Input interpretation
KOH potassium hydroxide + KMnO_4 potassium permanganate + CrCl_3 chromic chloride ⟶ H_2O water + KCl potassium chloride + K_2MnO_4 potassium manganate + K_2CrO_4 potassium chromate
Balanced equation
Balance the chemical equation algebraically: KOH + KMnO_4 + CrCl_3 ⟶ H_2O + KCl + K_2MnO_4 + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 CrCl_3 ⟶ c_4 H_2O + c_5 KCl + c_6 K_2MnO_4 + c_7 K_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn, Cl and Cr: H: | c_1 = 2 c_4 K: | c_1 + c_2 = c_5 + 2 c_6 + 2 c_7 O: | c_1 + 4 c_2 = c_4 + 4 c_6 + 4 c_7 Mn: | c_2 = c_6 Cl: | 3 c_3 = c_5 Cr: | c_3 = c_7 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 = 8 c_2 = 3 c_3 = 1 c_4 = 4 c_5 = 3 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 3 KMnO_4 + CrCl_3 ⟶ 4 H_2O + 3 KCl + 3 K_2MnO_4 + K_2CrO_4
Structures
+ + ⟶ + + +
Names
potassium hydroxide + potassium permanganate + chromic chloride ⟶ water + potassium chloride + potassium manganate + potassium chromate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + CrCl_3 ⟶ H_2O + KCl + K_2MnO_4 + 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: 8 KOH + 3 KMnO_4 + CrCl_3 ⟶ 4 H_2O + 3 KCl + 3 K_2MnO_4 + 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 | 8 | -8 KMnO_4 | 3 | -3 CrCl_3 | 1 | -1 H_2O | 4 | 4 KCl | 3 | 3 K_2MnO_4 | 3 | 3 K_2CrO_4 | 1 | 1 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) KMnO_4 | 3 | -3 | ([KMnO4])^(-3) CrCl_3 | 1 | -1 | ([CrCl3])^(-1) H_2O | 4 | 4 | ([H2O])^4 KCl | 3 | 3 | ([KCl])^3 K_2MnO_4 | 3 | 3 | ([K2MnO4])^3 K_2CrO_4 | 1 | 1 | [K2CrO4] 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) ([KMnO4])^(-3) ([CrCl3])^(-1) ([H2O])^4 ([KCl])^3 ([K2MnO4])^3 [K2CrO4] = (([H2O])^4 ([KCl])^3 ([K2MnO4])^3 [K2CrO4])/(([KOH])^8 ([KMnO4])^3 [CrCl3])](../image_source/5726c11f53db33cd2e92cd3c189fea7f.png)
Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + CrCl_3 ⟶ H_2O + KCl + K_2MnO_4 + 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: 8 KOH + 3 KMnO_4 + CrCl_3 ⟶ 4 H_2O + 3 KCl + 3 K_2MnO_4 + 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 | 8 | -8 KMnO_4 | 3 | -3 CrCl_3 | 1 | -1 H_2O | 4 | 4 KCl | 3 | 3 K_2MnO_4 | 3 | 3 K_2CrO_4 | 1 | 1 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) KMnO_4 | 3 | -3 | ([KMnO4])^(-3) CrCl_3 | 1 | -1 | ([CrCl3])^(-1) H_2O | 4 | 4 | ([H2O])^4 KCl | 3 | 3 | ([KCl])^3 K_2MnO_4 | 3 | 3 | ([K2MnO4])^3 K_2CrO_4 | 1 | 1 | [K2CrO4] 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) ([KMnO4])^(-3) ([CrCl3])^(-1) ([H2O])^4 ([KCl])^3 ([K2MnO4])^3 [K2CrO4] = (([H2O])^4 ([KCl])^3 ([K2MnO4])^3 [K2CrO4])/(([KOH])^8 ([KMnO4])^3 [CrCl3])
Rate of reaction
![Construct the rate of reaction expression for: KOH + KMnO_4 + CrCl_3 ⟶ H_2O + KCl + K_2MnO_4 + 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: 8 KOH + 3 KMnO_4 + CrCl_3 ⟶ 4 H_2O + 3 KCl + 3 K_2MnO_4 + 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 | 8 | -8 KMnO_4 | 3 | -3 CrCl_3 | 1 | -1 H_2O | 4 | 4 KCl | 3 | 3 K_2MnO_4 | 3 | 3 K_2CrO_4 | 1 | 1 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) KMnO_4 | 3 | -3 | -1/3 (Δ[KMnO4])/(Δt) CrCl_3 | 1 | -1 | -(Δ[CrCl3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) K_2MnO_4 | 3 | 3 | 1/3 (Δ[K2MnO4])/(Δt) K_2CrO_4 | 1 | 1 | (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 = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[KMnO4])/(Δt) = -(Δ[CrCl3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = 1/3 (Δ[K2MnO4])/(Δt) = (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/f7205b0ca7696ac9d421b4fd55ceaaed.png)
Construct the rate of reaction expression for: KOH + KMnO_4 + CrCl_3 ⟶ H_2O + KCl + K_2MnO_4 + 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: 8 KOH + 3 KMnO_4 + CrCl_3 ⟶ 4 H_2O + 3 KCl + 3 K_2MnO_4 + 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 | 8 | -8 KMnO_4 | 3 | -3 CrCl_3 | 1 | -1 H_2O | 4 | 4 KCl | 3 | 3 K_2MnO_4 | 3 | 3 K_2CrO_4 | 1 | 1 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) KMnO_4 | 3 | -3 | -1/3 (Δ[KMnO4])/(Δt) CrCl_3 | 1 | -1 | -(Δ[CrCl3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) K_2MnO_4 | 3 | 3 | 1/3 (Δ[K2MnO4])/(Δt) K_2CrO_4 | 1 | 1 | (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 = -1/8 (Δ[KOH])/(Δt) = -1/3 (Δ[KMnO4])/(Δt) = -(Δ[CrCl3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = 1/3 (Δ[K2MnO4])/(Δt) = (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| potassium hydroxide | potassium permanganate | chromic chloride | water | potassium chloride | potassium manganate | potassium chromate formula | KOH | KMnO_4 | CrCl_3 | H_2O | KCl | K_2MnO_4 | K_2CrO_4 Hill formula | HKO | KMnO_4 | Cl_3Cr | H_2O | ClK | K_2MnO_4 | CrK_2O_4 name | potassium hydroxide | potassium permanganate | chromic chloride | water | potassium chloride | potassium manganate | potassium chromate IUPAC name | potassium hydroxide | potassium permanganate | trichlorochromium | water | potassium chloride | dipotassium dioxido-dioxomanganese | dipotassium dioxido-dioxochromium