H2O + CaH2 = H2 + Ca(OH)2

H_2O water + CaH_2 calcium hydride ⟶ H_2 hydrogen + Ca(OH)_2 calcium hydroxide

Balance the chemical equation algebraically: H_2O + CaH_2 ⟶ H_2 + Ca(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CaH_2 ⟶ c_3 H_2 + c_4 Ca(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Ca: H: | 2 c_1 + 2 c_2 = 2 c_3 + 2 c_4 O: | c_1 = 2 c_4 Ca: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + CaH_2 ⟶ 2 H_2 + Ca(OH)_2

+ ⟶ +

water + calcium hydride ⟶ hydrogen + calcium hydroxide

| water | calcium hydride | hydrogen | calcium hydroxide molecular enthalpy | -285.8 kJ/mol | -181.5 kJ/mol | 0 kJ/mol | -985.2 kJ/mol total enthalpy | -571.7 kJ/mol | -181.5 kJ/mol | 0 kJ/mol | -985.2 kJ/mol | H_initial = -753.2 kJ/mol | | H_final = -985.2 kJ/mol | ΔH_rxn^0 | -985.2 kJ/mol - -753.2 kJ/mol = -232 kJ/mol (exothermic) | | |

| water | calcium hydride | hydrogen | calcium hydroxide molecular free energy | -237.1 kJ/mol | -142.5 kJ/mol | 0 kJ/mol | -897.5 kJ/mol total free energy | -474.2 kJ/mol | -142.5 kJ/mol | 0 kJ/mol | -897.5 kJ/mol | G_initial = -616.7 kJ/mol | | G_final = -897.5 kJ/mol | ΔG_rxn^0 | -897.5 kJ/mol - -616.7 kJ/mol = -280.8 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O + CaH_2 ⟶ H_2 + Ca(OH)_2 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: 2 H_2O + CaH_2 ⟶ 2 H_2 + Ca(OH)_2 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 H_2O | 2 | -2 CaH_2 | 1 | -1 H_2 | 2 | 2 Ca(OH)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) CaH_2 | 1 | -1 | ([CaH2])^(-1) H_2 | 2 | 2 | ([H2])^2 Ca(OH)_2 | 1 | 1 | [Ca(OH)2] 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 = ([H2O])^(-2) ([CaH2])^(-1) ([H2])^2 [Ca(OH)2] = (([H2])^2 [Ca(OH)2])/(([H2O])^2 [CaH2])

Construct the rate of reaction expression for: H_2O + CaH_2 ⟶ H_2 + Ca(OH)_2 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: 2 H_2O + CaH_2 ⟶ 2 H_2 + Ca(OH)_2 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 H_2O | 2 | -2 CaH_2 | 1 | -1 H_2 | 2 | 2 Ca(OH)_2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) CaH_2 | 1 | -1 | -(Δ[CaH2])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) Ca(OH)_2 | 1 | 1 | (Δ[Ca(OH)2])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[CaH2])/(Δt) = 1/2 (Δ[H2])/(Δt) = (Δ[Ca(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | calcium hydride | hydrogen | calcium hydroxide formula | H_2O | CaH_2 | H_2 | Ca(OH)_2 Hill formula | H_2O | CaH_2 | H_2 | CaH_2O_2 name | water | calcium hydride | hydrogen | calcium hydroxide IUPAC name | water | calcium hydride | molecular hydrogen | calcium dihydroxide

| water | calcium hydride | hydrogen | calcium hydroxide molar mass | 18.015 g/mol | 42.094 g/mol | 2.016 g/mol | 74.092 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 190 °C | -259.2 °C | 550 °C boiling point | 99.9839 °C | | -252.8 °C | density | 1 g/cm^3 | | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.24 g/cm^3 solubility in water | | | | slightly soluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless | odorless