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KOH + Cr2O3 + K3Fe(CN)6 = H2O + K2CrO4 + K4Fe(CN)6

Input interpretation

KOH potassium hydroxide + Cr_2O_3 chromium(III) oxide + K_3Fe(CN)_6 potassium hexacyanoferrate(III) ⟶ H_2O water + K_2CrO_4 potassium chromate + K4Fe(CN)6
KOH potassium hydroxide + Cr_2O_3 chromium(III) oxide + K_3Fe(CN)_6 potassium hexacyanoferrate(III) ⟶ H_2O water + K_2CrO_4 potassium chromate + K4Fe(CN)6

Balanced equation

Balance the chemical equation algebraically: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2O_3 + c_3 K_3Fe(CN)_6 ⟶ c_4 H_2O + c_5 K_2CrO_4 + c_6 K4Fe(CN)6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr, C, Fe and N: H: | c_1 = 2 c_4 K: | c_1 + 3 c_3 = 2 c_5 + 4 c_6 O: | c_1 + 3 c_2 = c_4 + 4 c_5 Cr: | 2 c_2 = c_5 C: | 6 c_3 = 6 c_6 Fe: | c_3 = c_6 N: | 6 c_3 = 6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 1 c_3 = 6 c_4 = 5 c_5 = 2 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6
Balance the chemical equation algebraically: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2O_3 + c_3 K_3Fe(CN)_6 ⟶ c_4 H_2O + c_5 K_2CrO_4 + c_6 K4Fe(CN)6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr, C, Fe and N: H: | c_1 = 2 c_4 K: | c_1 + 3 c_3 = 2 c_5 + 4 c_6 O: | c_1 + 3 c_2 = c_4 + 4 c_5 Cr: | 2 c_2 = c_5 C: | 6 c_3 = 6 c_6 Fe: | c_3 = c_6 N: | 6 c_3 = 6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 1 c_3 = 6 c_4 = 5 c_5 = 2 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6

Structures

+ + ⟶ + + K4Fe(CN)6
+ + ⟶ + + K4Fe(CN)6

Names

potassium hydroxide + chromium(III) oxide + potassium hexacyanoferrate(III) ⟶ water + potassium chromate + K4Fe(CN)6
potassium hydroxide + chromium(III) oxide + potassium hexacyanoferrate(III) ⟶ water + potassium chromate + K4Fe(CN)6

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 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: 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6 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 KOH | 10 | -10 Cr_2O_3 | 1 | -1 K_3Fe(CN)_6 | 6 | -6 H_2O | 5 | 5 K_2CrO_4 | 2 | 2 K4Fe(CN)6 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 10 | -10 | ([KOH])^(-10) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) K_3Fe(CN)_6 | 6 | -6 | ([K3Fe(CN)6])^(-6) H_2O | 5 | 5 | ([H2O])^5 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 K4Fe(CN)6 | 6 | 6 | ([K4Fe(CN)6])^6 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 = ([KOH])^(-10) ([Cr2O3])^(-1) ([K3Fe(CN)6])^(-6) ([H2O])^5 ([K2CrO4])^2 ([K4Fe(CN)6])^6 = (([H2O])^5 ([K2CrO4])^2 ([K4Fe(CN)6])^6)/(([KOH])^10 [Cr2O3] ([K3Fe(CN)6])^6)
Construct the equilibrium constant, K, expression for: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 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: 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6 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 KOH | 10 | -10 Cr_2O_3 | 1 | -1 K_3Fe(CN)_6 | 6 | -6 H_2O | 5 | 5 K_2CrO_4 | 2 | 2 K4Fe(CN)6 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 10 | -10 | ([KOH])^(-10) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) K_3Fe(CN)_6 | 6 | -6 | ([K3Fe(CN)6])^(-6) H_2O | 5 | 5 | ([H2O])^5 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 K4Fe(CN)6 | 6 | 6 | ([K4Fe(CN)6])^6 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 = ([KOH])^(-10) ([Cr2O3])^(-1) ([K3Fe(CN)6])^(-6) ([H2O])^5 ([K2CrO4])^2 ([K4Fe(CN)6])^6 = (([H2O])^5 ([K2CrO4])^2 ([K4Fe(CN)6])^6)/(([KOH])^10 [Cr2O3] ([K3Fe(CN)6])^6)

Rate of reaction

Construct the rate of reaction expression for: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 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: 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6 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 KOH | 10 | -10 Cr_2O_3 | 1 | -1 K_3Fe(CN)_6 | 6 | -6 H_2O | 5 | 5 K_2CrO_4 | 2 | 2 K4Fe(CN)6 | 6 | 6 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 KOH | 10 | -10 | -1/10 (Δ[KOH])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) K_3Fe(CN)_6 | 6 | -6 | -1/6 (Δ[K3Fe(CN)6])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) K4Fe(CN)6 | 6 | 6 | 1/6 (Δ[K4Fe(CN)6])/(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 = -1/10 (Δ[KOH])/(Δt) = -(Δ[Cr2O3])/(Δt) = -1/6 (Δ[K3Fe(CN)6])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/6 (Δ[K4Fe(CN)6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + Cr_2O_3 + K_3Fe(CN)_6 ⟶ H_2O + K_2CrO_4 + K4Fe(CN)6 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: 10 KOH + Cr_2O_3 + 6 K_3Fe(CN)_6 ⟶ 5 H_2O + 2 K_2CrO_4 + 6 K4Fe(CN)6 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 KOH | 10 | -10 Cr_2O_3 | 1 | -1 K_3Fe(CN)_6 | 6 | -6 H_2O | 5 | 5 K_2CrO_4 | 2 | 2 K4Fe(CN)6 | 6 | 6 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 KOH | 10 | -10 | -1/10 (Δ[KOH])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) K_3Fe(CN)_6 | 6 | -6 | -1/6 (Δ[K3Fe(CN)6])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) K4Fe(CN)6 | 6 | 6 | 1/6 (Δ[K4Fe(CN)6])/(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 = -1/10 (Δ[KOH])/(Δt) = -(Δ[Cr2O3])/(Δt) = -1/6 (Δ[K3Fe(CN)6])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/6 (Δ[K4Fe(CN)6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | K4Fe(CN)6 formula | KOH | Cr_2O_3 | K_3Fe(CN)_6 | H_2O | K_2CrO_4 | K4Fe(CN)6 Hill formula | HKO | Cr_2O_3 | C_6FeK_3N_6 | H_2O | CrK_2O_4 | C6FeK4N6 name | potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | IUPAC name | potassium hydroxide | | ferric tripotassium hexacyanide | water | dipotassium dioxido-dioxochromium |
| potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | K4Fe(CN)6 formula | KOH | Cr_2O_3 | K_3Fe(CN)_6 | H_2O | K_2CrO_4 | K4Fe(CN)6 Hill formula | HKO | Cr_2O_3 | C_6FeK_3N_6 | H_2O | CrK_2O_4 | C6FeK4N6 name | potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | IUPAC name | potassium hydroxide | | ferric tripotassium hexacyanide | water | dipotassium dioxido-dioxochromium |

Substance properties

| potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | K4Fe(CN)6 molar mass | 56.105 g/mol | 151.99 g/mol | 329.25 g/mol | 18.015 g/mol | 194.19 g/mol | 368.35 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 406 °C | 2435 °C | | 0 °C | 971 °C | boiling point | 1327 °C | 4000 °C | | 99.9839 °C | | density | 2.044 g/cm^3 | 4.8 g/cm^3 | 1.723 g/cm^3 | 1 g/cm^3 | 2.73 g/cm^3 | solubility in water | soluble | insoluble | | | soluble | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | odorless |
| potassium hydroxide | chromium(III) oxide | potassium hexacyanoferrate(III) | water | potassium chromate | K4Fe(CN)6 molar mass | 56.105 g/mol | 151.99 g/mol | 329.25 g/mol | 18.015 g/mol | 194.19 g/mol | 368.35 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 406 °C | 2435 °C | | 0 °C | 971 °C | boiling point | 1327 °C | 4000 °C | | 99.9839 °C | | density | 2.044 g/cm^3 | 4.8 g/cm^3 | 1.723 g/cm^3 | 1 g/cm^3 | 2.73 g/cm^3 | solubility in water | soluble | insoluble | | | soluble | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | odorless |

Units

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