H2SO4 + K2Cr2O7 + H2O2 = H2O + O2 + Cr2(SO4)3 + KHSO4

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + H_2O_2 hydrogen peroxide ⟶ H_2O water + O_2 oxygen + Cr_2(SO_4)_3 chromium sulfate + KHSO_4 potassium bisulfate

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + Cr_2(SO_4)_3 + KHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 Cr_2(SO_4)_3 + c_7 KHSO_4 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_3 = 2 c_4 + c_7 O: | 4 c_1 + 7 c_2 + 2 c_3 = c_4 + 2 c_5 + 12 c_6 + 4 c_7 S: | c_1 = 3 c_6 + c_7 Cr: | 2 c_2 = 2 c_6 K: | 2 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 1 c_4 = c_3 + 4 c_5 = c_3/2 + 3/2 c_6 = 1 c_7 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_3 = 1 and solve for the remaining coefficients: c_1 = 5 c_2 = 1 c_3 = 1 c_4 = 5 c_5 = 2 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + Cr_2(SO_4)_3 + 2 KHSO_4

+ + ⟶ + + +

sulfuric acid + potassium dichromate + hydrogen peroxide ⟶ water + oxygen + chromium sulfate + potassium bisulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + Cr_2(SO_4)_3 + KHSO_4 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: 5 H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + Cr_2(SO_4)_3 + 2 KHSO_4 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 | 5 | -5 K_2Cr_2O_7 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 KHSO_4 | 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 | 5 | -5 | ([H2SO4])^(-5) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 5 | 5 | ([H2O])^5 O_2 | 2 | 2 | ([O2])^2 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] KHSO_4 | 2 | 2 | ([KHSO4])^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])^(-5) ([K2Cr2O7])^(-1) ([H2O2])^(-1) ([H2O])^5 ([O2])^2 [Cr2(SO4)3] ([KHSO4])^2 = (([H2O])^5 ([O2])^2 [Cr2(SO4)3] ([KHSO4])^2)/(([H2SO4])^5 [K2Cr2O7] [H2O2])

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + Cr_2(SO_4)_3 + KHSO_4 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: 5 H_2SO_4 + K_2Cr_2O_7 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + Cr_2(SO_4)_3 + 2 KHSO_4 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 | 5 | -5 K_2Cr_2O_7 | 1 | -1 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 Cr_2(SO_4)_3 | 1 | 1 KHSO_4 | 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 | 5 | -5 | -1/5 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) KHSO_4 | 2 | 2 | 1/2 (Δ[KHSO4])/(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 = -1/5 (Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -(Δ[H2O2])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium dichromate | hydrogen peroxide | water | oxygen | chromium sulfate | potassium bisulfate formula | H_2SO_4 | K_2Cr_2O_7 | H_2O_2 | H_2O | O_2 | Cr_2(SO_4)_3 | KHSO_4 Hill formula | H_2O_4S | Cr_2K_2O_7 | H_2O_2 | H_2O | O_2 | Cr_2O_12S_3 | HKO_4S name | sulfuric acid | potassium dichromate | hydrogen peroxide | water | oxygen | chromium sulfate | potassium bisulfate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | hydrogen peroxide | water | molecular oxygen | chromium(+3) cation trisulfate | potassium hydrogen sulfate

| sulfuric acid | potassium dichromate | hydrogen peroxide | water | oxygen | chromium sulfate | potassium bisulfate molar mass | 98.07 g/mol | 294.18 g/mol | 34.014 g/mol | 18.015 g/mol | 31.998 g/mol | 392.2 g/mol | 136.16 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | 398 °C | -0.43 °C | 0 °C | -218 °C | | 214 °C boiling point | 279.6 °C | | 150.2 °C | 99.9839 °C | -183 °C | 330 °C | density | 1.8305 g/cm^3 | 2.67 g/cm^3 | 1.44 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.84 g/cm^3 | 2.32 g/cm^3 solubility in water | very soluble | | miscible | | | | surface tension | 0.0735 N/m | | 0.0804 N/m | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 0.001249 Pa s (at 20 °C) | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | | odorless | odorless | odorless |