Cr2(SO4)3 + AgNO3 = Ag2SO4 + Cr(NO3)3

Input interpretation

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Cr_2(SO_4)_3 chromium sulfate + AgNO_3 silver nitrate ⟶ Ag_2SO_4 silver sulfate + CrN_3O_9 chromium nitrate

Balanced equation

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Balance the chemical equation algebraically: Cr_2(SO_4)_3 + AgNO_3 ⟶ Ag_2SO_4 + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr_2(SO_4)_3 + c_2 AgNO_3 ⟶ c_3 Ag_2SO_4 + c_4 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, O, S, Ag and N: Cr: | 2 c_1 = c_4 O: | 12 c_1 + 3 c_2 = 4 c_3 + 9 c_4 S: | 3 c_1 = c_3 Ag: | c_2 = 2 c_3 N: | c_2 = 3 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 = 6 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cr_2(SO_4)_3 + 6 AgNO_3 ⟶ 3 Ag_2SO_4 + 2 CrN_3O_9

+ ⟶ +

Names

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chromium sulfate + silver nitrate ⟶ silver sulfate + chromium nitrate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Cr_2(SO_4)_3 + AgNO_3 ⟶ Ag_2SO_4 + CrN_3O_9 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: Cr_2(SO_4)_3 + 6 AgNO_3 ⟶ 3 Ag_2SO_4 + 2 CrN_3O_9 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 Cr_2(SO_4)_3 | 1 | -1 AgNO_3 | 6 | -6 Ag_2SO_4 | 3 | 3 CrN_3O_9 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) AgNO_3 | 6 | -6 | ([AgNO3])^(-6) Ag_2SO_4 | 3 | 3 | ([Ag2SO4])^3 CrN_3O_9 | 2 | 2 | ([CrN3O9])^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 = ([Cr2(SO4)3])^(-1) ([AgNO3])^(-6) ([Ag2SO4])^3 ([CrN3O9])^2 = (([Ag2SO4])^3 ([CrN3O9])^2)/([Cr2(SO4)3] ([AgNO3])^6)

Rate of reaction

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Construct the rate of reaction expression for: Cr_2(SO_4)_3 + AgNO_3 ⟶ Ag_2SO_4 + CrN_3O_9 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: Cr_2(SO_4)_3 + 6 AgNO_3 ⟶ 3 Ag_2SO_4 + 2 CrN_3O_9 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 Cr_2(SO_4)_3 | 1 | -1 AgNO_3 | 6 | -6 Ag_2SO_4 | 3 | 3 CrN_3O_9 | 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 Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) AgNO_3 | 6 | -6 | -1/6 (Δ[AgNO3])/(Δt) Ag_2SO_4 | 3 | 3 | 1/3 (Δ[Ag2SO4])/(Δt) CrN_3O_9 | 2 | 2 | 1/2 (Δ[CrN3O9])/(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[Cr2(SO4)3])/(Δt) = -1/6 (Δ[AgNO3])/(Δt) = 1/3 (Δ[Ag2SO4])/(Δt) = 1/2 (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)