HMnO4 + SiH4 = H2O + MnO2 + SiO2

HMnO4 + SiH_4 silane ⟶ H_2O water + MnO_2 manganese dioxide + SiO_2 silicon dioxide

Balance the chemical equation algebraically: HMnO4 + SiH_4 ⟶ H_2O + MnO_2 + SiO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HMnO4 + c_2 SiH_4 ⟶ c_3 H_2O + c_4 MnO_2 + c_5 SiO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Mn, O and Si: H: | c_1 + 4 c_2 = 2 c_3 Mn: | c_1 = c_4 O: | 4 c_1 = c_3 + 2 c_4 + 2 c_5 Si: | c_2 = c_5 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 = 8/3 c_2 = 1 c_3 = 10/3 c_4 = 8/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 10 c_4 = 8 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HMnO4 + 3 SiH_4 ⟶ 10 H_2O + 8 MnO_2 + 3 SiO_2

HMnO4 + ⟶ + +

HMnO4 + silane ⟶ water + manganese dioxide + silicon dioxide

Construct the equilibrium constant, K, expression for: HMnO4 + SiH_4 ⟶ H_2O + MnO_2 + SiO_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: 8 HMnO4 + 3 SiH_4 ⟶ 10 H_2O + 8 MnO_2 + 3 SiO_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 HMnO4 | 8 | -8 SiH_4 | 3 | -3 H_2O | 10 | 10 MnO_2 | 8 | 8 SiO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HMnO4 | 8 | -8 | ([HMnO4])^(-8) SiH_4 | 3 | -3 | ([SiH4])^(-3) H_2O | 10 | 10 | ([H2O])^10 MnO_2 | 8 | 8 | ([MnO2])^8 SiO_2 | 3 | 3 | ([SiO2])^3 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 = ([HMnO4])^(-8) ([SiH4])^(-3) ([H2O])^10 ([MnO2])^8 ([SiO2])^3 = (([H2O])^10 ([MnO2])^8 ([SiO2])^3)/(([HMnO4])^8 ([SiH4])^3)

Construct the rate of reaction expression for: HMnO4 + SiH_4 ⟶ H_2O + MnO_2 + SiO_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: 8 HMnO4 + 3 SiH_4 ⟶ 10 H_2O + 8 MnO_2 + 3 SiO_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 HMnO4 | 8 | -8 SiH_4 | 3 | -3 H_2O | 10 | 10 MnO_2 | 8 | 8 SiO_2 | 3 | 3 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 HMnO4 | 8 | -8 | -1/8 (Δ[HMnO4])/(Δt) SiH_4 | 3 | -3 | -1/3 (Δ[SiH4])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(Δt) SiO_2 | 3 | 3 | 1/3 (Δ[SiO2])/(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 = -1/8 (Δ[HMnO4])/(Δt) = -1/3 (Δ[SiH4])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/8 (Δ[MnO2])/(Δt) = 1/3 (Δ[SiO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| HMnO4 | silane | water | manganese dioxide | silicon dioxide formula | HMnO4 | SiH_4 | H_2O | MnO_2 | SiO_2 Hill formula | HMnO4 | H_4Si | H_2O | MnO_2 | O_2Si name | | silane | water | manganese dioxide | silicon dioxide IUPAC name | | silane | water | dioxomanganese | dioxosilane