. 
Step 3: Identify the correct statement.
Based on the analysis, the correct statement is (4).