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Fe(OH)3 + Cr = Fe(OH)2 + Cr(OH)3

Input interpretation

Fe(OH)_3 iron(III) hydroxide + Cr chromium ⟶ Fe(OH)_2 iron(II) hydroxide + Cr(OH)3
Fe(OH)_3 iron(III) hydroxide + Cr chromium ⟶ Fe(OH)_2 iron(II) hydroxide + Cr(OH)3

Balanced equation

Balance the chemical equation algebraically: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe(OH)_3 + c_2 Cr ⟶ c_3 Fe(OH)_2 + c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, H, O and Cr: Fe: | c_1 = c_3 H: | 3 c_1 = 2 c_3 + 3 c_4 O: | 3 c_1 = 2 c_3 + 3 c_4 Cr: | 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 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(OH)3
Balance the chemical equation algebraically: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe(OH)_3 + c_2 Cr ⟶ c_3 Fe(OH)_2 + c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, H, O and Cr: Fe: | c_1 = c_3 H: | 3 c_1 = 2 c_3 + 3 c_4 O: | 3 c_1 = 2 c_3 + 3 c_4 Cr: | 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 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(OH)3

Structures

+ ⟶ + Cr(OH)3
+ ⟶ + Cr(OH)3

Names

iron(III) hydroxide + chromium ⟶ iron(II) hydroxide + Cr(OH)3
iron(III) hydroxide + chromium ⟶ iron(II) hydroxide + Cr(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(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: 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(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 Fe(OH)_3 | 3 | -3 Cr | 1 | -1 Fe(OH)_2 | 3 | 3 Cr(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe(OH)_3 | 3 | -3 | ([Fe(OH)3])^(-3) Cr | 1 | -1 | ([Cr])^(-1) Fe(OH)_2 | 3 | 3 | ([Fe(OH)2])^3 Cr(OH)3 | 1 | 1 | [Cr(OH)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 = ([Fe(OH)3])^(-3) ([Cr])^(-1) ([Fe(OH)2])^3 [Cr(OH)3] = (([Fe(OH)2])^3 [Cr(OH)3])/(([Fe(OH)3])^3 [Cr])
Construct the equilibrium constant, K, expression for: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(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: 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(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 Fe(OH)_3 | 3 | -3 Cr | 1 | -1 Fe(OH)_2 | 3 | 3 Cr(OH)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe(OH)_3 | 3 | -3 | ([Fe(OH)3])^(-3) Cr | 1 | -1 | ([Cr])^(-1) Fe(OH)_2 | 3 | 3 | ([Fe(OH)2])^3 Cr(OH)3 | 1 | 1 | [Cr(OH)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 = ([Fe(OH)3])^(-3) ([Cr])^(-1) ([Fe(OH)2])^3 [Cr(OH)3] = (([Fe(OH)2])^3 [Cr(OH)3])/(([Fe(OH)3])^3 [Cr])

Rate of reaction

Construct the rate of reaction expression for: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(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: 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(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 Fe(OH)_3 | 3 | -3 Cr | 1 | -1 Fe(OH)_2 | 3 | 3 Cr(OH)3 | 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 Fe(OH)_3 | 3 | -3 | -1/3 (Δ[Fe(OH)3])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) Fe(OH)_2 | 3 | 3 | 1/3 (Δ[Fe(OH)2])/(Δt) Cr(OH)3 | 1 | 1 | (Δ[Cr(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 = -1/3 (Δ[Fe(OH)3])/(Δt) = -(Δ[Cr])/(Δt) = 1/3 (Δ[Fe(OH)2])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Fe(OH)_3 + Cr ⟶ Fe(OH)_2 + Cr(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: 3 Fe(OH)_3 + Cr ⟶ 3 Fe(OH)_2 + Cr(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 Fe(OH)_3 | 3 | -3 Cr | 1 | -1 Fe(OH)_2 | 3 | 3 Cr(OH)3 | 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 Fe(OH)_3 | 3 | -3 | -1/3 (Δ[Fe(OH)3])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) Fe(OH)_2 | 3 | 3 | 1/3 (Δ[Fe(OH)2])/(Δt) Cr(OH)3 | 1 | 1 | (Δ[Cr(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 = -1/3 (Δ[Fe(OH)3])/(Δt) = -(Δ[Cr])/(Δt) = 1/3 (Δ[Fe(OH)2])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| iron(III) hydroxide | chromium | iron(II) hydroxide | Cr(OH)3 formula | Fe(OH)_3 | Cr | Fe(OH)_2 | Cr(OH)3 Hill formula | FeH_3O_3 | Cr | FeH_2O_2 | H3CrO3 name | iron(III) hydroxide | chromium | iron(II) hydroxide | IUPAC name | ferric trihydroxide | chromium | ferrous dihydroxide |
| iron(III) hydroxide | chromium | iron(II) hydroxide | Cr(OH)3 formula | Fe(OH)_3 | Cr | Fe(OH)_2 | Cr(OH)3 Hill formula | FeH_3O_3 | Cr | FeH_2O_2 | H3CrO3 name | iron(III) hydroxide | chromium | iron(II) hydroxide | IUPAC name | ferric trihydroxide | chromium | ferrous dihydroxide |

Substance properties

| iron(III) hydroxide | chromium | iron(II) hydroxide | Cr(OH)3 molar mass | 106.87 g/mol | 51.9961 g/mol | 89.86 g/mol | 103.02 g/mol phase | | solid (at STP) | | melting point | | 1857 °C | | boiling point | | 2672 °C | | density | | 7.14 g/cm^3 | | solubility in water | | insoluble | | odor | | odorless | |
| iron(III) hydroxide | chromium | iron(II) hydroxide | Cr(OH)3 molar mass | 106.87 g/mol | 51.9961 g/mol | 89.86 g/mol | 103.02 g/mol phase | | solid (at STP) | | melting point | | 1857 °C | | boiling point | | 2672 °C | | density | | 7.14 g/cm^3 | | solubility in water | | insoluble | | odor | | odorless | |

Units

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