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Al(OH)3 + Ag2SO4 = Al2(SO4)3 + AgOH

Input interpretation

Al(OH)_3 aluminum hydroxide + Ag_2SO_4 silver sulfate ⟶ Al_2(SO_4)_3 aluminum sulfate + AgOH
Al(OH)_3 aluminum hydroxide + Ag_2SO_4 silver sulfate ⟶ Al_2(SO_4)_3 aluminum sulfate + AgOH

Balanced equation

Balance the chemical equation algebraically: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al(OH)_3 + c_2 Ag_2SO_4 ⟶ c_3 Al_2(SO_4)_3 + c_4 AgOH Set the number of atoms in the reactants equal to the number of atoms in the products for Al, H, O, Ag and S: Al: | c_1 = 2 c_3 H: | 3 c_1 = c_4 O: | 3 c_1 + 4 c_2 = 12 c_3 + c_4 Ag: | 2 c_2 = c_4 S: | c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH
Balance the chemical equation algebraically: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al(OH)_3 + c_2 Ag_2SO_4 ⟶ c_3 Al_2(SO_4)_3 + c_4 AgOH Set the number of atoms in the reactants equal to the number of atoms in the products for Al, H, O, Ag and S: Al: | c_1 = 2 c_3 H: | 3 c_1 = c_4 O: | 3 c_1 + 4 c_2 = 12 c_3 + c_4 Ag: | 2 c_2 = c_4 S: | c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH

Structures

+ ⟶ + AgOH
+ ⟶ + AgOH

Names

aluminum hydroxide + silver sulfate ⟶ aluminum sulfate + AgOH
aluminum hydroxide + silver sulfate ⟶ aluminum sulfate + AgOH

Equilibrium constant

Construct the equilibrium constant, K, expression for: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH 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: 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH 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 Al(OH)_3 | 2 | -2 Ag_2SO_4 | 3 | -3 Al_2(SO_4)_3 | 1 | 1 AgOH | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) Ag_2SO_4 | 3 | -3 | ([Ag2SO4])^(-3) Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)3] AgOH | 6 | 6 | ([AgOH])^6 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 = ([Al(OH)3])^(-2) ([Ag2SO4])^(-3) [Al2(SO4)3] ([AgOH])^6 = ([Al2(SO4)3] ([AgOH])^6)/(([Al(OH)3])^2 ([Ag2SO4])^3)
Construct the equilibrium constant, K, expression for: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH 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: 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH 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 Al(OH)_3 | 2 | -2 Ag_2SO_4 | 3 | -3 Al_2(SO_4)_3 | 1 | 1 AgOH | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) Ag_2SO_4 | 3 | -3 | ([Ag2SO4])^(-3) Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)3] AgOH | 6 | 6 | ([AgOH])^6 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 = ([Al(OH)3])^(-2) ([Ag2SO4])^(-3) [Al2(SO4)3] ([AgOH])^6 = ([Al2(SO4)3] ([AgOH])^6)/(([Al(OH)3])^2 ([Ag2SO4])^3)

Rate of reaction

Construct the rate of reaction expression for: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH 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: 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH 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 Al(OH)_3 | 2 | -2 Ag_2SO_4 | 3 | -3 Al_2(SO_4)_3 | 1 | 1 AgOH | 6 | 6 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 Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) Ag_2SO_4 | 3 | -3 | -1/3 (Δ[Ag2SO4])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)3])/(Δt) AgOH | 6 | 6 | 1/6 (Δ[AgOH])/(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 = -1/2 (Δ[Al(OH)3])/(Δt) = -1/3 (Δ[Ag2SO4])/(Δt) = (Δ[Al2(SO4)3])/(Δt) = 1/6 (Δ[AgOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Al(OH)_3 + Ag_2SO_4 ⟶ Al_2(SO_4)_3 + AgOH 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: 2 Al(OH)_3 + 3 Ag_2SO_4 ⟶ Al_2(SO_4)_3 + 6 AgOH 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 Al(OH)_3 | 2 | -2 Ag_2SO_4 | 3 | -3 Al_2(SO_4)_3 | 1 | 1 AgOH | 6 | 6 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 Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) Ag_2SO_4 | 3 | -3 | -1/3 (Δ[Ag2SO4])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)3])/(Δt) AgOH | 6 | 6 | 1/6 (Δ[AgOH])/(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 = -1/2 (Δ[Al(OH)3])/(Δt) = -1/3 (Δ[Ag2SO4])/(Δt) = (Δ[Al2(SO4)3])/(Δt) = 1/6 (Δ[AgOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| aluminum hydroxide | silver sulfate | aluminum sulfate | AgOH formula | Al(OH)_3 | Ag_2SO_4 | Al_2(SO_4)_3 | AgOH Hill formula | AlH_3O_3 | Ag_2O_4S | Al_2O_12S_3 | HAgO name | aluminum hydroxide | silver sulfate | aluminum sulfate | IUPAC name | aluminum hydroxide | disilver sulfate | dialuminum trisulfate |
| aluminum hydroxide | silver sulfate | aluminum sulfate | AgOH formula | Al(OH)_3 | Ag_2SO_4 | Al_2(SO_4)_3 | AgOH Hill formula | AlH_3O_3 | Ag_2O_4S | Al_2O_12S_3 | HAgO name | aluminum hydroxide | silver sulfate | aluminum sulfate | IUPAC name | aluminum hydroxide | disilver sulfate | dialuminum trisulfate |

Substance properties

| aluminum hydroxide | silver sulfate | aluminum sulfate | AgOH molar mass | 78.003 g/mol | 311.79 g/mol | 342.1 g/mol | 124.875 g/mol phase | | solid (at STP) | solid (at STP) | melting point | | 652 °C | 770 °C | density | | | 2.71 g/cm^3 | solubility in water | | slightly soluble | soluble |
| aluminum hydroxide | silver sulfate | aluminum sulfate | AgOH molar mass | 78.003 g/mol | 311.79 g/mol | 342.1 g/mol | 124.875 g/mol phase | | solid (at STP) | solid (at STP) | melting point | | 652 °C | 770 °C | density | | | 2.71 g/cm^3 | solubility in water | | slightly soluble | soluble |

Units

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