KOH + K2Cr2O7 + BaCl2 = H2O + KCl + BaCrO4

KOH potassium hydroxide + K_2Cr_2O_7 potassium dichromate + BaCl_2 barium chloride ⟶ H_2O water + KCl potassium chloride + BaCrO_4 barium chromate

Balance the chemical equation algebraically: KOH + K_2Cr_2O_7 + BaCl_2 ⟶ H_2O + KCl + BaCrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 K_2Cr_2O_7 + c_3 BaCl_2 ⟶ c_4 H_2O + c_5 KCl + c_6 BaCrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cr, Ba and Cl: H: | c_1 = 2 c_4 K: | c_1 + 2 c_2 = c_5 O: | c_1 + 7 c_2 = c_4 + 4 c_6 Cr: | 2 c_2 = c_6 Ba: | c_3 = c_6 Cl: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + K_2Cr_2O_7 + 2 BaCl_2 ⟶ H_2O + 4 KCl + 2 BaCrO_4

+ + ⟶ + +

potassium hydroxide + potassium dichromate + barium chloride ⟶ water + potassium chloride + barium chromate

Construct the equilibrium constant, K, expression for: KOH + K_2Cr_2O_7 + BaCl_2 ⟶ H_2O + KCl + BaCrO_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: 2 KOH + K_2Cr_2O_7 + 2 BaCl_2 ⟶ H_2O + 4 KCl + 2 BaCrO_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 | 2 | -2 K_2Cr_2O_7 | 1 | -1 BaCl_2 | 2 | -2 H_2O | 1 | 1 KCl | 4 | 4 BaCrO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) BaCl_2 | 2 | -2 | ([BaCl2])^(-2) H_2O | 1 | 1 | [H2O] KCl | 4 | 4 | ([KCl])^4 BaCrO_4 | 2 | 2 | ([BaCrO4])^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])^(-2) ([K2Cr2O7])^(-1) ([BaCl2])^(-2) [H2O] ([KCl])^4 ([BaCrO4])^2 = ([H2O] ([KCl])^4 ([BaCrO4])^2)/(([KOH])^2 [K2Cr2O7] ([BaCl2])^2)

Construct the rate of reaction expression for: KOH + K_2Cr_2O_7 + BaCl_2 ⟶ H_2O + KCl + BaCrO_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: 2 KOH + K_2Cr_2O_7 + 2 BaCl_2 ⟶ H_2O + 4 KCl + 2 BaCrO_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 | 2 | -2 K_2Cr_2O_7 | 1 | -1 BaCl_2 | 2 | -2 H_2O | 1 | 1 KCl | 4 | 4 BaCrO_4 | 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 | 2 | -2 | -1/2 (Δ[KOH])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) BaCl_2 | 2 | -2 | -1/2 (Δ[BaCl2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KCl | 4 | 4 | 1/4 (Δ[KCl])/(Δt) BaCrO_4 | 2 | 2 | 1/2 (Δ[BaCrO4])/(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 = -1/2 (Δ[KOH])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[BaCl2])/(Δt) = (Δ[H2O])/(Δt) = 1/4 (Δ[KCl])/(Δt) = 1/2 (Δ[BaCrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium dichromate | barium chloride | water | potassium chloride | barium chromate formula | KOH | K_2Cr_2O_7 | BaCl_2 | H_2O | KCl | BaCrO_4 Hill formula | HKO | Cr_2K_2O_7 | BaCl_2 | H_2O | ClK | BaCrO_4 name | potassium hydroxide | potassium dichromate | barium chloride | water | potassium chloride | barium chromate IUPAC name | potassium hydroxide | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | barium(+2) cation dichloride | water | potassium chloride | barium(+2) cation; dioxido-dioxochromium

| potassium hydroxide | potassium dichromate | barium chloride | water | potassium chloride | barium chromate molar mass | 56.105 g/mol | 294.18 g/mol | 208.2 g/mol | 18.015 g/mol | 74.55 g/mol | 253.32 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 398 °C | 963 °C | 0 °C | 770 °C | 210 °C boiling point | 1327 °C | | | 99.9839 °C | 1420 °C | density | 2.044 g/cm^3 | 2.67 g/cm^3 | 3.856 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | 4.5 g/cm^3 solubility in water | 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 |