H2SO4 + K2Cr2O7 + KF = H2O + K2SO4 + Cr2(SO4)3 + F2

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + KF potassium fluoride ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + F_2 fluorine

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + KF ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + F_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 KF ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 F_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K and F: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_2 = c_4 + 4 c_5 + 12 c_6 S: | c_1 = c_5 + 3 c_6 Cr: | 2 c_2 = 2 c_6 K: | 2 c_2 + c_3 = 2 c_5 F: | c_3 = 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 = 7 c_2 = 1 c_3 = 6 c_4 = 7 c_5 = 4 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + K_2Cr_2O_7 + 6 KF ⟶ 7 H_2O + 4 K_2SO_4 + Cr_2(SO_4)_3 + 3 F_2

+ + ⟶ + + +

sulfuric acid + potassium dichromate + potassium fluoride ⟶ water + potassium sulfate + chromium sulfate + fluorine

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + KF ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + F_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: 7 H_2SO_4 + K_2Cr_2O_7 + 6 KF ⟶ 7 H_2O + 4 K_2SO_4 + Cr_2(SO_4)_3 + 3 F_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 | 7 | -7 K_2Cr_2O_7 | 1 | -1 KF | 6 | -6 H_2O | 7 | 7 K_2SO_4 | 4 | 4 Cr_2(SO_4)_3 | 1 | 1 F_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 7 | -7 | ([H2SO4])^(-7) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KF | 6 | -6 | ([KF])^(-6) H_2O | 7 | 7 | ([H2O])^7 K_2SO_4 | 4 | 4 | ([K2SO4])^4 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] F_2 | 3 | 3 | ([F2])^3 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])^(-7) ([K2Cr2O7])^(-1) ([KF])^(-6) ([H2O])^7 ([K2SO4])^4 [Cr2(SO4)3] ([F2])^3 = (([H2O])^7 ([K2SO4])^4 [Cr2(SO4)3] ([F2])^3)/(([H2SO4])^7 [K2Cr2O7] ([KF])^6)

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + KF ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + F_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: 7 H_2SO_4 + K_2Cr_2O_7 + 6 KF ⟶ 7 H_2O + 4 K_2SO_4 + Cr_2(SO_4)_3 + 3 F_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 | 7 | -7 K_2Cr_2O_7 | 1 | -1 KF | 6 | -6 H_2O | 7 | 7 K_2SO_4 | 4 | 4 Cr_2(SO_4)_3 | 1 | 1 F_2 | 3 | 3 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KF | 6 | -6 | -1/6 (Δ[KF])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) K_2SO_4 | 4 | 4 | 1/4 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) F_2 | 3 | 3 | 1/3 (Δ[F2])/(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 = -1/7 (Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/6 (Δ[KF])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/4 (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[F2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium dichromate | potassium fluoride | water | potassium sulfate | chromium sulfate | fluorine formula | H_2SO_4 | K_2Cr_2O_7 | KF | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | F_2 Hill formula | H_2O_4S | Cr_2K_2O_7 | FK | H_2O | K_2O_4S | Cr_2O_12S_3 | F_2 name | sulfuric acid | potassium dichromate | potassium fluoride | water | potassium sulfate | chromium sulfate | fluorine IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium fluoride | water | dipotassium sulfate | chromium(+3) cation trisulfate | molecular fluorine

| sulfuric acid | potassium dichromate | potassium fluoride | water | potassium sulfate | chromium sulfate | fluorine molar mass | 98.07 g/mol | 294.18 g/mol | 58.0967 g/mol | 18.015 g/mol | 174.25 g/mol | 392.2 g/mol | 37.996806326 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | | liquid (at STP) | gas (at STP) melting point | 10.371 °C | 398 °C | 858 °C | 0 °C | | | -219.6 °C boiling point | 279.6 °C | | 1505 °C | 99.9839 °C | | 330 °C | -188.12 °C density | 1.8305 g/cm^3 | 2.67 g/cm^3 | 1.89 g/cm^3 | 1 g/cm^3 | | 1.84 g/cm^3 | 0.001696 g/cm^3 (at 0 °C) solubility in water | very soluble | | | | soluble | | reacts surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | 2.344×10^-5 Pa s (at 25 °C) odor | odorless | odorless | | odorless | | odorless |