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H2O + Fe = H2 + Fe(OH)3

Input interpretation

H_2O water + Fe iron ⟶ H_2 hydrogen + Fe(OH)_3 iron(III) hydroxide
H_2O water + Fe iron ⟶ H_2 hydrogen + Fe(OH)_3 iron(III) hydroxide

Balanced equation

Balance the chemical equation algebraically: H_2O + Fe ⟶ H_2 + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Fe ⟶ c_3 H_2 + c_4 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Fe: H: | 2 c_1 = 2 c_3 + 3 c_4 O: | c_1 = 3 c_4 Fe: | c_2 = c_4 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 = 3 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3
Balance the chemical equation algebraically: H_2O + Fe ⟶ H_2 + Fe(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Fe ⟶ c_3 H_2 + c_4 Fe(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Fe: H: | 2 c_1 = 2 c_3 + 3 c_4 O: | c_1 = 3 c_4 Fe: | c_2 = c_4 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 = 3 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3

Structures

+ ⟶ +
+ ⟶ +

Names

water + iron ⟶ hydrogen + iron(III) hydroxide
water + iron ⟶ hydrogen + iron(III) hydroxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Fe ⟶ H_2 + Fe(OH)_3 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 + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3 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 Fe | 2 | -2 H_2 | 3 | 3 Fe(OH)_3 | 2 | 2 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) Fe | 2 | -2 | ([Fe])^(-2) H_2 | 3 | 3 | ([H2])^3 Fe(OH)_3 | 2 | 2 | ([Fe(OH)3])^2 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) ([Fe])^(-2) ([H2])^3 ([Fe(OH)3])^2 = (([H2])^3 ([Fe(OH)3])^2)/(([H2O])^6 ([Fe])^2)
Construct the equilibrium constant, K, expression for: H_2O + Fe ⟶ H_2 + Fe(OH)_3 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 + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3 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 Fe | 2 | -2 H_2 | 3 | 3 Fe(OH)_3 | 2 | 2 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) Fe | 2 | -2 | ([Fe])^(-2) H_2 | 3 | 3 | ([H2])^3 Fe(OH)_3 | 2 | 2 | ([Fe(OH)3])^2 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) ([Fe])^(-2) ([H2])^3 ([Fe(OH)3])^2 = (([H2])^3 ([Fe(OH)3])^2)/(([H2O])^6 ([Fe])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + Fe ⟶ H_2 + Fe(OH)_3 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 + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3 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 Fe | 2 | -2 H_2 | 3 | 3 Fe(OH)_3 | 2 | 2 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) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)3])/(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) = -1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Fe ⟶ H_2 + Fe(OH)_3 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 + 2 Fe ⟶ 3 H_2 + 2 Fe(OH)_3 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 Fe | 2 | -2 H_2 | 3 | 3 Fe(OH)_3 | 2 | 2 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) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Fe(OH)_3 | 2 | 2 | 1/2 (Δ[Fe(OH)3])/(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) = -1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[Fe(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | iron | hydrogen | iron(III) hydroxide formula | H_2O | Fe | H_2 | Fe(OH)_3 Hill formula | H_2O | Fe | H_2 | FeH_3O_3 name | water | iron | hydrogen | iron(III) hydroxide IUPAC name | water | iron | molecular hydrogen | ferric trihydroxide
| water | iron | hydrogen | iron(III) hydroxide formula | H_2O | Fe | H_2 | Fe(OH)_3 Hill formula | H_2O | Fe | H_2 | FeH_3O_3 name | water | iron | hydrogen | iron(III) hydroxide IUPAC name | water | iron | molecular hydrogen | ferric trihydroxide

Substance properties

| water | iron | hydrogen | iron(III) hydroxide molar mass | 18.015 g/mol | 55.845 g/mol | 2.016 g/mol | 106.87 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 1535 °C | -259.2 °C | boiling point | 99.9839 °C | 2750 °C | -252.8 °C | density | 1 g/cm^3 | 7.874 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | insoluble | | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |
| water | iron | hydrogen | iron(III) hydroxide molar mass | 18.015 g/mol | 55.845 g/mol | 2.016 g/mol | 106.87 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 1535 °C | -259.2 °C | boiling point | 99.9839 °C | 2750 °C | -252.8 °C | density | 1 g/cm^3 | 7.874 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | insoluble | | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |

Units

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