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H2O + O2 + Ti2(SO4)3 = H2SO4 + Ti(OH)2SO4

Input interpretation

H_2O water + O_2 oxygen + Ti_2(SO_4)_3 titanium(III) sulfate ⟶ H_2SO_4 sulfuric acid + Ti(OH)2SO4
H_2O water + O_2 oxygen + Ti_2(SO_4)_3 titanium(III) sulfate ⟶ H_2SO_4 sulfuric acid + Ti(OH)2SO4

Balanced equation

Balance the chemical equation algebraically: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Ti_2(SO_4)_3 ⟶ c_4 H_2SO_4 + c_5 Ti(OH)2SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Ti: H: | 2 c_1 = 2 c_4 + 2 c_5 O: | c_1 + 2 c_2 + 12 c_3 = 4 c_4 + 6 c_5 S: | 3 c_3 = c_4 + c_5 Ti: | 2 c_3 = 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 = 6 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4
Balance the chemical equation algebraically: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Ti_2(SO_4)_3 ⟶ c_4 H_2SO_4 + c_5 Ti(OH)2SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Ti: H: | 2 c_1 = 2 c_4 + 2 c_5 O: | c_1 + 2 c_2 + 12 c_3 = 4 c_4 + 6 c_5 S: | 3 c_3 = c_4 + c_5 Ti: | 2 c_3 = 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 = 6 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4

Structures

+ + ⟶ + Ti(OH)2SO4
+ + ⟶ + Ti(OH)2SO4

Names

water + oxygen + titanium(III) sulfate ⟶ sulfuric acid + Ti(OH)2SO4
water + oxygen + titanium(III) sulfate ⟶ sulfuric acid + Ti(OH)2SO4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 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 + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4 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 O_2 | 1 | -1 Ti_2(SO_4)_3 | 2 | -2 H_2SO_4 | 2 | 2 Ti(OH)2SO4 | 4 | 4 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) O_2 | 1 | -1 | ([O2])^(-1) Ti_2(SO_4)_3 | 2 | -2 | ([Ti2(SO4)3])^(-2) H_2SO_4 | 2 | 2 | ([H2SO4])^2 Ti(OH)2SO4 | 4 | 4 | ([Ti(OH)2SO4])^4 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) ([O2])^(-1) ([Ti2(SO4)3])^(-2) ([H2SO4])^2 ([Ti(OH)2SO4])^4 = (([H2SO4])^2 ([Ti(OH)2SO4])^4)/(([H2O])^6 [O2] ([Ti2(SO4)3])^2)
Construct the equilibrium constant, K, expression for: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 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 + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4 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 O_2 | 1 | -1 Ti_2(SO_4)_3 | 2 | -2 H_2SO_4 | 2 | 2 Ti(OH)2SO4 | 4 | 4 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) O_2 | 1 | -1 | ([O2])^(-1) Ti_2(SO_4)_3 | 2 | -2 | ([Ti2(SO4)3])^(-2) H_2SO_4 | 2 | 2 | ([H2SO4])^2 Ti(OH)2SO4 | 4 | 4 | ([Ti(OH)2SO4])^4 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) ([O2])^(-1) ([Ti2(SO4)3])^(-2) ([H2SO4])^2 ([Ti(OH)2SO4])^4 = (([H2SO4])^2 ([Ti(OH)2SO4])^4)/(([H2O])^6 [O2] ([Ti2(SO4)3])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 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 + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4 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 O_2 | 1 | -1 Ti_2(SO_4)_3 | 2 | -2 H_2SO_4 | 2 | 2 Ti(OH)2SO4 | 4 | 4 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) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Ti_2(SO_4)_3 | 2 | -2 | -1/2 (Δ[Ti2(SO4)3])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) Ti(OH)2SO4 | 4 | 4 | 1/4 (Δ[Ti(OH)2SO4])/(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[O2])/(Δt) = -1/2 (Δ[Ti2(SO4)3])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/4 (Δ[Ti(OH)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + O_2 + Ti_2(SO_4)_3 ⟶ H_2SO_4 + Ti(OH)2SO4 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 + O_2 + 2 Ti_2(SO_4)_3 ⟶ 2 H_2SO_4 + 4 Ti(OH)2SO4 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 O_2 | 1 | -1 Ti_2(SO_4)_3 | 2 | -2 H_2SO_4 | 2 | 2 Ti(OH)2SO4 | 4 | 4 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) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Ti_2(SO_4)_3 | 2 | -2 | -1/2 (Δ[Ti2(SO4)3])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) Ti(OH)2SO4 | 4 | 4 | 1/4 (Δ[Ti(OH)2SO4])/(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[O2])/(Δt) = -1/2 (Δ[Ti2(SO4)3])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/4 (Δ[Ti(OH)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | oxygen | titanium(III) sulfate | sulfuric acid | Ti(OH)2SO4 formula | H_2O | O_2 | Ti_2(SO_4)_3 | H_2SO_4 | Ti(OH)2SO4 Hill formula | H_2O | O_2 | O_12S_3Ti_2 | H_2O_4S | H2O6STi name | water | oxygen | titanium(III) sulfate | sulfuric acid | IUPAC name | water | molecular oxygen | titanium(+3) cation trisulfate | sulfuric acid |
| water | oxygen | titanium(III) sulfate | sulfuric acid | Ti(OH)2SO4 formula | H_2O | O_2 | Ti_2(SO_4)_3 | H_2SO_4 | Ti(OH)2SO4 Hill formula | H_2O | O_2 | O_12S_3Ti_2 | H_2O_4S | H2O6STi name | water | oxygen | titanium(III) sulfate | sulfuric acid | IUPAC name | water | molecular oxygen | titanium(+3) cation trisulfate | sulfuric acid |

Substance properties

| water | oxygen | titanium(III) sulfate | sulfuric acid | Ti(OH)2SO4 molar mass | 18.015 g/mol | 31.998 g/mol | 383.9 g/mol | 98.07 g/mol | 177.94 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | melting point | 0 °C | -218 °C | | 10.371 °C | boiling point | 99.9839 °C | -183 °C | | 279.6 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.456 g/cm^3 | 1.8305 g/cm^3 | solubility in water | | | | very soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | 0.0735 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 0.021 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |
| water | oxygen | titanium(III) sulfate | sulfuric acid | Ti(OH)2SO4 molar mass | 18.015 g/mol | 31.998 g/mol | 383.9 g/mol | 98.07 g/mol | 177.94 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | melting point | 0 °C | -218 °C | | 10.371 °C | boiling point | 99.9839 °C | -183 °C | | 279.6 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.456 g/cm^3 | 1.8305 g/cm^3 | solubility in water | | | | very soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | 0.0735 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 0.021 Pa s (at 25 °C) | odor | odorless | odorless | | odorless |

Units

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