KOH + KNO3 + Cr2O4 = H2O + K2CrO4 + KNO2

KOH potassium hydroxide + KNO_3 potassium nitrate + Cr2O4 ⟶ H_2O water + K_2CrO_4 potassium chromate + KNO_2 potassium nitrite

Balance the chemical equation algebraically: KOH + KNO_3 + Cr2O4 ⟶ H_2O + K_2CrO_4 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KNO_3 + c_3 Cr2O4 ⟶ c_4 H_2O + c_5 K_2CrO_4 + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, N and Cr: H: | c_1 = 2 c_4 K: | c_1 + c_2 = 2 c_5 + c_6 O: | c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 2 c_6 N: | c_2 = c_6 Cr: | 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KOH + 2 KNO_3 + Cr2O4 ⟶ 2 H_2O + 2 K_2CrO_4 + 2 KNO_2

+ + Cr2O4 ⟶ + +

potassium hydroxide + potassium nitrate + Cr2O4 ⟶ water + potassium chromate + potassium nitrite

Construct the equilibrium constant, K, expression for: KOH + KNO_3 + Cr2O4 ⟶ H_2O + K_2CrO_4 + KNO_2 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 KOH + 2 KNO_3 + Cr2O4 ⟶ 2 H_2O + 2 K_2CrO_4 + 2 KNO_2 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 | 4 | -4 KNO_3 | 2 | -2 Cr2O4 | 1 | -1 H_2O | 2 | 2 K_2CrO_4 | 2 | 2 KNO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 4 | -4 | ([KOH])^(-4) KNO_3 | 2 | -2 | ([KNO3])^(-2) Cr2O4 | 1 | -1 | ([Cr2O4])^(-1) H_2O | 2 | 2 | ([H2O])^2 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 KNO_2 | 2 | 2 | ([KNO2])^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 = ([KOH])^(-4) ([KNO3])^(-2) ([Cr2O4])^(-1) ([H2O])^2 ([K2CrO4])^2 ([KNO2])^2 = (([H2O])^2 ([K2CrO4])^2 ([KNO2])^2)/(([KOH])^4 ([KNO3])^2 [Cr2O4])

Construct the rate of reaction expression for: KOH + KNO_3 + Cr2O4 ⟶ H_2O + K_2CrO_4 + KNO_2 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 KOH + 2 KNO_3 + Cr2O4 ⟶ 2 H_2O + 2 K_2CrO_4 + 2 KNO_2 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 | 4 | -4 KNO_3 | 2 | -2 Cr2O4 | 1 | -1 H_2O | 2 | 2 K_2CrO_4 | 2 | 2 KNO_2 | 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 KOH | 4 | -4 | -1/4 (Δ[KOH])/(Δt) KNO_3 | 2 | -2 | -1/2 (Δ[KNO3])/(Δt) Cr2O4 | 1 | -1 | -(Δ[Cr2O4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) KNO_2 | 2 | 2 | 1/2 (Δ[KNO2])/(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[KOH])/(Δt) = -1/2 (Δ[KNO3])/(Δt) = -(Δ[Cr2O4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/2 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium nitrate | Cr2O4 | water | potassium chromate | potassium nitrite formula | KOH | KNO_3 | Cr2O4 | H_2O | K_2CrO_4 | KNO_2 Hill formula | HKO | KNO_3 | Cr2O4 | H_2O | CrK_2O_4 | KNO_2 name | potassium hydroxide | potassium nitrate | | water | potassium chromate | potassium nitrite IUPAC name | potassium hydroxide | potassium nitrate | | water | dipotassium dioxido-dioxochromium | potassium nitrite

| potassium hydroxide | potassium nitrate | Cr2O4 | water | potassium chromate | potassium nitrite molar mass | 56.105 g/mol | 101.1 g/mol | 167.99 g/mol | 18.015 g/mol | 194.19 g/mol | 85.103 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 334 °C | | 0 °C | 971 °C | 350 °C boiling point | 1327 °C | | | 99.9839 °C | | density | 2.044 g/cm^3 | | | 1 g/cm^3 | 2.73 g/cm^3 | 1.915 g/cm^3 solubility in water | 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 |