H2O + KI + K2CrO4 = KOH + I2 + KCrO2

H_2O water + KI potassium iodide + K_2CrO_4 potassium chromate ⟶ KOH potassium hydroxide + I_2 iodine + KCrO2

Balance the chemical equation algebraically: H_2O + KI + K_2CrO_4 ⟶ KOH + I_2 + KCrO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KI + c_3 K_2CrO_4 ⟶ c_4 KOH + c_5 I_2 + c_6 KCrO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I, K and Cr: H: | 2 c_1 = c_4 O: | c_1 + 4 c_3 = c_4 + 2 c_6 I: | c_2 = 2 c_5 K: | c_2 + 2 c_3 = c_4 + c_6 Cr: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 c_4 = 4 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 6 c_3 = 2 c_4 = 8 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + 6 KI + 2 K_2CrO_4 ⟶ 8 KOH + 3 I_2 + 2 KCrO2

+ + ⟶ + + KCrO2

water + potassium iodide + potassium chromate ⟶ potassium hydroxide + iodine + KCrO2

Construct the equilibrium constant, K, expression for: H_2O + KI + K_2CrO_4 ⟶ KOH + I_2 + KCrO2 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: 4 H_2O + 6 KI + 2 K_2CrO_4 ⟶ 8 KOH + 3 I_2 + 2 KCrO2 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 | 4 | -4 KI | 6 | -6 K_2CrO_4 | 2 | -2 KOH | 8 | 8 I_2 | 3 | 3 KCrO2 | 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 | 4 | -4 | ([H2O])^(-4) KI | 6 | -6 | ([KI])^(-6) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) KOH | 8 | 8 | ([KOH])^8 I_2 | 3 | 3 | ([I2])^3 KCrO2 | 2 | 2 | ([KCrO2])^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])^(-4) ([KI])^(-6) ([K2CrO4])^(-2) ([KOH])^8 ([I2])^3 ([KCrO2])^2 = (([KOH])^8 ([I2])^3 ([KCrO2])^2)/(([H2O])^4 ([KI])^6 ([K2CrO4])^2)

Construct the rate of reaction expression for: H_2O + KI + K_2CrO_4 ⟶ KOH + I_2 + KCrO2 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: 4 H_2O + 6 KI + 2 K_2CrO_4 ⟶ 8 KOH + 3 I_2 + 2 KCrO2 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 | 4 | -4 KI | 6 | -6 K_2CrO_4 | 2 | -2 KOH | 8 | 8 I_2 | 3 | 3 KCrO2 | 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) KI | 6 | -6 | -1/6 (Δ[KI])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) KOH | 8 | 8 | 1/8 (Δ[KOH])/(Δt) I_2 | 3 | 3 | 1/3 (Δ[I2])/(Δt) KCrO2 | 2 | 2 | 1/2 (Δ[KCrO2])/(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 = -1/4 (Δ[H2O])/(Δt) = -1/6 (Δ[KI])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/8 (Δ[KOH])/(Δt) = 1/3 (Δ[I2])/(Δt) = 1/2 (Δ[KCrO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium iodide | potassium chromate | potassium hydroxide | iodine | KCrO2 formula | H_2O | KI | K_2CrO_4 | KOH | I_2 | KCrO2 Hill formula | H_2O | IK | CrK_2O_4 | HKO | I_2 | CrKO2 name | water | potassium iodide | potassium chromate | potassium hydroxide | iodine | IUPAC name | water | potassium iodide | dipotassium dioxido-dioxochromium | potassium hydroxide | molecular iodine |

| water | potassium iodide | potassium chromate | potassium hydroxide | iodine | KCrO2 molar mass | 18.015 g/mol | 166.0028 g/mol | 194.19 g/mol | 56.105 g/mol | 253.80894 g/mol | 123.09 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 681 °C | 971 °C | 406 °C | 113 °C | boiling point | 99.9839 °C | 1330 °C | | 1327 °C | 184 °C | density | 1 g/cm^3 | 3.123 g/cm^3 | 2.73 g/cm^3 | 2.044 g/cm^3 | 4.94 g/cm^3 | solubility in water | | | soluble | soluble | | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.0010227 Pa s (at 732.9 °C) | | 0.001 Pa s (at 550 °C) | 0.00227 Pa s (at 116 °C) | odor | odorless | | odorless | | |