Answer :
To determine which reaction shows that the enthalpy of formation of carbon disulfide (CS₂) is ΔH_f = 89.4 kJ/mol, we need to understand the concept of enthalpy of formation. The enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states under standard conditions (usually 1 atm pressure and 298 K).
Let’s analyze each option to see which one correctly represents this scenario:
1. Option A: [tex]\( C (s) + 2 S (s) \rightarrow CS_2(l) + 89.4 \, \text{kJ} \)[/tex]
- This shows that energy is released during the formation of CS₂ (not absorbed), which contradicts the given enthalpy of formation of +89.4 kJ/mol.
2. Option B: [tex]\( C(s) + 2 S(s) \rightarrow CS_2(l) \)[/tex]
- This does not include any mention of the enthalpy change. While it shows the correct formation of CS₂ from its elements, it lacks the description of the absorption of 89.4 kJ of energy.
3. Option C: [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) + 89.4 \, \text{kJ} \)[/tex]
- This erroneous reaction suggests that both the reactants and the product have the same enthalpy value (which is incorrect), and it does not make sense thermodynamically as it suggests no net change in enthalpy.
4. Option D: [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) \)[/tex]
- This reaction correctly indicates that the formation of CS₂ from carbon (C) and sulfur (S) requires the absorption of 89.4 kJ of energy, which aligns perfectly with the definition of the enthalpy of formation.
Therefore, the reaction that correctly represents the enthalpy of formation for CS₂ being ΔH_f = 89.4 kJ/mol is:
D. [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) \)[/tex]
Let’s analyze each option to see which one correctly represents this scenario:
1. Option A: [tex]\( C (s) + 2 S (s) \rightarrow CS_2(l) + 89.4 \, \text{kJ} \)[/tex]
- This shows that energy is released during the formation of CS₂ (not absorbed), which contradicts the given enthalpy of formation of +89.4 kJ/mol.
2. Option B: [tex]\( C(s) + 2 S(s) \rightarrow CS_2(l) \)[/tex]
- This does not include any mention of the enthalpy change. While it shows the correct formation of CS₂ from its elements, it lacks the description of the absorption of 89.4 kJ of energy.
3. Option C: [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) + 89.4 \, \text{kJ} \)[/tex]
- This erroneous reaction suggests that both the reactants and the product have the same enthalpy value (which is incorrect), and it does not make sense thermodynamically as it suggests no net change in enthalpy.
4. Option D: [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) \)[/tex]
- This reaction correctly indicates that the formation of CS₂ from carbon (C) and sulfur (S) requires the absorption of 89.4 kJ of energy, which aligns perfectly with the definition of the enthalpy of formation.
Therefore, the reaction that correctly represents the enthalpy of formation for CS₂ being ΔH_f = 89.4 kJ/mol is:
D. [tex]\( C (s) + 2 S (s) + 89.4 \, \text{kJ} \rightarrow CS_2(l) \)[/tex]
