K2SO4 + Al2(SO4)3 = KAl(SO4)2

K_2SO_4 potassium sulfate + Al_2(SO_4)_3 aluminum sulfate ⟶ AlKO_8S_2 potassium alum

Balance the chemical equation algebraically: K_2SO_4 + Al_2(SO_4)_3 ⟶ AlKO_8S_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2SO_4 + c_2 Al_2(SO_4)_3 ⟶ c_3 AlKO_8S_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, O, S and Al: K: | 2 c_1 = c_3 O: | 4 c_1 + 12 c_2 = 8 c_3 S: | c_1 + 3 c_2 = 2 c_3 Al: | 2 c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2SO_4 + Al_2(SO_4)_3 ⟶ 2 AlKO_8S_2

+ ⟶

potassium sulfate + aluminum sulfate ⟶ potassium alum

Construct the equilibrium constant, K, expression for: K_2SO_4 + Al_2(SO_4)_3 ⟶ AlKO_8S_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: K_2SO_4 + Al_2(SO_4)_3 ⟶ 2 AlKO_8S_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 K_2SO_4 | 1 | -1 Al_2(SO_4)_3 | 1 | -1 AlKO_8S_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2SO_4 | 1 | -1 | ([K2SO4])^(-1) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) AlKO_8S_2 | 2 | 2 | ([AlKO8S2])^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 = ([K2SO4])^(-1) ([Al2(SO4)3])^(-1) ([AlKO8S2])^2 = ([AlKO8S2])^2/([K2SO4] [Al2(SO4)3])

Construct the rate of reaction expression for: K_2SO_4 + Al_2(SO_4)_3 ⟶ AlKO_8S_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: K_2SO_4 + Al_2(SO_4)_3 ⟶ 2 AlKO_8S_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 K_2SO_4 | 1 | -1 Al_2(SO_4)_3 | 1 | -1 AlKO_8S_2 | 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 K_2SO_4 | 1 | -1 | -(Δ[K2SO4])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) AlKO_8S_2 | 2 | 2 | 1/2 (Δ[AlKO8S2])/(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[K2SO4])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[AlKO8S2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium sulfate | aluminum sulfate | potassium alum formula | K_2SO_4 | Al_2(SO_4)_3 | AlKO_8S_2 Hill formula | K_2O_4S | Al_2O_12S_3 | AlKO_8S_2 name | potassium sulfate | aluminum sulfate | potassium alum IUPAC name | dipotassium sulfate | dialuminum trisulfate | potassium aluminum(+3) cation disulfate

| potassium sulfate | aluminum sulfate | potassium alum molar mass | 174.25 g/mol | 342.1 g/mol | 258.19 g/mol phase | | solid (at STP) | solid (at STP) melting point | | 770 °C | 92.5 °C density | | 2.71 g/cm^3 | 1.725 g/cm^3 solubility in water | soluble | soluble | odor | | | odorless