CH3COOH + K2CrO4 = H2O + K2Cr2O7 + CH3COOK

CH_3CO_2H (acetic acid) + K_2CrO_4 (potassium chromate) ⟶ H_2O (water) + K_2Cr_2O_7 (potassium dichromate) + CH_3COOK (potassium acetate)

Balance the chemical equation algebraically: CH_3CO_2H + K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + CH_3COOK Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CO_2H + c_2 K_2CrO_4 ⟶ c_3 H_2O + c_4 K_2Cr_2O_7 + c_5 CH_3COOK Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O, Cr and K: C: | 2 c_1 = 2 c_5 H: | 4 c_1 = 2 c_3 + 3 c_5 O: | 2 c_1 + 4 c_2 = c_3 + 7 c_4 + 2 c_5 Cr: | c_2 = 2 c_4 K: | 2 c_2 = 2 c_4 + 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 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 CH_3CO_2H + 2 K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + 2 CH_3COOK

+ ⟶ + +

acetic acid + potassium chromate ⟶ water + potassium dichromate + potassium acetate

Construct the equilibrium constant, K, expression for: CH_3CO_2H + K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + CH_3COOK 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 CH_3CO_2H + 2 K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + 2 CH_3COOK 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 CH_3CO_2H | 2 | -2 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2Cr_2O_7 | 1 | 1 CH_3COOK | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3CO_2H | 2 | -2 | ([CH3CO2H])^(-2) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) H_2O | 1 | 1 | [H2O] K_2Cr_2O_7 | 1 | 1 | [K2Cr2O7] CH_3COOK | 2 | 2 | ([CH3COOK])^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 = ([CH3CO2H])^(-2) ([K2CrO4])^(-2) [H2O] [K2Cr2O7] ([CH3COOK])^2 = ([H2O] [K2Cr2O7] ([CH3COOK])^2)/(([CH3CO2H])^2 ([K2CrO4])^2)

Construct the rate of reaction expression for: CH_3CO_2H + K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + CH_3COOK 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 CH_3CO_2H + 2 K_2CrO_4 ⟶ H_2O + K_2Cr_2O_7 + 2 CH_3COOK 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 CH_3CO_2H | 2 | -2 K_2CrO_4 | 2 | -2 H_2O | 1 | 1 K_2Cr_2O_7 | 1 | 1 CH_3COOK | 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 CH_3CO_2H | 2 | -2 | -1/2 (Δ[CH3CO2H])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) K_2Cr_2O_7 | 1 | 1 | (Δ[K2Cr2O7])/(Δt) CH_3COOK | 2 | 2 | 1/2 (Δ[CH3COOK])/(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[CH3CO2H])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[K2Cr2O7])/(Δt) = 1/2 (Δ[CH3COOK])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| acetic acid | potassium chromate | water | potassium dichromate | potassium acetate formula | CH_3CO_2H | K_2CrO_4 | H_2O | K_2Cr_2O_7 | CH_3COOK Hill formula | C_2H_4O_2 | CrK_2O_4 | H_2O | Cr_2K_2O_7 | C_2H_3KO_2 name | acetic acid | potassium chromate | water | potassium dichromate | potassium acetate IUPAC name | acetic acid | dipotassium dioxido-dioxochromium | water | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium acetate