H2SO4 + H2S + K2Cr2O7 = H2O + K2SO4 + Cr2(SO4)3

sulfuric acid + hydrogen sulfide + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate

Balance the chemical equation algebraically: + + ⟶ + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 + 2 c_2 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 12 c_6 S: | c_1 + c_2 = c_5 + 3 c_6 Cr: | 2 c_3 = 2 c_6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 13/3 c_2 = 1 c_3 = 4/3 c_4 = 16/3 c_5 = 4/3 c_6 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 13 c_2 = 3 c_3 = 4 c_4 = 16 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 13 + 3 + 4 ⟶ 16 + 4 + 4

+ + ⟶ + +

sulfuric acid + hydrogen sulfide + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate

K_c = ([H2O]^16 [K2SO4]^4 [Cr2(SO4)3]^4)/([H2SO4]^13 [H2S]^3 [K2Cr2O7]^4)

rate = -1/13 (Δ[H2SO4])/(Δt) = -1/3 (Δ[H2S])/(Δt) = -1/4 (Δ[K2Cr2O7])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/4 (Δ[K2SO4])/(Δt) = 1/4 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | hydrogen sulfide | potassium dichromate | water | potassium sulfate | chromium sulfate Hill formula | H_2O_4S | H_2S | Cr_2K_2O_7 | H_2O | K_2O_4S | Cr_2O_12S_3 name | sulfuric acid | hydrogen sulfide | potassium dichromate | water | potassium sulfate | chromium sulfate IUPAC name | sulfuric acid | hydrogen sulfide | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate