H2O + K2Cr2O7 + SiH4 = KOH + Cr(OH)3 + H2SiO3

H_2O water + K_2Cr_2O_7 potassium dichromate + SiH_4 silane ⟶ KOH potassium hydroxide + Cr(OH)3 + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: H_2O + K_2Cr_2O_7 + SiH_4 ⟶ KOH + Cr(OH)3 + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K_2Cr_2O_7 + c_3 SiH_4 ⟶ c_4 KOH + c_5 Cr(OH)3 + c_6 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cr, K and Si: H: | 2 c_1 + 4 c_3 = c_4 + 3 c_5 + 2 c_6 O: | c_1 + 7 c_2 = c_4 + 3 c_5 + 3 c_6 Cr: | 2 c_2 = c_5 K: | 2 c_2 = c_4 Si: | c_3 = 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 = 13/3 c_2 = 4/3 c_3 = 1 c_4 = 8/3 c_5 = 8/3 c_6 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 13 c_2 = 4 c_3 = 3 c_4 = 8 c_5 = 8 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 13 H_2O + 4 K_2Cr_2O_7 + 3 SiH_4 ⟶ 8 KOH + 8 Cr(OH)3 + 3 H_2O_3Si

+ + ⟶ + Cr(OH)3 +

water + potassium dichromate + silane ⟶ potassium hydroxide + Cr(OH)3 + metasilicic acid

Construct the equilibrium constant, K, expression for: H_2O + K_2Cr_2O_7 + SiH_4 ⟶ KOH + Cr(OH)3 + H_2O_3Si 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: 13 H_2O + 4 K_2Cr_2O_7 + 3 SiH_4 ⟶ 8 KOH + 8 Cr(OH)3 + 3 H_2O_3Si 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 | 13 | -13 K_2Cr_2O_7 | 4 | -4 SiH_4 | 3 | -3 KOH | 8 | 8 Cr(OH)3 | 8 | 8 H_2O_3Si | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 13 | -13 | ([H2O])^(-13) K_2Cr_2O_7 | 4 | -4 | ([K2Cr2O7])^(-4) SiH_4 | 3 | -3 | ([SiH4])^(-3) KOH | 8 | 8 | ([KOH])^8 Cr(OH)3 | 8 | 8 | ([Cr(OH)3])^8 H_2O_3Si | 3 | 3 | ([H2O3Si])^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 = ([H2O])^(-13) ([K2Cr2O7])^(-4) ([SiH4])^(-3) ([KOH])^8 ([Cr(OH)3])^8 ([H2O3Si])^3 = (([KOH])^8 ([Cr(OH)3])^8 ([H2O3Si])^3)/(([H2O])^13 ([K2Cr2O7])^4 ([SiH4])^3)

Construct the rate of reaction expression for: H_2O + K_2Cr_2O_7 + SiH_4 ⟶ KOH + Cr(OH)3 + H_2O_3Si 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: 13 H_2O + 4 K_2Cr_2O_7 + 3 SiH_4 ⟶ 8 KOH + 8 Cr(OH)3 + 3 H_2O_3Si 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 | 13 | -13 K_2Cr_2O_7 | 4 | -4 SiH_4 | 3 | -3 KOH | 8 | 8 Cr(OH)3 | 8 | 8 H_2O_3Si | 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 H_2O | 13 | -13 | -1/13 (Δ[H2O])/(Δt) K_2Cr_2O_7 | 4 | -4 | -1/4 (Δ[K2Cr2O7])/(Δt) SiH_4 | 3 | -3 | -1/3 (Δ[SiH4])/(Δt) KOH | 8 | 8 | 1/8 (Δ[KOH])/(Δt) Cr(OH)3 | 8 | 8 | 1/8 (Δ[Cr(OH)3])/(Δt) H_2O_3Si | 3 | 3 | 1/3 (Δ[H2O3Si])/(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 = -1/13 (Δ[H2O])/(Δt) = -1/4 (Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[SiH4])/(Δt) = 1/8 (Δ[KOH])/(Δt) = 1/8 (Δ[Cr(OH)3])/(Δt) = 1/3 (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium dichromate | silane | potassium hydroxide | Cr(OH)3 | metasilicic acid formula | H_2O | K_2Cr_2O_7 | SiH_4 | KOH | Cr(OH)3 | H_2O_3Si Hill formula | H_2O | Cr_2K_2O_7 | H_4Si | HKO | H3CrO3 | H_2O_3Si name | water | potassium dichromate | silane | potassium hydroxide | | metasilicic acid IUPAC name | water | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | silane | potassium hydroxide | | dihydroxy-oxo-silane

| water | potassium dichromate | silane | potassium hydroxide | Cr(OH)3 | metasilicic acid molar mass | 18.015 g/mol | 294.18 g/mol | 32.117 g/mol | 56.105 g/mol | 103.02 g/mol | 78.098 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | | solid (at STP) melting point | 0 °C | 398 °C | -185 °C | 406 °C | | 1704 °C boiling point | 99.9839 °C | | -112 °C | 1327 °C | | density | 1 g/cm^3 | 2.67 g/cm^3 | 0.001313 g/cm^3 (at 25 °C) | 2.044 g/cm^3 | | 1 g/cm^3 solubility in water | | | | soluble | | 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 | | | |