H2 + CaCl2 = HCl + CaH2

H_2 hydrogen + CaCl_2 calcium chloride ⟶ HCl hydrogen chloride + CaH_2 calcium hydride

Balance the chemical equation algebraically: H_2 + CaCl_2 ⟶ HCl + CaH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 CaCl_2 ⟶ c_3 HCl + c_4 CaH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Ca and Cl: H: | 2 c_1 = c_3 + 2 c_4 Ca: | c_2 = c_4 Cl: | 2 c_2 = c_3 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_2 + CaCl_2 ⟶ 2 HCl + CaH_2

+ ⟶ +

hydrogen + calcium chloride ⟶ hydrogen chloride + calcium hydride

| hydrogen | calcium chloride | hydrogen chloride | calcium hydride molecular enthalpy | 0 kJ/mol | -795.4 kJ/mol | -92.3 kJ/mol | -181.5 kJ/mol total enthalpy | 0 kJ/mol | -795.4 kJ/mol | -184.6 kJ/mol | -181.5 kJ/mol | H_initial = -795.4 kJ/mol | | H_final = -366.1 kJ/mol | ΔH_rxn^0 | -366.1 kJ/mol - -795.4 kJ/mol = 429.3 kJ/mol (endothermic) | | |

| hydrogen | calcium chloride | hydrogen chloride | calcium hydride molecular free energy | 0 kJ/mol | -748.8 kJ/mol | -95.3 kJ/mol | -142.5 kJ/mol total free energy | 0 kJ/mol | -748.8 kJ/mol | -190.6 kJ/mol | -142.5 kJ/mol | G_initial = -748.8 kJ/mol | | G_final = -333.1 kJ/mol | ΔG_rxn^0 | -333.1 kJ/mol - -748.8 kJ/mol = 415.7 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: H_2 + CaCl_2 ⟶ HCl + CaH_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_2 + CaCl_2 ⟶ 2 HCl + CaH_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_2 | 2 | -2 CaCl_2 | 1 | -1 HCl | 2 | 2 CaH_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_2 | 2 | -2 | ([H2])^(-2) CaCl_2 | 1 | -1 | ([CaCl2])^(-1) HCl | 2 | 2 | ([HCl])^2 CaH_2 | 1 | 1 | [CaH2] 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 = ([H2])^(-2) ([CaCl2])^(-1) ([HCl])^2 [CaH2] = (([HCl])^2 [CaH2])/(([H2])^2 [CaCl2])

Construct the rate of reaction expression for: H_2 + CaCl_2 ⟶ HCl + CaH_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_2 + CaCl_2 ⟶ 2 HCl + CaH_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_2 | 2 | -2 CaCl_2 | 1 | -1 HCl | 2 | 2 CaH_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_2 | 2 | -2 | -1/2 (Δ[H2])/(Δt) CaCl_2 | 1 | -1 | -(Δ[CaCl2])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) CaH_2 | 1 | 1 | (Δ[CaH2])/(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[H2])/(Δt) = -(Δ[CaCl2])/(Δt) = 1/2 (Δ[HCl])/(Δt) = (Δ[CaH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | calcium chloride | hydrogen chloride | calcium hydride formula | H_2 | CaCl_2 | HCl | CaH_2 Hill formula | H_2 | CaCl_2 | ClH | CaH_2 name | hydrogen | calcium chloride | hydrogen chloride | calcium hydride IUPAC name | molecular hydrogen | calcium dichloride | hydrogen chloride | calcium hydride

| hydrogen | calcium chloride | hydrogen chloride | calcium hydride molar mass | 2.016 g/mol | 111 g/mol | 36.46 g/mol | 42.094 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -259.2 °C | 772 °C | -114.17 °C | 190 °C boiling point | -252.8 °C | | -85 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.15 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | solubility in water | | soluble | miscible | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | | odor | odorless | | |