AgNO3 + NaClO = NaNO3 + AgCl + AgClO3

Input interpretation

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AgNO_3 silver nitrate + NaOCl sodium hypochlorite ⟶ NaNO_3 sodium nitrate + AgCl silver chloride + AgClO_3 silver chlorate

Balanced equation

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Balance the chemical equation algebraically: AgNO_3 + NaOCl ⟶ NaNO_3 + AgCl + AgClO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 NaOCl ⟶ c_3 NaNO_3 + c_4 AgCl + c_5 AgClO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Cl and Na: Ag: | c_1 = c_4 + c_5 N: | c_1 = c_3 O: | 3 c_1 + c_2 = 3 c_3 + 3 c_5 Cl: | c_2 = c_4 + c_5 Na: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 3 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 AgNO_3 + 3 NaOCl ⟶ 3 NaNO_3 + 2 AgCl + AgClO_3

+ ⟶ + +

Names

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silver nitrate + sodium hypochlorite ⟶ sodium nitrate + silver chloride + silver chlorate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: AgNO_3 + NaOCl ⟶ NaNO_3 + AgCl + AgClO_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: 3 AgNO_3 + 3 NaOCl ⟶ 3 NaNO_3 + 2 AgCl + AgClO_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 AgNO_3 | 3 | -3 NaOCl | 3 | -3 NaNO_3 | 3 | 3 AgCl | 2 | 2 AgClO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 3 | -3 | ([AgNO3])^(-3) NaOCl | 3 | -3 | ([NaOCl])^(-3) NaNO_3 | 3 | 3 | ([NaNO3])^3 AgCl | 2 | 2 | ([AgCl])^2 AgClO_3 | 1 | 1 | [AgClO3] 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])^(-3) ([NaOCl])^(-3) ([NaNO3])^3 ([AgCl])^2 [AgClO3] = (([NaNO3])^3 ([AgCl])^2 [AgClO3])/(([AgNO3])^3 ([NaOCl])^3)

Rate of reaction

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Construct the rate of reaction expression for: AgNO_3 + NaOCl ⟶ NaNO_3 + AgCl + AgClO_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: 3 AgNO_3 + 3 NaOCl ⟶ 3 NaNO_3 + 2 AgCl + AgClO_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 AgNO_3 | 3 | -3 NaOCl | 3 | -3 NaNO_3 | 3 | 3 AgCl | 2 | 2 AgClO_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 AgNO_3 | 3 | -3 | -1/3 (Δ[AgNO3])/(Δt) NaOCl | 3 | -3 | -1/3 (Δ[NaOCl])/(Δt) NaNO_3 | 3 | 3 | 1/3 (Δ[NaNO3])/(Δt) AgCl | 2 | 2 | 1/2 (Δ[AgCl])/(Δt) AgClO_3 | 1 | 1 | (Δ[AgClO3])/(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 = -1/3 (Δ[AgNO3])/(Δt) = -1/3 (Δ[NaOCl])/(Δt) = 1/3 (Δ[NaNO3])/(Δt) = 1/2 (Δ[AgCl])/(Δt) = (Δ[AgClO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)