Al + AgNO3 = Ag + Al(NO3)3

Input interpretation

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Al (aluminum) + AgNO_3 (silver nitrate) ⟶ Ag (silver) + Al(NO_3)_3 (aluminum nitrate)

Balanced equation

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Balance the chemical equation algebraically: Al + AgNO_3 ⟶ Ag + Al(NO_3)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 AgNO_3 ⟶ c_3 Ag + c_4 Al(NO_3)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ag, N and O: Al: | c_1 = c_4 Ag: | c_2 = c_3 N: | c_2 = 3 c_4 O: | 3 c_2 = 9 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 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al + 3 AgNO_3 ⟶ 3 Ag + Al(NO_3)_3

+ ⟶ +

Names

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aluminum + silver nitrate ⟶ silver + aluminum nitrate

Equilibrium constant

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

Rate of reaction

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Construct the rate of reaction expression for: Al + AgNO_3 ⟶ Ag + Al(NO_3)_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: Al + 3 AgNO_3 ⟶ 3 Ag + Al(NO_3)_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 Al | 1 | -1 AgNO_3 | 3 | -3 Ag | 3 | 3 Al(NO_3)_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 Al | 1 | -1 | -(Δ[Al])/(Δt) AgNO_3 | 3 | -3 | -1/3 (Δ[AgNO3])/(Δt) Ag | 3 | 3 | 1/3 (Δ[Ag])/(Δt) Al(NO_3)_3 | 1 | 1 | (Δ[Al(NO3)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 = -(Δ[Al])/(Δt) = -1/3 (Δ[AgNO3])/(Δt) = 1/3 (Δ[Ag])/(Δt) = (Δ[Al(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)