H2 + Ba = BaH2

H_2 hydrogen + Ba barium ⟶ BaH_2 barium hydride

Balance the chemical equation algebraically: H_2 + Ba ⟶ BaH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Ba ⟶ c_3 BaH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H and Ba: H: | 2 c_1 = 2 c_3 Ba: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2 + Ba ⟶ BaH_2

+ ⟶

hydrogen + barium ⟶ barium hydride

| hydrogen | barium | barium hydride molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -177 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -177 kJ/mol | H_initial = 0 kJ/mol | | H_final = -177 kJ/mol ΔH_rxn^0 | -177 kJ/mol - 0 kJ/mol = -177 kJ/mol (exothermic) | |

Construct the equilibrium constant, K, expression for: H_2 + Ba ⟶ BaH_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: H_2 + Ba ⟶ BaH_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 | 1 | -1 Ba | 1 | -1 BaH_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 | 1 | -1 | ([H2])^(-1) Ba | 1 | -1 | ([Ba])^(-1) BaH_2 | 1 | 1 | [BaH2] 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])^(-1) ([Ba])^(-1) [BaH2] = ([BaH2])/([H2] [Ba])

Construct the rate of reaction expression for: H_2 + Ba ⟶ BaH_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: H_2 + Ba ⟶ BaH_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 | 1 | -1 Ba | 1 | -1 BaH_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 | 1 | -1 | -(Δ[H2])/(Δt) Ba | 1 | -1 | -(Δ[Ba])/(Δt) BaH_2 | 1 | 1 | (Δ[BaH2])/(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[H2])/(Δt) = -(Δ[Ba])/(Δt) = (Δ[BaH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | barium | barium hydride formula | H_2 | Ba | BaH_2 name | hydrogen | barium | barium hydride IUPAC name | molecular hydrogen | barium | barium(+2) cation; hydrogen(-1) anion

| hydrogen | barium | barium hydride molar mass | 2.016 g/mol | 137.327 g/mol | 139.343 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -259.2 °C | 725 °C | 1200 °C boiling point | -252.8 °C | 1640 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | 3.6 g/cm^3 | 4.21 g/cm^3 solubility in water | | insoluble | surface tension | | 0.224 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | odor | odorless | |