Answer :
To determine for which of the given reactions the enthalpy change, [tex]\(\Delta H_m^\rho\)[/tex], is equal to the standard enthalpy of formation, [tex]\(\Delta H_i^\rho\)[/tex], of the product(s), we need to identify the reactions where the reactants are in their standard states and form the products directly.
The definition of the standard enthalpy of formation, [tex]\(\Delta H_i^\rho\)[/tex], is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. Elements in their standard states have an enthalpy of formation, [tex]\(\Delta H_i^\rho\)[/tex], of zero.
Let's analyze each reaction one by one:
1. Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (l) [tex]\(\rightarrow\)[/tex] NaF (s)
- Sodium (Na) is in its standard state (solid).
- Fluorine (F[tex]\(_2\)[/tex]) is in the liquid state, but its standard state is gaseous.
- Hence, the reactants are not all in their standard states.
- This reaction does not meet the criteria.
2. CaCO[tex]\(_3\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CaO + CO[tex]\(_2\)[/tex] (g)
- This is a decomposition reaction, breaking down calcium carbonate into calcium oxide and carbon dioxide.
- It’s not forming a compound from elements in their standard states.
- This reaction does not meet the criteria.
3. CO (g) + [tex]\(\frac{1}{2}\)[/tex] O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Carbon monoxide (CO) and oxygen (O[tex]\(_2\)[/tex]) are both in their standard gaseous states.
- The reaction forms carbon dioxide (CO[tex]\(_2\)[/tex]) directly.
- This reaction meets the criteria.
4. 2 Na (s) + F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] 2 NaF (s)
- Sodium (Na) is in its standard state (solid), and fluorine (F[tex]\(_2\)[/tex]) is in its standard state (gas).
- However, this reaction involves the formation of two moles of NaF, not one mole.
- This reaction does not meet the criteria strictly as per the standard formation definition.
5. Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] NaF (s)
- Sodium (Na) is in its standard state (solid), and fluorine (F[tex]\(_2\)[/tex]) is in its standard state (gas).
- The reaction forms one mole of NaF.
- This reaction meets the criteria.
6. C (s, graphite) + O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Carbon in its graphite form is in its standard state (solid), and oxygen (O[tex]\(_2\)[/tex]) is in its standard state (gas).
- The reaction forms carbon dioxide (CO[tex]\(_2\)[/tex]) directly.
- This reaction meets the criteria.
Therefore, the reactions for which [tex]\(\Delta H_m^\rho\)[/tex] is equal to [tex]\(\Delta H_i^\rho\)[/tex] of the product(s) are:
- CO (g) + [tex]\(\frac{1}{2}\)[/tex] O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] NaF (s)
- C (s, graphite) + O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
The definition of the standard enthalpy of formation, [tex]\(\Delta H_i^\rho\)[/tex], is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. Elements in their standard states have an enthalpy of formation, [tex]\(\Delta H_i^\rho\)[/tex], of zero.
Let's analyze each reaction one by one:
1. Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (l) [tex]\(\rightarrow\)[/tex] NaF (s)
- Sodium (Na) is in its standard state (solid).
- Fluorine (F[tex]\(_2\)[/tex]) is in the liquid state, but its standard state is gaseous.
- Hence, the reactants are not all in their standard states.
- This reaction does not meet the criteria.
2. CaCO[tex]\(_3\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CaO + CO[tex]\(_2\)[/tex] (g)
- This is a decomposition reaction, breaking down calcium carbonate into calcium oxide and carbon dioxide.
- It’s not forming a compound from elements in their standard states.
- This reaction does not meet the criteria.
3. CO (g) + [tex]\(\frac{1}{2}\)[/tex] O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Carbon monoxide (CO) and oxygen (O[tex]\(_2\)[/tex]) are both in their standard gaseous states.
- The reaction forms carbon dioxide (CO[tex]\(_2\)[/tex]) directly.
- This reaction meets the criteria.
4. 2 Na (s) + F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] 2 NaF (s)
- Sodium (Na) is in its standard state (solid), and fluorine (F[tex]\(_2\)[/tex]) is in its standard state (gas).
- However, this reaction involves the formation of two moles of NaF, not one mole.
- This reaction does not meet the criteria strictly as per the standard formation definition.
5. Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] NaF (s)
- Sodium (Na) is in its standard state (solid), and fluorine (F[tex]\(_2\)[/tex]) is in its standard state (gas).
- The reaction forms one mole of NaF.
- This reaction meets the criteria.
6. C (s, graphite) + O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Carbon in its graphite form is in its standard state (solid), and oxygen (O[tex]\(_2\)[/tex]) is in its standard state (gas).
- The reaction forms carbon dioxide (CO[tex]\(_2\)[/tex]) directly.
- This reaction meets the criteria.
Therefore, the reactions for which [tex]\(\Delta H_m^\rho\)[/tex] is equal to [tex]\(\Delta H_i^\rho\)[/tex] of the product(s) are:
- CO (g) + [tex]\(\frac{1}{2}\)[/tex] O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)
- Na (s) + [tex]\(\frac{1}{2}\)[/tex] F[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] NaF (s)
- C (s, graphite) + O[tex]\(_2\)[/tex] (g) [tex]\(\rightarrow\)[/tex] CO[tex]\(_2\)[/tex] (g)