KOH + K2CrO4 + Sn = H2O + K2SnO3 + KCr

KOH potassium hydroxide + K_2CrO_4 potassium chromate + Sn white tin ⟶ H_2O water + K_2O_3Sn potassium stannate + KCr

Balance the chemical equation algebraically: KOH + K_2CrO_4 + Sn ⟶ H_2O + K_2O_3Sn + KCr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 K_2CrO_4 + c_3 Sn ⟶ c_4 H_2O + c_5 K_2O_3Sn + c_6 KCr Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr and Sn: H: | c_1 = 2 c_4 K: | c_1 + 2 c_2 = 2 c_5 + c_6 O: | c_1 + 4 c_2 = c_4 + 3 c_5 Cr: | c_2 = c_6 Sn: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/2 c_2 = 1 c_3 = 7/4 c_4 = 5/4 c_5 = 7/4 c_6 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 10 c_2 = 4 c_3 = 7 c_4 = 5 c_5 = 7 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 KOH + 4 K_2CrO_4 + 7 Sn ⟶ 5 H_2O + 7 K_2O_3Sn + 4 KCr

+ + ⟶ + + KCr

potassium hydroxide + potassium chromate + white tin ⟶ water + potassium stannate + KCr

Construct the equilibrium constant, K, expression for: KOH + K_2CrO_4 + Sn ⟶ H_2O + K_2O_3Sn + KCr 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: 10 KOH + 4 K_2CrO_4 + 7 Sn ⟶ 5 H_2O + 7 K_2O_3Sn + 4 KCr 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 | 10 | -10 K_2CrO_4 | 4 | -4 Sn | 7 | -7 H_2O | 5 | 5 K_2O_3Sn | 7 | 7 KCr | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 10 | -10 | ([KOH])^(-10) K_2CrO_4 | 4 | -4 | ([K2CrO4])^(-4) Sn | 7 | -7 | ([Sn])^(-7) H_2O | 5 | 5 | ([H2O])^5 K_2O_3Sn | 7 | 7 | ([K2O3Sn])^7 KCr | 4 | 4 | ([KCr])^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])^(-10) ([K2CrO4])^(-4) ([Sn])^(-7) ([H2O])^5 ([K2O3Sn])^7 ([KCr])^4 = (([H2O])^5 ([K2O3Sn])^7 ([KCr])^4)/(([KOH])^10 ([K2CrO4])^4 ([Sn])^7)

Construct the rate of reaction expression for: KOH + K_2CrO_4 + Sn ⟶ H_2O + K_2O_3Sn + KCr 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: 10 KOH + 4 K_2CrO_4 + 7 Sn ⟶ 5 H_2O + 7 K_2O_3Sn + 4 KCr 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 | 10 | -10 K_2CrO_4 | 4 | -4 Sn | 7 | -7 H_2O | 5 | 5 K_2O_3Sn | 7 | 7 KCr | 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 | 10 | -10 | -1/10 (Δ[KOH])/(Δt) K_2CrO_4 | 4 | -4 | -1/4 (Δ[K2CrO4])/(Δt) Sn | 7 | -7 | -1/7 (Δ[Sn])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) K_2O_3Sn | 7 | 7 | 1/7 (Δ[K2O3Sn])/(Δt) KCr | 4 | 4 | 1/4 (Δ[KCr])/(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 = -1/10 (Δ[KOH])/(Δt) = -1/4 (Δ[K2CrO4])/(Δt) = -1/7 (Δ[Sn])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/7 (Δ[K2O3Sn])/(Δt) = 1/4 (Δ[KCr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium chromate | white tin | water | potassium stannate | KCr formula | KOH | K_2CrO_4 | Sn | H_2O | K_2O_3Sn | KCr Hill formula | HKO | CrK_2O_4 | Sn | H_2O | K_2O_3Sn | CrK name | potassium hydroxide | potassium chromate | white tin | water | potassium stannate | IUPAC name | potassium hydroxide | dipotassium dioxido-dioxochromium | tin | water | dipotassium dioxido-oxo-tin |

| potassium hydroxide | potassium chromate | white tin | water | potassium stannate | KCr molar mass | 56.105 g/mol | 194.19 g/mol | 118.71 g/mol | 18.015 g/mol | 244.904 g/mol | 91.0944 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | | melting point | 406 °C | 971 °C | 231.9 °C | 0 °C | | boiling point | 1327 °C | | 2602 °C | 99.9839 °C | | density | 2.044 g/cm^3 | 2.73 g/cm^3 | 7.31 g/cm^3 | 1 g/cm^3 | 3.19 g/cm^3 | solubility in water | soluble | soluble | insoluble | | | surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 0.001 Pa s (at 600 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | odorless | odorless | |