H2SO4 + NaCl + K2Cr2O7 = H2O + K2SO4 + Na2SO4 + CrO2Cl2

H_2SO_4 sulfuric acid + NaCl sodium chloride + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + CrO_2Cl_2 chromyl chloride

Balance the chemical equation algebraically: H_2SO_4 + NaCl + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + CrO_2Cl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 NaCl + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Na_2SO_4 + c_7 CrO_2Cl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, Na, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 4 c_6 + 2 c_7 S: | c_1 = c_5 + c_6 Cl: | c_2 = 2 c_7 Na: | c_2 = 2 c_6 Cr: | 2 c_3 = c_7 K: | 2 c_3 = 2 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 = 3 c_2 = 4 c_3 = 1 c_4 = 3 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 4 NaCl + K_2Cr_2O_7 ⟶ 3 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 CrO_2Cl_2

+ + ⟶ + + +

sulfuric acid + sodium chloride + potassium dichromate ⟶ water + potassium sulfate + sodium sulfate + chromyl chloride

Construct the equilibrium constant, K, expression for: H_2SO_4 + NaCl + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + CrO_2Cl_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: 3 H_2SO_4 + 4 NaCl + K_2Cr_2O_7 ⟶ 3 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 CrO_2Cl_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 H_2SO_4 | 3 | -3 NaCl | 4 | -4 K_2Cr_2O_7 | 1 | -1 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 CrO_2Cl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) NaCl | 4 | -4 | ([NaCl])^(-4) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 CrO_2Cl_2 | 2 | 2 | ([CrO2Cl2])^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 = ([H2SO4])^(-3) ([NaCl])^(-4) ([K2Cr2O7])^(-1) ([H2O])^3 [K2SO4] ([Na2SO4])^2 ([CrO2Cl2])^2 = (([H2O])^3 [K2SO4] ([Na2SO4])^2 ([CrO2Cl2])^2)/(([H2SO4])^3 ([NaCl])^4 [K2Cr2O7])

Construct the rate of reaction expression for: H_2SO_4 + NaCl + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Na_2SO_4 + CrO_2Cl_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: 3 H_2SO_4 + 4 NaCl + K_2Cr_2O_7 ⟶ 3 H_2O + K_2SO_4 + 2 Na_2SO_4 + 2 CrO_2Cl_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 H_2SO_4 | 3 | -3 NaCl | 4 | -4 K_2Cr_2O_7 | 1 | -1 H_2O | 3 | 3 K_2SO_4 | 1 | 1 Na_2SO_4 | 2 | 2 CrO_2Cl_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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) NaCl | 4 | -4 | -1/4 (Δ[NaCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) CrO_2Cl_2 | 2 | 2 | 1/2 (Δ[CrO2Cl2])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/4 (Δ[NaCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[CrO2Cl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | sodium chloride | potassium dichromate | water | potassium sulfate | sodium sulfate | chromyl chloride formula | H_2SO_4 | NaCl | K_2Cr_2O_7 | H_2O | K_2SO_4 | Na_2SO_4 | CrO_2Cl_2 Hill formula | H_2O_4S | ClNa | Cr_2K_2O_7 | H_2O | K_2O_4S | Na_2O_4S | Cl_2CrO_2 name | sulfuric acid | sodium chloride | potassium dichromate | water | potassium sulfate | sodium sulfate | chromyl chloride IUPAC name | sulfuric acid | sodium chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | disodium sulfate |