## Step-by-Step Solution **Given:** - Write two possible reactions for **dissolution of CaO** into the oxide **ZrO₂₋ᵧ**. ### Understanding the Problem - **ZrO₂₋ᵧ**: This is zirconium oxide with oxygen vacancies (non-stoichiometric, y = oxygen vacancy concentration). - **CaO**: Calcium oxide, which can act as a dopant in ZrO₂. When CaO is added to ZrO₂₋ᵧ, Ca²⁺ can substitute for Zr⁴⁺ in the lattice, and to maintain charge neutrality, oxygen vacancies (V₀) or other defects may be created/annihilated. ### Notation - \( \text{Ca}_\text{Zr}^{''} \): Ca²⁺ ion substituting for Zr⁴⁺ (2 negative effective charges) - \( V_O^{\cdot\cdot} \): Oxygen vacancy (2 positive effective charges) - \( O_O^x \): Regular oxygen ion on an oxygen site (neutral) - \( Zr_{Zr}^x \): Regular Zr ion on a zirconium site (neutral) --- ## **Reaction 1: Formation of Oxygen Vacancies** When CaO dissolves, Ca²⁺ replaces Zr⁴⁺, and oxygen from CaO goes to an oxygen site in ZrO₂, creating an oxygen vacancy for charge compensation: \[ \text{CaO} + \text{ZrO}_{2} \rightarrow \text{Ca}_{\text{Zr}}^{''} + V_O^{\cdot\cdot} + 2 O_O^x \] **Explanation:** - Ca²⁺ replaces Zr⁴⁺ (\(\text{Ca}_{\text{Zr}}^{''}\)), creating 2 negative charges. - To balance, one oxygen vacancy (\(V_O^{\cdot\cdot}\), 2+) is created. --- ## **Reaction 2: Filling an Existing Oxygen Vacancy** If ZrO₂₋ᵧ already has oxygen vacancies, the incoming oxygen from CaO can fill a vacancy: \[ \text{CaO} + V_O^{\cdot\cdot} \rightarrow \text{Ca}_{\text{Zr}}^{''} + 2 O_O^x \] **Explanation:** - The oxygen from CaO fills an existing vacancy, so no new vacancy is created. - Ca²⁺ still replaces Zr⁴⁺, compensated by the filled vacancy. --- ## **Final Answers** ### **1. Formation of Oxygen Vacancy:** \[ \boxed{ \text{CaO} + \text{ZrO}_{2} \rightarrow \text{Ca}_{\text{Zr}}^{''} + V_O^{\cdot\cdot} + 2 O_O^x } \] ### **2. Filling of an Existing Vacancy:** \[ \boxed{ \text{CaO} + V_O^{\cdot\cdot} \rightarrow \text{Ca}_{\text{Zr}}^{''} + 2 O_O^x } \] These are the two possible reactions for the dissolution of CaO into ZrO₂₋ᵧ.