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KOH + KClO3 + Cr2O3 = H2O + Cl2 + K2CrO4

Input interpretation

KOH potassium hydroxide + KClO_3 potassium chlorate + Cr_2O_3 chromium(III) oxide ⟶ H_2O water + Cl_2 chlorine + K_2CrO_4 potassium chromate
KOH potassium hydroxide + KClO_3 potassium chlorate + Cr_2O_3 chromium(III) oxide ⟶ H_2O water + Cl_2 chlorine + K_2CrO_4 potassium chromate

Balanced equation

Balance the chemical equation algebraically: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KClO_3 + c_3 Cr_2O_3 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl and Cr: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_6 O: | c_1 + 3 c_2 + 3 c_3 = c_4 + 4 c_6 Cl: | c_2 = 2 c_5 Cr: | 2 c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14/3 c_2 = 2 c_3 = 5/3 c_4 = 7/3 c_5 = 1 c_6 = 10/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 14 c_2 = 6 c_3 = 5 c_4 = 7 c_5 = 3 c_6 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 K_2CrO_4
Balance the chemical equation algebraically: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KClO_3 + c_3 Cr_2O_3 ⟶ c_4 H_2O + c_5 Cl_2 + c_6 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl and Cr: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_6 O: | c_1 + 3 c_2 + 3 c_3 = c_4 + 4 c_6 Cl: | c_2 = 2 c_5 Cr: | 2 c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14/3 c_2 = 2 c_3 = 5/3 c_4 = 7/3 c_5 = 1 c_6 = 10/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 14 c_2 = 6 c_3 = 5 c_4 = 7 c_5 = 3 c_6 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 K_2CrO_4

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

potassium hydroxide + potassium chlorate + chromium(III) oxide ⟶ water + chlorine + potassium chromate
potassium hydroxide + potassium chlorate + chromium(III) oxide ⟶ water + chlorine + potassium chromate

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + 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: 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 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 KOH | 14 | -14 KClO_3 | 6 | -6 Cr_2O_3 | 5 | -5 H_2O | 7 | 7 Cl_2 | 3 | 3 K_2CrO_4 | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 14 | -14 | ([KOH])^(-14) KClO_3 | 6 | -6 | ([KClO3])^(-6) Cr_2O_3 | 5 | -5 | ([Cr2O3])^(-5) H_2O | 7 | 7 | ([H2O])^7 Cl_2 | 3 | 3 | ([Cl2])^3 K_2CrO_4 | 10 | 10 | ([K2CrO4])^10 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])^(-14) ([KClO3])^(-6) ([Cr2O3])^(-5) ([H2O])^7 ([Cl2])^3 ([K2CrO4])^10 = (([H2O])^7 ([Cl2])^3 ([K2CrO4])^10)/(([KOH])^14 ([KClO3])^6 ([Cr2O3])^5)
Construct the equilibrium constant, K, expression for: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + 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: 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 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 KOH | 14 | -14 KClO_3 | 6 | -6 Cr_2O_3 | 5 | -5 H_2O | 7 | 7 Cl_2 | 3 | 3 K_2CrO_4 | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 14 | -14 | ([KOH])^(-14) KClO_3 | 6 | -6 | ([KClO3])^(-6) Cr_2O_3 | 5 | -5 | ([Cr2O3])^(-5) H_2O | 7 | 7 | ([H2O])^7 Cl_2 | 3 | 3 | ([Cl2])^3 K_2CrO_4 | 10 | 10 | ([K2CrO4])^10 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])^(-14) ([KClO3])^(-6) ([Cr2O3])^(-5) ([H2O])^7 ([Cl2])^3 ([K2CrO4])^10 = (([H2O])^7 ([Cl2])^3 ([K2CrO4])^10)/(([KOH])^14 ([KClO3])^6 ([Cr2O3])^5)

Rate of reaction

Construct the rate of reaction expression for: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + 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: 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 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 KOH | 14 | -14 KClO_3 | 6 | -6 Cr_2O_3 | 5 | -5 H_2O | 7 | 7 Cl_2 | 3 | 3 K_2CrO_4 | 10 | 10 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 | 14 | -14 | -1/14 (Δ[KOH])/(Δt) KClO_3 | 6 | -6 | -1/6 (Δ[KClO3])/(Δt) Cr_2O_3 | 5 | -5 | -1/5 (Δ[Cr2O3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(Δt) K_2CrO_4 | 10 | 10 | 1/10 (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 = -1/14 (Δ[KOH])/(Δt) = -1/6 (Δ[KClO3])/(Δt) = -1/5 (Δ[Cr2O3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/10 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + KClO_3 + Cr_2O_3 ⟶ H_2O + Cl_2 + 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: 14 KOH + 6 KClO_3 + 5 Cr_2O_3 ⟶ 7 H_2O + 3 Cl_2 + 10 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 KOH | 14 | -14 KClO_3 | 6 | -6 Cr_2O_3 | 5 | -5 H_2O | 7 | 7 Cl_2 | 3 | 3 K_2CrO_4 | 10 | 10 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 | 14 | -14 | -1/14 (Δ[KOH])/(Δt) KClO_3 | 6 | -6 | -1/6 (Δ[KClO3])/(Δt) Cr_2O_3 | 5 | -5 | -1/5 (Δ[Cr2O3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(Δt) K_2CrO_4 | 10 | 10 | 1/10 (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 = -1/14 (Δ[KOH])/(Δt) = -1/6 (Δ[KClO3])/(Δt) = -1/5 (Δ[Cr2O3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/10 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate formula | KOH | KClO_3 | Cr_2O_3 | H_2O | Cl_2 | K_2CrO_4 Hill formula | HKO | ClKO_3 | Cr_2O_3 | H_2O | Cl_2 | CrK_2O_4 name | potassium hydroxide | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate IUPAC name | potassium hydroxide | potassium chlorate | | water | molecular chlorine | dipotassium dioxido-dioxochromium
| potassium hydroxide | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate formula | KOH | KClO_3 | Cr_2O_3 | H_2O | Cl_2 | K_2CrO_4 Hill formula | HKO | ClKO_3 | Cr_2O_3 | H_2O | Cl_2 | CrK_2O_4 name | potassium hydroxide | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate IUPAC name | potassium hydroxide | potassium chlorate | | water | molecular chlorine | dipotassium dioxido-dioxochromium

Substance properties

| potassium hydroxide | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate molar mass | 56.105 g/mol | 122.5 g/mol | 151.99 g/mol | 18.015 g/mol | 70.9 g/mol | 194.19 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 406 °C | 356 °C | 2435 °C | 0 °C | -101 °C | 971 °C boiling point | 1327 °C | | 4000 °C | 99.9839 °C | -34 °C | density | 2.044 g/cm^3 | 2.34 g/cm^3 | 4.8 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 2.73 g/cm^3 solubility in water | soluble | 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 | potassium chlorate | chromium(III) oxide | water | chlorine | potassium chromate molar mass | 56.105 g/mol | 122.5 g/mol | 151.99 g/mol | 18.015 g/mol | 70.9 g/mol | 194.19 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 406 °C | 356 °C | 2435 °C | 0 °C | -101 °C | 971 °C boiling point | 1327 °C | | 4000 °C | 99.9839 °C | -34 °C | density | 2.044 g/cm^3 | 2.34 g/cm^3 | 4.8 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 2.73 g/cm^3 solubility in water | soluble | 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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