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H2O + Na2SO3 + K2CrO4 = KOH + Na2SO4 + KCr(OH)4

Input interpretation

H_2O water + Na_2SO_3 sodium sulfite + K_2CrO_4 potassium chromate ⟶ KOH potassium hydroxide + Na_2SO_4 sodium sulfate + KCr(OH)4
H_2O water + Na_2SO_3 sodium sulfite + K_2CrO_4 potassium chromate ⟶ KOH potassium hydroxide + Na_2SO_4 sodium sulfate + KCr(OH)4

Balanced equation

Balance the chemical equation algebraically: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2SO_3 + c_3 K_2CrO_4 ⟶ c_4 KOH + c_5 Na_2SO_4 + c_6 KCr(OH)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na, S, Cr and K: H: | 2 c_1 = c_4 + 4 c_6 O: | c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 Na: | 2 c_2 = 2 c_5 S: | c_2 = c_5 Cr: | c_3 = c_6 K: | 2 c_3 = c_4 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/2 c_2 = 3/2 c_3 = 1 c_4 = 1 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 3 c_3 = 2 c_4 = 2 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)4
Balance the chemical equation algebraically: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2SO_3 + c_3 K_2CrO_4 ⟶ c_4 KOH + c_5 Na_2SO_4 + c_6 KCr(OH)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na, S, Cr and K: H: | 2 c_1 = c_4 + 4 c_6 O: | c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 Na: | 2 c_2 = 2 c_5 S: | c_2 = c_5 Cr: | c_3 = c_6 K: | 2 c_3 = c_4 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/2 c_2 = 3/2 c_3 = 1 c_4 = 1 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 3 c_3 = 2 c_4 = 2 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)4

Structures

+ + ⟶ + + KCr(OH)4
+ + ⟶ + + KCr(OH)4

Names

water + sodium sulfite + potassium chromate ⟶ potassium hydroxide + sodium sulfate + KCr(OH)4
water + sodium sulfite + potassium chromate ⟶ potassium hydroxide + sodium sulfate + KCr(OH)4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)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: 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)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 | 5 | -5 Na_2SO_3 | 3 | -3 K_2CrO_4 | 2 | -2 KOH | 2 | 2 Na_2SO_4 | 3 | 3 KCr(OH)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 | 5 | -5 | ([H2O])^(-5) Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) KOH | 2 | 2 | ([KOH])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 KCr(OH)4 | 2 | 2 | ([KCr(OH)4])^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])^(-5) ([Na2SO3])^(-3) ([K2CrO4])^(-2) ([KOH])^2 ([Na2SO4])^3 ([KCr(OH)4])^2 = (([KOH])^2 ([Na2SO4])^3 ([KCr(OH)4])^2)/(([H2O])^5 ([Na2SO3])^3 ([K2CrO4])^2)
Construct the equilibrium constant, K, expression for: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)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: 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)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 | 5 | -5 Na_2SO_3 | 3 | -3 K_2CrO_4 | 2 | -2 KOH | 2 | 2 Na_2SO_4 | 3 | 3 KCr(OH)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 | 5 | -5 | ([H2O])^(-5) Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) KOH | 2 | 2 | ([KOH])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 KCr(OH)4 | 2 | 2 | ([KCr(OH)4])^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])^(-5) ([Na2SO3])^(-3) ([K2CrO4])^(-2) ([KOH])^2 ([Na2SO4])^3 ([KCr(OH)4])^2 = (([KOH])^2 ([Na2SO4])^3 ([KCr(OH)4])^2)/(([H2O])^5 ([Na2SO3])^3 ([K2CrO4])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)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: 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)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 | 5 | -5 Na_2SO_3 | 3 | -3 K_2CrO_4 | 2 | -2 KOH | 2 | 2 Na_2SO_4 | 3 | 3 KCr(OH)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 | 5 | -5 | -1/5 (Δ[H2O])/(Δt) Na_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) KCr(OH)4 | 2 | 2 | 1/2 (Δ[KCr(OH)4])/(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 = -1/5 (Δ[H2O])/(Δt) = -1/3 (Δ[Na2SO3])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[KCr(OH)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Na_2SO_3 + K_2CrO_4 ⟶ KOH + Na_2SO_4 + KCr(OH)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: 5 H_2O + 3 Na_2SO_3 + 2 K_2CrO_4 ⟶ 2 KOH + 3 Na_2SO_4 + 2 KCr(OH)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 | 5 | -5 Na_2SO_3 | 3 | -3 K_2CrO_4 | 2 | -2 KOH | 2 | 2 Na_2SO_4 | 3 | 3 KCr(OH)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 | 5 | -5 | -1/5 (Δ[H2O])/(Δt) Na_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) KOH | 2 | 2 | 1/2 (Δ[KOH])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) KCr(OH)4 | 2 | 2 | 1/2 (Δ[KCr(OH)4])/(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 = -1/5 (Δ[H2O])/(Δt) = -1/3 (Δ[Na2SO3])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/2 (Δ[KOH])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[KCr(OH)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | sodium sulfite | potassium chromate | potassium hydroxide | sodium sulfate | KCr(OH)4 formula | H_2O | Na_2SO_3 | K_2CrO_4 | KOH | Na_2SO_4 | KCr(OH)4 Hill formula | H_2O | Na_2O_3S | CrK_2O_4 | HKO | Na_2O_4S | H4CrKO4 name | water | sodium sulfite | potassium chromate | potassium hydroxide | sodium sulfate | IUPAC name | water | disodium sulfite | dipotassium dioxido-dioxochromium | potassium hydroxide | disodium sulfate |
| water | sodium sulfite | potassium chromate | potassium hydroxide | sodium sulfate | KCr(OH)4 formula | H_2O | Na_2SO_3 | K_2CrO_4 | KOH | Na_2SO_4 | KCr(OH)4 Hill formula | H_2O | Na_2O_3S | CrK_2O_4 | HKO | Na_2O_4S | H4CrKO4 name | water | sodium sulfite | potassium chromate | potassium hydroxide | sodium sulfate | IUPAC name | water | disodium sulfite | dipotassium dioxido-dioxochromium | potassium hydroxide | disodium sulfate |

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