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H2O2 + K3[Cr(OH)6] = H2O + KOH + K2CrO4

Input interpretation

H_2O_2 hydrogen peroxide + K3Cr(OH)6 ⟶ H_2O water + KOH potassium hydroxide + K_2CrO_4 potassium chromate
H_2O_2 hydrogen peroxide + K3Cr(OH)6 ⟶ H_2O water + KOH potassium hydroxide + K_2CrO_4 potassium chromate

Balanced equation

Balance the chemical equation algebraically: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 K3Cr(OH)6 ⟶ c_3 H_2O + c_4 KOH + c_5 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and Cr: H: | 2 c_1 + 6 c_2 = 2 c_3 + c_4 O: | 2 c_1 + 6 c_2 = c_3 + c_4 + 4 c_5 K: | 3 c_2 = c_4 + 2 c_5 Cr: | 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 = 3/2 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 8 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4
Balance the chemical equation algebraically: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 K3Cr(OH)6 ⟶ c_3 H_2O + c_4 KOH + c_5 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and Cr: H: | 2 c_1 + 6 c_2 = 2 c_3 + c_4 O: | 2 c_1 + 6 c_2 = c_3 + c_4 + 4 c_5 K: | 3 c_2 = c_4 + 2 c_5 Cr: | 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 = 3/2 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 8 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4

Structures

+ K3Cr(OH)6 ⟶ + +
+ K3Cr(OH)6 ⟶ + +

Names

hydrogen peroxide + K3Cr(OH)6 ⟶ water + potassium hydroxide + potassium chromate
hydrogen peroxide + K3Cr(OH)6 ⟶ water + potassium hydroxide + potassium chromate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 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 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4 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_2 | 3 | -3 K3Cr(OH)6 | 2 | -2 H_2O | 8 | 8 KOH | 2 | 2 K_2CrO_4 | 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_2 | 3 | -3 | ([H2O2])^(-3) K3Cr(OH)6 | 2 | -2 | ([K3Cr(OH)6])^(-2) H_2O | 8 | 8 | ([H2O])^8 KOH | 2 | 2 | ([KOH])^2 K_2CrO_4 | 2 | 2 | ([K2CrO4])^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 = ([H2O2])^(-3) ([K3Cr(OH)6])^(-2) ([H2O])^8 ([KOH])^2 ([K2CrO4])^2 = (([H2O])^8 ([KOH])^2 ([K2CrO4])^2)/(([H2O2])^3 ([K3Cr(OH)6])^2)
Construct the equilibrium constant, K, expression for: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 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 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4 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_2 | 3 | -3 K3Cr(OH)6 | 2 | -2 H_2O | 8 | 8 KOH | 2 | 2 K_2CrO_4 | 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_2 | 3 | -3 | ([H2O2])^(-3) K3Cr(OH)6 | 2 | -2 | ([K3Cr(OH)6])^(-2) H_2O | 8 | 8 | ([H2O])^8 KOH | 2 | 2 | ([KOH])^2 K_2CrO_4 | 2 | 2 | ([K2CrO4])^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 = ([H2O2])^(-3) ([K3Cr(OH)6])^(-2) ([H2O])^8 ([KOH])^2 ([K2CrO4])^2 = (([H2O])^8 ([KOH])^2 ([K2CrO4])^2)/(([H2O2])^3 ([K3Cr(OH)6])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 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 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4 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_2 | 3 | -3 K3Cr(OH)6 | 2 | -2 H_2O | 8 | 8 KOH | 2 | 2 K_2CrO_4 | 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_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) K3Cr(OH)6 | 2 | -2 | -1/2 (Δ[K3Cr(OH)6])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(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[H2O2])/(Δt) = -1/2 (Δ[K3Cr(OH)6])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O_2 + K3Cr(OH)6 ⟶ H_2O + KOH + K_2CrO_4 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 H_2O_2 + 2 K3Cr(OH)6 ⟶ 8 H_2O + 2 KOH + 2 K_2CrO_4 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_2 | 3 | -3 K3Cr(OH)6 | 2 | -2 H_2O | 8 | 8 KOH | 2 | 2 K_2CrO_4 | 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_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) K3Cr(OH)6 | 2 | -2 | -1/2 (Δ[K3Cr(OH)6])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(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[H2O2])/(Δt) = -1/2 (Δ[K3Cr(OH)6])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen peroxide | K3Cr(OH)6 | water | potassium hydroxide | potassium chromate formula | H_2O_2 | K3Cr(OH)6 | H_2O | KOH | K_2CrO_4 Hill formula | H_2O_2 | H6CrK3O6 | H_2O | HKO | CrK_2O_4 name | hydrogen peroxide | | water | potassium hydroxide | potassium chromate IUPAC name | hydrogen peroxide | | water | potassium hydroxide | dipotassium dioxido-dioxochromium
| hydrogen peroxide | K3Cr(OH)6 | water | potassium hydroxide | potassium chromate formula | H_2O_2 | K3Cr(OH)6 | H_2O | KOH | K_2CrO_4 Hill formula | H_2O_2 | H6CrK3O6 | H_2O | HKO | CrK_2O_4 name | hydrogen peroxide | | water | potassium hydroxide | potassium chromate IUPAC name | hydrogen peroxide | | water | potassium hydroxide | dipotassium dioxido-dioxochromium

Substance properties

| hydrogen peroxide | K3Cr(OH)6 | water | potassium hydroxide | potassium chromate molar mass | 34.014 g/mol | 271.33 g/mol | 18.015 g/mol | 56.105 g/mol | 194.19 g/mol phase | liquid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -0.43 °C | | 0 °C | 406 °C | 971 °C boiling point | 150.2 °C | | 99.9839 °C | 1327 °C | density | 1.44 g/cm^3 | | 1 g/cm^3 | 2.044 g/cm^3 | 2.73 g/cm^3 solubility in water | miscible | | | soluble | soluble surface tension | 0.0804 N/m | | 0.0728 N/m | | dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | odor | | | odorless | | odorless
| hydrogen peroxide | K3Cr(OH)6 | water | potassium hydroxide | potassium chromate molar mass | 34.014 g/mol | 271.33 g/mol | 18.015 g/mol | 56.105 g/mol | 194.19 g/mol phase | liquid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -0.43 °C | | 0 °C | 406 °C | 971 °C boiling point | 150.2 °C | | 99.9839 °C | 1327 °C | density | 1.44 g/cm^3 | | 1 g/cm^3 | 2.044 g/cm^3 | 2.73 g/cm^3 solubility in water | miscible | | | soluble | soluble surface tension | 0.0804 N/m | | 0.0728 N/m | | dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | odor | | | odorless | | odorless

Units

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