H2S + K2Cr2O7 + H3PO4 = H2O + K3PO4 + S8 + CrPO4

H_2S hydrogen sulfide + K_2Cr_2O_7 potassium dichromate + H_3PO_4 phosphoric acid ⟶ H_2O water + K3PO4 + S_8 rhombic sulfur + O_4PCr chromium(III) phosphate

Balance the chemical equation algebraically: H_2S + K_2Cr_2O_7 + H_3PO_4 ⟶ H_2O + K3PO4 + S_8 + O_4PCr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 K_2Cr_2O_7 + c_3 H_3PO_4 ⟶ c_4 H_2O + c_5 K3PO4 + c_6 S_8 + c_7 O_4PCr Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Cr, K, O and P: H: | 2 c_1 + 3 c_3 = 2 c_4 S: | c_1 = 8 c_6 Cr: | 2 c_2 = c_7 K: | 2 c_2 = 3 c_5 O: | 7 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_7 P: | c_3 = c_5 + c_7 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 8/3 c_3 = 64/9 c_4 = 56/3 c_5 = 16/9 c_6 = 1 c_7 = 16/3 Multiply by the least common denominator, 9, to eliminate fractional coefficients: c_1 = 72 c_2 = 24 c_3 = 64 c_4 = 168 c_5 = 16 c_6 = 9 c_7 = 48 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 72 H_2S + 24 K_2Cr_2O_7 + 64 H_3PO_4 ⟶ 168 H_2O + 16 K3PO4 + 9 S_8 + 48 O_4PCr

+ + ⟶ + K3PO4 + +

hydrogen sulfide + potassium dichromate + phosphoric acid ⟶ water + K3PO4 + rhombic sulfur + chromium(III) phosphate

Construct the equilibrium constant, K, expression for: H_2S + K_2Cr_2O_7 + H_3PO_4 ⟶ H_2O + K3PO4 + S_8 + O_4PCr 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: 72 H_2S + 24 K_2Cr_2O_7 + 64 H_3PO_4 ⟶ 168 H_2O + 16 K3PO4 + 9 S_8 + 48 O_4PCr 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_2S | 72 | -72 K_2Cr_2O_7 | 24 | -24 H_3PO_4 | 64 | -64 H_2O | 168 | 168 K3PO4 | 16 | 16 S_8 | 9 | 9 O_4PCr | 48 | 48 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 72 | -72 | ([H2S])^(-72) K_2Cr_2O_7 | 24 | -24 | ([K2Cr2O7])^(-24) H_3PO_4 | 64 | -64 | ([H3PO4])^(-64) H_2O | 168 | 168 | ([H2O])^168 K3PO4 | 16 | 16 | ([K3PO4])^16 S_8 | 9 | 9 | ([S8])^9 O_4PCr | 48 | 48 | ([O4P1Cr1])^48 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 = ([H2S])^(-72) ([K2Cr2O7])^(-24) ([H3PO4])^(-64) ([H2O])^168 ([K3PO4])^16 ([S8])^9 ([O4P1Cr1])^48 = (([H2O])^168 ([K3PO4])^16 ([S8])^9 ([O4P1Cr1])^48)/(([H2S])^72 ([K2Cr2O7])^24 ([H3PO4])^64)

Construct the rate of reaction expression for: H_2S + K_2Cr_2O_7 + H_3PO_4 ⟶ H_2O + K3PO4 + S_8 + O_4PCr 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: 72 H_2S + 24 K_2Cr_2O_7 + 64 H_3PO_4 ⟶ 168 H_2O + 16 K3PO4 + 9 S_8 + 48 O_4PCr 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_2S | 72 | -72 K_2Cr_2O_7 | 24 | -24 H_3PO_4 | 64 | -64 H_2O | 168 | 168 K3PO4 | 16 | 16 S_8 | 9 | 9 O_4PCr | 48 | 48 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_2S | 72 | -72 | -1/72 (Δ[H2S])/(Δt) K_2Cr_2O_7 | 24 | -24 | -1/24 (Δ[K2Cr2O7])/(Δt) H_3PO_4 | 64 | -64 | -1/64 (Δ[H3PO4])/(Δt) H_2O | 168 | 168 | 1/168 (Δ[H2O])/(Δt) K3PO4 | 16 | 16 | 1/16 (Δ[K3PO4])/(Δt) S_8 | 9 | 9 | 1/9 (Δ[S8])/(Δt) O_4PCr | 48 | 48 | 1/48 (Δ[O4P1Cr1])/(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 = -1/72 (Δ[H2S])/(Δt) = -1/24 (Δ[K2Cr2O7])/(Δt) = -1/64 (Δ[H3PO4])/(Δt) = 1/168 (Δ[H2O])/(Δt) = 1/16 (Δ[K3PO4])/(Δt) = 1/9 (Δ[S8])/(Δt) = 1/48 (Δ[O4P1Cr1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | potassium dichromate | phosphoric acid | water | K3PO4 | rhombic sulfur | chromium(III) phosphate formula | H_2S | K_2Cr_2O_7 | H_3PO_4 | H_2O | K3PO4 | S_8 | O_4PCr Hill formula | H_2S | Cr_2K_2O_7 | H_3O_4P | H_2O | K3O4P | S_8 | CrO_4P name | hydrogen sulfide | potassium dichromate | phosphoric acid | water | | rhombic sulfur | chromium(III) phosphate IUPAC name | hydrogen sulfide | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | phosphoric acid | water | | octathiocane | chromium(3+) phosphate

| hydrogen sulfide | potassium dichromate | phosphoric acid | water | K3PO4 | rhombic sulfur | chromium(III) phosphate molar mass | 34.08 g/mol | 294.18 g/mol | 97.994 g/mol | 18.015 g/mol | 212.26 g/mol | 256.5 g/mol | 146.97 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | | solid (at STP) | melting point | -85 °C | 398 °C | 42.4 °C | 0 °C | | | boiling point | -60 °C | | 158 °C | 99.9839 °C | | | density | 0.001393 g/cm^3 (at 25 °C) | 2.67 g/cm^3 | 1.685 g/cm^3 | 1 g/cm^3 | | 2.07 g/cm^3 | solubility in water | | | very 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 | odorless | | |