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KOH + Br2 + Cr(OH)3 = H2O + K2Cr2O7 + KBr

Input interpretation

KOH potassium hydroxide + Br_2 bromine + Cr(OH)3 ⟶ H_2O water + K_2Cr_2O_7 potassium dichromate + KBr potassium bromide
KOH potassium hydroxide + Br_2 bromine + Cr(OH)3 ⟶ H_2O water + K_2Cr_2O_7 potassium dichromate + KBr potassium bromide

Balanced equation

Balance the chemical equation algebraically: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Br_2 + c_3 Cr(OH)3 ⟶ c_4 H_2O + c_5 K_2Cr_2O_7 + c_6 KBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Br and Cr: H: | c_1 + 3 c_3 = 2 c_4 K: | c_1 = 2 c_5 + c_6 O: | c_1 + 3 c_3 = c_4 + 7 c_5 Br: | 2 c_2 = c_6 Cr: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 7 c_5 = 1 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr
Balance the chemical equation algebraically: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Br_2 + c_3 Cr(OH)3 ⟶ c_4 H_2O + c_5 K_2Cr_2O_7 + c_6 KBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Br and Cr: H: | c_1 + 3 c_3 = 2 c_4 K: | c_1 = 2 c_5 + c_6 O: | c_1 + 3 c_3 = c_4 + 7 c_5 Br: | 2 c_2 = c_6 Cr: | c_3 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 7 c_5 = 1 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr

Structures

+ + Cr(OH)3 ⟶ + +
+ + Cr(OH)3 ⟶ + +

Names

potassium hydroxide + bromine + Cr(OH)3 ⟶ water + potassium dichromate + potassium bromide
potassium hydroxide + bromine + Cr(OH)3 ⟶ water + potassium dichromate + potassium bromide

Equilibrium constant

Construct the equilibrium constant, K, expression for: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr 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: 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr 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 | 8 | -8 Br_2 | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 7 | 7 K_2Cr_2O_7 | 1 | 1 KBr | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 8 | -8 | ([KOH])^(-8) Br_2 | 3 | -3 | ([Br2])^(-3) Cr(OH)3 | 2 | -2 | ([Cr(OH)3])^(-2) H_2O | 7 | 7 | ([H2O])^7 K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] KBr | 6 | 6 | ([KBr])^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])^(-8) ([Br2])^(-3) ([Cr(OH)3])^(-2) ([H2O])^7 [K2Cr2O7] ([KBr])^6 = (([H2O])^7 [K2Cr2O7] ([KBr])^6)/(([KOH])^8 ([Br2])^3 ([Cr(OH)3])^2)
Construct the equilibrium constant, K, expression for: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr 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: 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr 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 | 8 | -8 Br_2 | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 7 | 7 K_2Cr_2O_7 | 1 | 1 KBr | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 8 | -8 | ([KOH])^(-8) Br_2 | 3 | -3 | ([Br2])^(-3) Cr(OH)3 | 2 | -2 | ([Cr(OH)3])^(-2) H_2O | 7 | 7 | ([H2O])^7 K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] KBr | 6 | 6 | ([KBr])^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])^(-8) ([Br2])^(-3) ([Cr(OH)3])^(-2) ([H2O])^7 [K2Cr2O7] ([KBr])^6 = (([H2O])^7 [K2Cr2O7] ([KBr])^6)/(([KOH])^8 ([Br2])^3 ([Cr(OH)3])^2)

Rate of reaction

Construct the rate of reaction expression for: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr 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: 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr 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 | 8 | -8 Br_2 | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 7 | 7 K_2Cr_2O_7 | 1 | 1 KBr | 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 | 8 | -8 | -1/8 (Δ[KOH])/(Δt) Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) Cr(OH)3 | 2 | -2 | -1/2 (Δ[Cr(OH)3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(Δt) KBr | 6 | 6 | 1/6 (Δ[KBr])/(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 = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[Br2])/(Δt) = -1/2 (Δ[Cr(OH)3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2Cr2O7])/(Δt) = 1/6 (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KOH + Br_2 + Cr(OH)3 ⟶ H_2O + K_2Cr_2O_7 + KBr 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: 8 KOH + 3 Br_2 + 2 Cr(OH)3 ⟶ 7 H_2O + K_2Cr_2O_7 + 6 KBr 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 | 8 | -8 Br_2 | 3 | -3 Cr(OH)3 | 2 | -2 H_2O | 7 | 7 K_2Cr_2O_7 | 1 | 1 KBr | 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 | 8 | -8 | -1/8 (Δ[KOH])/(Δt) Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) Cr(OH)3 | 2 | -2 | -1/2 (Δ[Cr(OH)3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(Δt) KBr | 6 | 6 | 1/6 (Δ[KBr])/(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 = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[Br2])/(Δt) = -1/2 (Δ[Cr(OH)3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2Cr2O7])/(Δt) = 1/6 (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium hydroxide | bromine | Cr(OH)3 | water | potassium dichromate | potassium bromide formula | KOH | Br_2 | Cr(OH)3 | H_2O | K_2Cr_2O_7 | KBr Hill formula | HKO | Br_2 | H3CrO3 | H_2O | Cr_2K_2O_7 | BrK name | potassium hydroxide | bromine | | water | potassium dichromate | potassium bromide IUPAC name | potassium hydroxide | molecular bromine | | water | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium bromide
| potassium hydroxide | bromine | Cr(OH)3 | water | potassium dichromate | potassium bromide formula | KOH | Br_2 | Cr(OH)3 | H_2O | K_2Cr_2O_7 | KBr Hill formula | HKO | Br_2 | H3CrO3 | H_2O | Cr_2K_2O_7 | BrK name | potassium hydroxide | bromine | | water | potassium dichromate | potassium bromide IUPAC name | potassium hydroxide | molecular bromine | | water | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium bromide

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