KMnO4 + SiH4 = H2O + KOH + MnO2 + SiO2

KMnO_4 potassium permanganate + SiH_4 silane ⟶ H_2O water + KOH potassium hydroxide + MnO_2 manganese dioxide + SiO_2 silicon dioxide

Balance the chemical equation algebraically: KMnO_4 + SiH_4 ⟶ H_2O + KOH + MnO_2 + SiO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 SiH_4 ⟶ c_3 H_2O + c_4 KOH + c_5 MnO_2 + c_6 SiO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, H and Si: K: | c_1 = c_4 Mn: | c_1 = c_5 O: | 4 c_1 = c_3 + c_4 + 2 c_5 + 2 c_6 H: | 4 c_2 = 2 c_3 + c_4 Si: | c_2 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3/2 c_3 = 1 c_4 = 4 c_5 = 4 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 8 c_5 = 8 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KMnO_4 + 3 SiH_4 ⟶ 2 H_2O + 8 KOH + 8 MnO_2 + 3 SiO_2

+ ⟶ + + +

potassium permanganate + silane ⟶ water + potassium hydroxide + manganese dioxide + silicon dioxide

Construct the equilibrium constant, K, expression for: KMnO_4 + SiH_4 ⟶ H_2O + KOH + 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 KMnO_4 + 3 SiH_4 ⟶ 2 H_2O + 8 KOH + 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 KMnO_4 | 8 | -8 SiH_4 | 3 | -3 H_2O | 2 | 2 KOH | 8 | 8 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 KMnO_4 | 8 | -8 | ([KMnO4])^(-8) SiH_4 | 3 | -3 | ([SiH4])^(-3) H_2O | 2 | 2 | ([H2O])^2 KOH | 8 | 8 | ([KOH])^8 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 = ([KMnO4])^(-8) ([SiH4])^(-3) ([H2O])^2 ([KOH])^8 ([MnO2])^8 ([SiO2])^3 = (([H2O])^2 ([KOH])^8 ([MnO2])^8 ([SiO2])^3)/(([KMnO4])^8 ([SiH4])^3)

Construct the rate of reaction expression for: KMnO_4 + SiH_4 ⟶ H_2O + KOH + 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 KMnO_4 + 3 SiH_4 ⟶ 2 H_2O + 8 KOH + 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 KMnO_4 | 8 | -8 SiH_4 | 3 | -3 H_2O | 2 | 2 KOH | 8 | 8 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 KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) SiH_4 | 3 | -3 | -1/3 (Δ[SiH4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) KOH | 8 | 8 | 1/8 (Δ[KOH])/(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[KMnO4])/(Δt) = -1/3 (Δ[SiH4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/8 (Δ[KOH])/(Δt) = 1/8 (Δ[MnO2])/(Δt) = 1/3 (Δ[SiO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | silane | water | potassium hydroxide | manganese dioxide | silicon dioxide formula | KMnO_4 | SiH_4 | H_2O | KOH | MnO_2 | SiO_2 Hill formula | KMnO_4 | H_4Si | H_2O | HKO | MnO_2 | O_2Si name | potassium permanganate | silane | water | potassium hydroxide | manganese dioxide | silicon dioxide IUPAC name | potassium permanganate | silane | water | potassium hydroxide | dioxomanganese | dioxosilane

| potassium permanganate | silane | water | potassium hydroxide | manganese dioxide | silicon dioxide molar mass | 158.03 g/mol | 32.117 g/mol | 18.015 g/mol | 56.105 g/mol | 86.936 g/mol | 60.083 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 240 °C | -185 °C | 0 °C | 406 °C | 535 °C | 1713 °C boiling point | | -112 °C | 99.9839 °C | 1327 °C | | 2950 °C density | 1 g/cm^3 | 0.001313 g/cm^3 (at 25 °C) | 1 g/cm^3 | 2.044 g/cm^3 | 5.03 g/cm^3 | 2.196 g/cm^3 solubility in water | | | | soluble | insoluble | insoluble surface tension | | | 0.0728 N/m | | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | | odor | odorless | | odorless | | | odorless