HCl + H2S + Na2Cr2O7 = H2O + S + NaCl + CrCl3

HCl hydrogen chloride + H_2S hydrogen sulfide + Na_2Cr_2O_7 sodium bichromate ⟶ H_2O water + S mixed sulfur + NaCl sodium chloride + CrCl_3 chromic chloride

Balance the chemical equation algebraically: HCl + H_2S + Na_2Cr_2O_7 ⟶ H_2O + S + NaCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 H_2S + c_3 Na_2Cr_2O_7 ⟶ c_4 H_2O + c_5 S + c_6 NaCl + c_7 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, S, Cr, Na and O: Cl: | c_1 = c_6 + 3 c_7 H: | c_1 + 2 c_2 = 2 c_4 S: | c_2 = c_5 Cr: | 2 c_3 = c_7 Na: | 2 c_3 = c_6 O: | 7 c_3 = c_4 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 = 8 c_2 = 3 c_3 = 1 c_4 = 7 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 3 H_2S + Na_2Cr_2O_7 ⟶ 7 H_2O + 3 S + 2 NaCl + 2 CrCl_3

+ + ⟶ + + +

hydrogen chloride + hydrogen sulfide + sodium bichromate ⟶ water + mixed sulfur + sodium chloride + chromic chloride

Construct the equilibrium constant, K, expression for: HCl + H_2S + Na_2Cr_2O_7 ⟶ H_2O + S + NaCl + CrCl_3 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: 8 HCl + 3 H_2S + Na_2Cr_2O_7 ⟶ 7 H_2O + 3 S + 2 NaCl + 2 CrCl_3 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 HCl | 8 | -8 H_2S | 3 | -3 Na_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 S | 3 | 3 NaCl | 2 | 2 CrCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) H_2S | 3 | -3 | ([H2S])^(-3) Na_2Cr_2O_7 | 1 | -1 | ([Na2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 S | 3 | 3 | ([S])^3 NaCl | 2 | 2 | ([NaCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^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 = ([HCl])^(-8) ([H2S])^(-3) ([Na2Cr2O7])^(-1) ([H2O])^7 ([S])^3 ([NaCl])^2 ([CrCl3])^2 = (([H2O])^7 ([S])^3 ([NaCl])^2 ([CrCl3])^2)/(([HCl])^8 ([H2S])^3 [Na2Cr2O7])

Construct the rate of reaction expression for: HCl + H_2S + Na_2Cr_2O_7 ⟶ H_2O + S + NaCl + CrCl_3 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: 8 HCl + 3 H_2S + Na_2Cr_2O_7 ⟶ 7 H_2O + 3 S + 2 NaCl + 2 CrCl_3 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 HCl | 8 | -8 H_2S | 3 | -3 Na_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 S | 3 | 3 NaCl | 2 | 2 CrCl_3 | 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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) H_2S | 3 | -3 | -1/3 (Δ[H2S])/(Δt) Na_2Cr_2O_7 | 1 | -1 | -(Δ[Na2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(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 = -1/8 (Δ[HCl])/(Δt) = -1/3 (Δ[H2S])/(Δt) = -(Δ[Na2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | hydrogen sulfide | sodium bichromate | water | mixed sulfur | sodium chloride | chromic chloride formula | HCl | H_2S | Na_2Cr_2O_7 | H_2O | S | NaCl | CrCl_3 Hill formula | ClH | H_2S | Cr_2Na_2O_7 | H_2O | S | ClNa | Cl_3Cr name | hydrogen chloride | hydrogen sulfide | sodium bichromate | water | mixed sulfur | sodium chloride | chromic chloride IUPAC name | hydrogen chloride | hydrogen sulfide | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | water | sulfur | sodium chloride | trichlorochromium

| hydrogen chloride | hydrogen sulfide | sodium bichromate | water | mixed sulfur | sodium chloride | chromic chloride molar mass | 36.46 g/mol | 34.08 g/mol | 261.96 g/mol | 18.015 g/mol | 32.06 g/mol | 58.44 g/mol | 158.3 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | -85 °C | 356.7 °C | 0 °C | 112.8 °C | 801 °C | 1152 °C boiling point | -85 °C | -60 °C | | 99.9839 °C | 444.7 °C | 1413 °C | density | 0.00149 g/cm^3 (at 25 °C) | 0.001393 g/cm^3 (at 25 °C) | 2.35 g/cm^3 | 1 g/cm^3 | 2.07 g/cm^3 | 2.16 g/cm^3 | 2.87 g/cm^3 solubility in water | miscible | | | | | soluble | slightly soluble surface tension | | | | 0.0728 N/m | | | dynamic viscosity | | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | | odorless | | odorless |