Sn + AuCl3 = Au + SnCl2

Input interpretation

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Sn white tin + AuCl_3 gold(III) chloride ⟶ Au gold + SnCl_2 stannous chloride

Balanced equation

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$Balance the chemical equation algebraically: Sn + AuCl_3 ⟶ Au + SnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Sn + c_2 AuCl_3 ⟶ c_3 Au + c_4 SnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Sn, Au and Cl: Sn: | c_1 = c_4 Au: | c_2 = c_3 Cl: | 3 c_2 = 2 c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Sn + 2 AuCl_3 ⟶ 2 Au + 3 SnCl_2$

Balance the chemical equation algebraically: Sn + AuCl_3 ⟶ Au + SnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Sn + c_2 AuCl_3 ⟶ c_3 Au + c_4 SnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Sn, Au and Cl: Sn: | c_1 = c_4 Au: | c_2 = c_3 Cl: | 3 c_2 = 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 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Sn + 2 AuCl_3 ⟶ 2 Au + 3 SnCl_2

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Names

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white tin + gold(III) chloride ⟶ gold + stannous chloride

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Sn + AuCl_3 ⟶ Au + SnCl_2 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 Sn + 2 AuCl_3 ⟶ 2 Au + 3 SnCl_2 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 Sn | 3 | -3 AuCl_3 | 2 | -2 Au | 2 | 2 SnCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Sn | 3 | -3 | ([Sn])^(-3) AuCl_3 | 2 | -2 | ([AuCl3])^(-2) Au | 2 | 2 | ([Au])^2 SnCl_2 | 3 | 3 | ([SnCl2])^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 = ([Sn])^(-3) ([AuCl3])^(-2) ([Au])^2 ([SnCl2])^3 = (([Au])^2 ([SnCl2])^3)/(([Sn])^3 ([AuCl3])^2)

Rate of reaction

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Construct the rate of reaction expression for: Sn + AuCl_3 ⟶ Au + SnCl_2 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 Sn + 2 AuCl_3 ⟶ 2 Au + 3 SnCl_2 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 Sn | 3 | -3 AuCl_3 | 2 | -2 Au | 2 | 2 SnCl_2 | 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 Sn | 3 | -3 | -1/3 (Δ[Sn])/(Δt) AuCl_3 | 2 | -2 | -1/2 (Δ[AuCl3])/(Δt) Au | 2 | 2 | 1/2 (Δ[Au])/(Δt) SnCl_2 | 3 | 3 | 1/3 (Δ[SnCl2])/(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[Sn])/(Δt) = -1/2 (Δ[AuCl3])/(Δt) = 1/2 (Δ[Au])/(Δt) = 1/3 (Δ[SnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)