KOH + Cr2(SO4)3 + KClO2 = H2O + K2SO4 + KCl + K2CrO4

KOH potassium hydroxide + Cr_2(SO_4)_3 chromium sulfate + KClO2 ⟶ H_2O water + K_2SO_4 potassium sulfate + KCl potassium chloride + K_2CrO_4 potassium chromate

Balance the chemical equation algebraically: KOH + Cr_2(SO_4)_3 + KClO2 ⟶ H_2O + K_2SO_4 + KCl + K_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Cr_2(SO_4)_3 + c_3 KClO2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KCl + 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, Cr, S and Cl: H: | c_1 = 2 c_4 K: | c_1 + c_3 = 2 c_5 + c_6 + 2 c_7 O: | c_1 + 12 c_2 + 2 c_3 = c_4 + 4 c_5 + 4 c_7 Cr: | 2 c_2 = c_7 S: | 3 c_2 = c_5 Cl: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 1 c_3 = 3/2 c_4 = 5 c_5 = 3 c_6 = 3/2 c_7 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 20 c_2 = 2 c_3 = 3 c_4 = 10 c_5 = 6 c_6 = 3 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 20 KOH + 2 Cr_2(SO_4)_3 + 3 KClO2 ⟶ 10 H_2O + 6 K_2SO_4 + 3 KCl + 4 K_2CrO_4

+ + KClO2 ⟶ + + +

potassium hydroxide + chromium sulfate + KClO2 ⟶ water + potassium sulfate + potassium chloride + potassium chromate

Construct the equilibrium constant, K, expression for: KOH + Cr_2(SO_4)_3 + KClO2 ⟶ H_2O + K_2SO_4 + KCl + 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: 20 KOH + 2 Cr_2(SO_4)_3 + 3 KClO2 ⟶ 10 H_2O + 6 K_2SO_4 + 3 KCl + 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 | 20 | -20 Cr_2(SO_4)_3 | 2 | -2 KClO2 | 3 | -3 H_2O | 10 | 10 K_2SO_4 | 6 | 6 KCl | 3 | 3 K_2CrO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 20 | -20 | ([KOH])^(-20) Cr_2(SO_4)_3 | 2 | -2 | ([Cr2(SO4)3])^(-2) KClO2 | 3 | -3 | ([KClO2])^(-3) H_2O | 10 | 10 | ([H2O])^10 K_2SO_4 | 6 | 6 | ([K2SO4])^6 KCl | 3 | 3 | ([KCl])^3 K_2CrO_4 | 4 | 4 | ([K2CrO4])^4 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])^(-20) ([Cr2(SO4)3])^(-2) ([KClO2])^(-3) ([H2O])^10 ([K2SO4])^6 ([KCl])^3 ([K2CrO4])^4 = (([H2O])^10 ([K2SO4])^6 ([KCl])^3 ([K2CrO4])^4)/(([KOH])^20 ([Cr2(SO4)3])^2 ([KClO2])^3)

Construct the rate of reaction expression for: KOH + Cr_2(SO_4)_3 + KClO2 ⟶ H_2O + K_2SO_4 + KCl + 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: 20 KOH + 2 Cr_2(SO_4)_3 + 3 KClO2 ⟶ 10 H_2O + 6 K_2SO_4 + 3 KCl + 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 | 20 | -20 Cr_2(SO_4)_3 | 2 | -2 KClO2 | 3 | -3 H_2O | 10 | 10 K_2SO_4 | 6 | 6 KCl | 3 | 3 K_2CrO_4 | 4 | 4 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 | 20 | -20 | -1/20 (Δ[KOH])/(Δt) Cr_2(SO_4)_3 | 2 | -2 | -1/2 (Δ[Cr2(SO4)3])/(Δt) KClO2 | 3 | -3 | -1/3 (Δ[KClO2])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) K_2SO_4 | 6 | 6 | 1/6 (Δ[K2SO4])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) K_2CrO_4 | 4 | 4 | 1/4 (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 = -1/20 (Δ[KOH])/(Δt) = -1/2 (Δ[Cr2(SO4)3])/(Δt) = -1/3 (Δ[KClO2])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/6 (Δ[K2SO4])/(Δt) = 1/3 (Δ[KCl])/(Δt) = 1/4 (Δ[K2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | chromium sulfate | KClO2 | water | potassium sulfate | potassium chloride | potassium chromate formula | KOH | Cr_2(SO_4)_3 | KClO2 | H_2O | K_2SO_4 | KCl | K_2CrO_4 Hill formula | HKO | Cr_2O_12S_3 | ClKO2 | H_2O | K_2O_4S | ClK | CrK_2O_4 name | potassium hydroxide | chromium sulfate | | water | potassium sulfate | potassium chloride | potassium chromate IUPAC name | potassium hydroxide | chromium(+3) cation trisulfate | | water | dipotassium sulfate | potassium chloride | dipotassium dioxido-dioxochromium

| potassium hydroxide | chromium sulfate | KClO2 | water | potassium sulfate | potassium chloride | potassium chromate molar mass | 56.105 g/mol | 392.2 g/mol | 106.5 g/mol | 18.015 g/mol | 174.25 g/mol | 74.55 g/mol | 194.19 g/mol phase | solid (at STP) | liquid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 406 °C | | | 0 °C | | 770 °C | 971 °C boiling point | 1327 °C | 330 °C | | 99.9839 °C | | 1420 °C | density | 2.044 g/cm^3 | 1.84 g/cm^3 | | 1 g/cm^3 | | 1.98 g/cm^3 | 2.73 g/cm^3 solubility in water | soluble | | | | soluble | soluble | 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 | | odorless | odorless