CaO + Mg(OH)2 = Ca(OH)2 + MgO

CaO lime + Mg(OH)_2 magnesium hydroxide ⟶ Ca(OH)_2 calcium hydroxide + MgO magnesium oxide

Balance the chemical equation algebraically: CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaO + c_2 Mg(OH)_2 ⟶ c_3 Ca(OH)_2 + c_4 MgO Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O, H and Mg: Ca: | c_1 = c_3 O: | c_1 + 2 c_2 = 2 c_3 + c_4 H: | 2 c_2 = 2 c_3 Mg: | c_2 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO

+ ⟶ +

lime + magnesium hydroxide ⟶ calcium hydroxide + magnesium oxide

| lime | magnesium hydroxide | calcium hydroxide | magnesium oxide molecular enthalpy | -634.9 kJ/mol | -924.5 kJ/mol | -985.2 kJ/mol | -601.6 kJ/mol total enthalpy | -634.9 kJ/mol | -924.5 kJ/mol | -985.2 kJ/mol | -601.6 kJ/mol | H_initial = -1559 kJ/mol | | H_final = -1587 kJ/mol | ΔH_rxn^0 | -1587 kJ/mol - -1559 kJ/mol = -27.4 kJ/mol (exothermic) | | |

| lime | magnesium hydroxide | calcium hydroxide | magnesium oxide molecular free energy | -603.3 kJ/mol | -833.5 kJ/mol | -897.5 kJ/mol | -569.3 kJ/mol total free energy | -603.3 kJ/mol | -833.5 kJ/mol | -897.5 kJ/mol | -569.3 kJ/mol | G_initial = -1437 kJ/mol | | G_final = -1467 kJ/mol | ΔG_rxn^0 | -1467 kJ/mol - -1437 kJ/mol = -30 kJ/mol (exergonic) | | |

| lime | magnesium hydroxide | calcium hydroxide | magnesium oxide molecular entropy | 40 J/(mol K) | 64 J/(mol K) | 83 J/(mol K) | 27 J/(mol K) total entropy | 40 J/(mol K) | 64 J/(mol K) | 83 J/(mol K) | 27 J/(mol K) | S_initial = 104 J/(mol K) | | S_final = 110 J/(mol K) | ΔS_rxn^0 | 110 J/(mol K) - 104 J/(mol K) = 6 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i CaO | 1 | -1 Mg(OH)_2 | 1 | -1 Ca(OH)_2 | 1 | 1 MgO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaO | 1 | -1 | ([CaO])^(-1) Mg(OH)_2 | 1 | -1 | ([Mg(OH)2])^(-1) Ca(OH)_2 | 1 | 1 | [Ca(OH)2] MgO | 1 | 1 | [MgO] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([CaO])^(-1) ([Mg(OH)2])^(-1) [Ca(OH)2] [MgO] = ([Ca(OH)2] [MgO])/([CaO] [Mg(OH)2])

Construct the rate of reaction expression for: CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: CaO + Mg(OH)_2 ⟶ Ca(OH)_2 + MgO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i CaO | 1 | -1 Mg(OH)_2 | 1 | -1 Ca(OH)_2 | 1 | 1 MgO | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term CaO | 1 | -1 | -(Δ[CaO])/(Δt) Mg(OH)_2 | 1 | -1 | -(Δ[Mg(OH)2])/(Δt) Ca(OH)_2 | 1 | 1 | (Δ[Ca(OH)2])/(Δt) MgO | 1 | 1 | (Δ[MgO])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[CaO])/(Δt) = -(Δ[Mg(OH)2])/(Δt) = (Δ[Ca(OH)2])/(Δt) = (Δ[MgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lime | magnesium hydroxide | calcium hydroxide | magnesium oxide formula | CaO | Mg(OH)_2 | Ca(OH)_2 | MgO Hill formula | CaO | H_2MgO_2 | CaH_2O_2 | MgO name | lime | magnesium hydroxide | calcium hydroxide | magnesium oxide IUPAC name | | magnesium dihydroxide | calcium dihydroxide | oxomagnesium

| lime | magnesium hydroxide | calcium hydroxide | magnesium oxide molar mass | 56.077 g/mol | 58.319 g/mol | 74.092 g/mol | 40.304 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 2580 °C | 350 °C | 550 °C | 2852 °C boiling point | 2850 °C | | | 3600 °C density | 3.3 g/cm^3 | 2.3446 g/cm^3 | 2.24 g/cm^3 | 3.58 g/cm^3 solubility in water | reacts | insoluble | slightly soluble | odor | | | odorless | odorless