CaSO4 + CoBr3 = CaBr2 + Co2(SO4)3

CaSO_4 calcium sulfate + CoBr3 ⟶ CaBr_2 calcium bromide + Co2(SO4)3

Balance the chemical equation algebraically: CaSO_4 + CoBr3 ⟶ CaBr_2 + Co2(SO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaSO_4 + c_2 CoBr3 ⟶ c_3 CaBr_2 + c_4 Co2(SO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O, S, Co and Br: Ca: | c_1 = c_3 O: | 4 c_1 = 12 c_4 S: | c_1 = 3 c_4 Co: | c_2 = 2 c_4 Br: | 3 c_2 = 2 c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CaSO_4 + 2 CoBr3 ⟶ 3 CaBr_2 + Co2(SO4)3

+ CoBr3 ⟶ + Co2(SO4)3

calcium sulfate + CoBr3 ⟶ calcium bromide + Co2(SO4)3

Construct the equilibrium constant, K, expression for: CaSO_4 + CoBr3 ⟶ CaBr_2 + Co2(SO4)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: 3 CaSO_4 + 2 CoBr3 ⟶ 3 CaBr_2 + Co2(SO4)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 CaSO_4 | 3 | -3 CoBr3 | 2 | -2 CaBr_2 | 3 | 3 Co2(SO4)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaSO_4 | 3 | -3 | ([CaSO4])^(-3) CoBr3 | 2 | -2 | ([CoBr3])^(-2) CaBr_2 | 3 | 3 | ([CaBr2])^3 Co2(SO4)3 | 1 | 1 | [Co2(SO4)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 = ([CaSO4])^(-3) ([CoBr3])^(-2) ([CaBr2])^3 [Co2(SO4)3] = (([CaBr2])^3 [Co2(SO4)3])/(([CaSO4])^3 ([CoBr3])^2)

Construct the rate of reaction expression for: CaSO_4 + CoBr3 ⟶ CaBr_2 + Co2(SO4)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: 3 CaSO_4 + 2 CoBr3 ⟶ 3 CaBr_2 + Co2(SO4)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 CaSO_4 | 3 | -3 CoBr3 | 2 | -2 CaBr_2 | 3 | 3 Co2(SO4)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 CaSO_4 | 3 | -3 | -1/3 (Δ[CaSO4])/(Δt) CoBr3 | 2 | -2 | -1/2 (Δ[CoBr3])/(Δt) CaBr_2 | 3 | 3 | 1/3 (Δ[CaBr2])/(Δt) Co2(SO4)3 | 1 | 1 | (Δ[Co2(SO4)3])/(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 = -1/3 (Δ[CaSO4])/(Δt) = -1/2 (Δ[CoBr3])/(Δt) = 1/3 (Δ[CaBr2])/(Δt) = (Δ[Co2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium sulfate | CoBr3 | calcium bromide | Co2(SO4)3 formula | CaSO_4 | CoBr3 | CaBr_2 | Co2(SO4)3 Hill formula | CaO_4S | Br3Co | Br_2Ca | Co2O12S3 name | calcium sulfate | | calcium bromide | IUPAC name | calcium sulfate | | calcium dibromide |

| calcium sulfate | CoBr3 | calcium bromide | Co2(SO4)3 molar mass | 136.13 g/mol | 298.65 g/mol | 199.89 g/mol | 406 g/mol phase | | | solid (at STP) | melting point | | | 730 °C | boiling point | | | 810 °C | density | | | 3.353 g/cm^3 | solubility in water | slightly soluble | | soluble | odor | odorless | | |