The standard heat of formation, in kcal/mol of Ba²⁺ is: [Given: standard heat of formation of SO₄²⁻ ion (aq) = –216 kcal/mol, standard heat of crystallization of BaSO₄(s) = –4.5 kcal/mol, standard heat of formation of BaSO₄(s) = –349 kcal/mol]

CONCEPT:

Standard Heat of Formation

• The standard heat of formation of a substance is the amount of heat absorbed or evolved when one mole of the substance is formed from its constituent elements in their standard states under standard conditions (usually 298 K and 1 atm).
• The standard heat of formation of ions in aqueous solution can be calculated using thermodynamic data such as heats of crystallization and formation of compounds containing these ions.

EXPLANATION:

Standard heat of formation of BaSO₄(s) = Standard heat of formation of Ba²⁺ (aq) + Standard heat of formation of SO₄²⁻ (aq) + Standard heat of crystallization of BaSO₄(s)

• Rearranging the equation:

  Standard heat of formation of Ba²⁺ (aq) = Standard heat of formation of BaSO₄(s) – Standard heat of formation of SO₄²⁻ (aq) – Standard heat of crystallization of BaSO₄(s)

• Substituting the values:
  • Standard heat of formation of Ba²⁺ (aq) = –349 kcal/mol – (–216 kcal/mol) – (–4.5 kcal/mol)
  • = –349 + 216 + 4.5
  • = –128.5 kcal/mol

Therefore, the standard heat of formation of Ba²⁺ (aq) is –128.5 kcal/mol.