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AgNO3 + Al2(SO4)3 = Al(NO3)3 + Ag2SO4

Input interpretation

AgNO_3 silver nitrate + Al_2(SO_4)_3 aluminum sulfate ⟶ Al(NO_3)_3 aluminum nitrate + Ag_2SO_4 silver sulfate
AgNO_3 silver nitrate + Al_2(SO_4)_3 aluminum sulfate ⟶ Al(NO_3)_3 aluminum nitrate + Ag_2SO_4 silver sulfate

Balanced equation

Balance the chemical equation algebraically: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 Al_2(SO_4)_3 ⟶ c_3 Al(NO_3)_3 + c_4 Ag_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Al and S: Ag: | c_1 = 2 c_4 N: | c_1 = 3 c_3 O: | 3 c_1 + 12 c_2 = 9 c_3 + 4 c_4 Al: | 2 c_2 = c_3 S: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4
Balance the chemical equation algebraically: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 Al_2(SO_4)_3 ⟶ c_3 Al(NO_3)_3 + c_4 Ag_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Al and S: Ag: | c_1 = 2 c_4 N: | c_1 = 3 c_3 O: | 3 c_1 + 12 c_2 = 9 c_3 + 4 c_4 Al: | 2 c_2 = c_3 S: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4

Structures

+ ⟶ +
+ ⟶ +

Names

silver nitrate + aluminum sulfate ⟶ aluminum nitrate + silver sulfate
silver nitrate + aluminum sulfate ⟶ aluminum nitrate + silver sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 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: 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4 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 AgNO_3 | 6 | -6 Al_2(SO_4)_3 | 1 | -1 Al(NO_3)_3 | 2 | 2 Ag_2SO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 6 | -6 | ([AgNO3])^(-6) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Al(NO_3)_3 | 2 | 2 | ([Al(NO3)3])^2 Ag_2SO_4 | 3 | 3 | ([Ag2SO4])^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 = ([AgNO3])^(-6) ([Al2(SO4)3])^(-1) ([Al(NO3)3])^2 ([Ag2SO4])^3 = (([Al(NO3)3])^2 ([Ag2SO4])^3)/(([AgNO3])^6 [Al2(SO4)3])
Construct the equilibrium constant, K, expression for: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 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: 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4 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 AgNO_3 | 6 | -6 Al_2(SO_4)_3 | 1 | -1 Al(NO_3)_3 | 2 | 2 Ag_2SO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 6 | -6 | ([AgNO3])^(-6) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) Al(NO_3)_3 | 2 | 2 | ([Al(NO3)3])^2 Ag_2SO_4 | 3 | 3 | ([Ag2SO4])^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 = ([AgNO3])^(-6) ([Al2(SO4)3])^(-1) ([Al(NO3)3])^2 ([Ag2SO4])^3 = (([Al(NO3)3])^2 ([Ag2SO4])^3)/(([AgNO3])^6 [Al2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 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: 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4 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 AgNO_3 | 6 | -6 Al_2(SO_4)_3 | 1 | -1 Al(NO_3)_3 | 2 | 2 Ag_2SO_4 | 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 AgNO_3 | 6 | -6 | -1/6 (Δ[AgNO3])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Al(NO_3)_3 | 2 | 2 | 1/2 (Δ[Al(NO3)3])/(Δt) Ag_2SO_4 | 3 | 3 | 1/3 (Δ[Ag2SO4])/(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 = -1/6 (Δ[AgNO3])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[Al(NO3)3])/(Δt) = 1/3 (Δ[Ag2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: AgNO_3 + Al_2(SO_4)_3 ⟶ Al(NO_3)_3 + Ag_2SO_4 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: 6 AgNO_3 + Al_2(SO_4)_3 ⟶ 2 Al(NO_3)_3 + 3 Ag_2SO_4 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 AgNO_3 | 6 | -6 Al_2(SO_4)_3 | 1 | -1 Al(NO_3)_3 | 2 | 2 Ag_2SO_4 | 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 AgNO_3 | 6 | -6 | -1/6 (Δ[AgNO3])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) Al(NO_3)_3 | 2 | 2 | 1/2 (Δ[Al(NO3)3])/(Δt) Ag_2SO_4 | 3 | 3 | 1/3 (Δ[Ag2SO4])/(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 = -1/6 (Δ[AgNO3])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = 1/2 (Δ[Al(NO3)3])/(Δt) = 1/3 (Δ[Ag2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate formula | AgNO_3 | Al_2(SO_4)_3 | Al(NO_3)_3 | Ag_2SO_4 Hill formula | AgNO_3 | Al_2O_12S_3 | AlN_3O_9 | Ag_2O_4S name | silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate IUPAC name | silver nitrate | dialuminum trisulfate | aluminum(+3) cation trinitrate | disilver sulfate
| silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate formula | AgNO_3 | Al_2(SO_4)_3 | Al(NO_3)_3 | Ag_2SO_4 Hill formula | AgNO_3 | Al_2O_12S_3 | AlN_3O_9 | Ag_2O_4S name | silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate IUPAC name | silver nitrate | dialuminum trisulfate | aluminum(+3) cation trinitrate | disilver sulfate

Substance properties

| silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate molar mass | 169.87 g/mol | 342.1 g/mol | 212.99 g/mol | 311.79 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 212 °C | 770 °C | 72.8 °C | 652 °C density | | 2.71 g/cm^3 | 1.401 g/cm^3 | solubility in water | soluble | soluble | | slightly soluble dynamic viscosity | | | 0.001338 Pa s (at 22 °C) | odor | odorless | | |
| silver nitrate | aluminum sulfate | aluminum nitrate | silver sulfate molar mass | 169.87 g/mol | 342.1 g/mol | 212.99 g/mol | 311.79 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 212 °C | 770 °C | 72.8 °C | 652 °C density | | 2.71 g/cm^3 | 1.401 g/cm^3 | solubility in water | soluble | soluble | | slightly soluble dynamic viscosity | | | 0.001338 Pa s (at 22 °C) | odor | odorless | | |

Units

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