H2SO4 + Si = H2O + SO2 + H2SiO3

H_2SO_4 sulfuric acid + Si silicon ⟶ H_2O water + SO_2 sulfur dioxide + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: H_2SO_4 + Si ⟶ H_2O + SO_2 + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Si ⟶ c_3 H_2O + c_4 SO_2 + c_5 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Si: H: | 2 c_1 = 2 c_3 + 2 c_5 O: | 4 c_1 = c_3 + 2 c_4 + 3 c_5 S: | c_1 = c_4 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 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + Si ⟶ H_2O + 2 SO_2 + H_2O_3Si

+ ⟶ + +

sulfuric acid + silicon ⟶ water + sulfur dioxide + metasilicic acid

| sulfuric acid | silicon | water | sulfur dioxide | metasilicic acid molecular enthalpy | -814 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -296.8 kJ/mol | -1189 kJ/mol total enthalpy | -1628 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -593.6 kJ/mol | -1189 kJ/mol | H_initial = -1628 kJ/mol | | H_final = -2068 kJ/mol | | ΔH_rxn^0 | -2068 kJ/mol - -1628 kJ/mol = -440.1 kJ/mol (exothermic) | | | |

Construct the equilibrium constant, K, expression for: H_2SO_4 + Si ⟶ H_2O + SO_2 + 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: 2 H_2SO_4 + Si ⟶ H_2O + 2 SO_2 + 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_2SO_4 | 2 | -2 Si | 1 | -1 H_2O | 1 | 1 SO_2 | 2 | 2 H_2O_3Si | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) Si | 1 | -1 | ([Si])^(-1) H_2O | 1 | 1 | [H2O] SO_2 | 2 | 2 | ([SO2])^2 H_2O_3Si | 1 | 1 | [H2O3Si] 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 = ([H2SO4])^(-2) ([Si])^(-1) [H2O] ([SO2])^2 [H2O3Si] = ([H2O] ([SO2])^2 [H2O3Si])/(([H2SO4])^2 [Si])

Construct the rate of reaction expression for: H_2SO_4 + Si ⟶ H_2O + SO_2 + 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: 2 H_2SO_4 + Si ⟶ H_2O + 2 SO_2 + 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_2SO_4 | 2 | -2 Si | 1 | -1 H_2O | 1 | 1 SO_2 | 2 | 2 H_2O_3Si | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) Si | 1 | -1 | -(Δ[Si])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) H_2O_3Si | 1 | 1 | (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 = -1/2 (Δ[H2SO4])/(Δt) = -(Δ[Si])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[SO2])/(Δt) = (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | silicon | water | sulfur dioxide | metasilicic acid formula | H_2SO_4 | Si | H_2O | SO_2 | H_2O_3Si Hill formula | H_2O_4S | Si | H_2O | O_2S | H_2O_3Si name | sulfuric acid | silicon | water | sulfur dioxide | metasilicic acid IUPAC name | sulfuric acid | silicon | water | sulfur dioxide | dihydroxy-oxo-silane