S + K2Cr2O7 = K2SO4 + Cr2O3

S mixed sulfur + K_2Cr_2O_7 potassium dichromate ⟶ K_2SO_4 potassium sulfate + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 K_2Cr_2O_7 ⟶ c_3 K_2SO_4 + c_4 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S, Cr, K and O: S: | c_1 = c_3 Cr: | 2 c_2 = 2 c_4 K: | 2 c_2 = 2 c_3 O: | 7 c_2 = 4 c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_3

+ ⟶ +

mixed sulfur + potassium dichromate ⟶ potassium sulfate + chromium(III) oxide

Construct the equilibrium constant, K, expression for: S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_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: S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_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 S | 1 | -1 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 Cr_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 1 | -1 | ([S])^(-1) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] Cr_2O_3 | 1 | 1 | [Cr2O3] 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 = ([S])^(-1) ([K2Cr2O7])^(-1) [K2SO4] [Cr2O3] = ([K2SO4] [Cr2O3])/([S] [K2Cr2O7])

Construct the rate of reaction expression for: S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_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: S + K_2Cr_2O_7 ⟶ K_2SO_4 + Cr_2O_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 S | 1 | -1 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 Cr_2O_3 | 1 | 1 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 S | 1 | -1 | -(Δ[S])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Cr_2O_3 | 1 | 1 | (Δ[Cr2O3])/(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 = -(Δ[S])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | potassium dichromate | potassium sulfate | chromium(III) oxide formula | S | K_2Cr_2O_7 | K_2SO_4 | Cr_2O_3 Hill formula | S | Cr_2K_2O_7 | K_2O_4S | Cr_2O_3 name | mixed sulfur | potassium dichromate | potassium sulfate | chromium(III) oxide IUPAC name | sulfur | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | dipotassium sulfate |

| mixed sulfur | potassium dichromate | potassium sulfate | chromium(III) oxide molar mass | 32.06 g/mol | 294.18 g/mol | 174.25 g/mol | 151.99 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) melting point | 112.8 °C | 398 °C | | 2435 °C boiling point | 444.7 °C | | | 4000 °C density | 2.07 g/cm^3 | 2.67 g/cm^3 | | 4.8 g/cm^3 solubility in water | | | soluble | insoluble odor | | odorless | |