H2O + Zn3Sb2 = Zn(OH)2 + SbH3

H_2O water + Zn3Sb2 ⟶ Zn(OH)_2 zinc hydroxide + SbH_3 stibine

Balance the chemical equation algebraically: H_2O + Zn3Sb2 ⟶ Zn(OH)_2 + SbH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Zn3Sb2 ⟶ c_3 Zn(OH)_2 + c_4 SbH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Zn and Sb: H: | 2 c_1 = 2 c_3 + 3 c_4 O: | c_1 = 2 c_3 Zn: | 3 c_2 = c_3 Sb: | 2 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + Zn3Sb2 ⟶ 3 Zn(OH)_2 + 2 SbH_3

+ Zn3Sb2 ⟶ +

water + Zn3Sb2 ⟶ zinc hydroxide + stibine

Construct the equilibrium constant, K, expression for: H_2O + Zn3Sb2 ⟶ Zn(OH)_2 + SbH_3 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: 6 H_2O + Zn3Sb2 ⟶ 3 Zn(OH)_2 + 2 SbH_3 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 | 6 | -6 Zn3Sb2 | 1 | -1 Zn(OH)_2 | 3 | 3 SbH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Zn3Sb2 | 1 | -1 | ([Zn3Sb2])^(-1) Zn(OH)_2 | 3 | 3 | ([Zn(OH)2])^3 SbH_3 | 2 | 2 | ([SbH3])^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])^(-6) ([Zn3Sb2])^(-1) ([Zn(OH)2])^3 ([SbH3])^2 = (([Zn(OH)2])^3 ([SbH3])^2)/(([H2O])^6 [Zn3Sb2])

Construct the rate of reaction expression for: H_2O + Zn3Sb2 ⟶ Zn(OH)_2 + SbH_3 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: 6 H_2O + Zn3Sb2 ⟶ 3 Zn(OH)_2 + 2 SbH_3 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 | 6 | -6 Zn3Sb2 | 1 | -1 Zn(OH)_2 | 3 | 3 SbH_3 | 2 | 2 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 | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Zn3Sb2 | 1 | -1 | -(Δ[Zn3Sb2])/(Δt) Zn(OH)_2 | 3 | 3 | 1/3 (Δ[Zn(OH)2])/(Δt) SbH_3 | 2 | 2 | 1/2 (Δ[SbH3])/(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 = -1/6 (Δ[H2O])/(Δt) = -(Δ[Zn3Sb2])/(Δt) = 1/3 (Δ[Zn(OH)2])/(Δt) = 1/2 (Δ[SbH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | Zn3Sb2 | zinc hydroxide | stibine formula | H_2O | Zn3Sb2 | Zn(OH)_2 | SbH_3 Hill formula | H_2O | Sb2Zn3 | H_2O_2Zn | H_3Sb_1 name | water | | zinc hydroxide | stibine IUPAC name | water | | zinc dihydroxide |

| water | Zn3Sb2 | zinc hydroxide | stibine molar mass | 18.015 g/mol | 439.7 g/mol | 99.39 g/mol | 124.78 g/mol phase | liquid (at STP) | | | melting point | 0 °C | | | -88 °C boiling point | 99.9839 °C | | | -17 °C density | 1 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) | | | odor | odorless | | |