H2O + O2 + Au + NaCN = NaOH + Na[Au(CN)2]

Input interpretation

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H_2O (water) + O_2 (oxygen) + Au (gold) + NaCN (sodium cyanide) ⟶ NaOH (sodium hydroxide) + NaAu(CN)_2 (sodium dicyanoaurate)

Balanced equation

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Balance the chemical equation algebraically: H_2O + O_2 + Au + NaCN ⟶ NaOH + NaAu(CN)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Au + c_4 NaCN ⟶ c_5 NaOH + c_6 NaAu(CN)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Au, C, N and Na: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 = c_5 Au: | c_3 = c_6 C: | c_4 = 2 c_6 N: | c_4 = 2 c_6 Na: | c_4 = c_5 + c_6 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 = 2 c_2 = 1 c_3 = 4 c_4 = 8 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + 4 Au + 8 NaCN ⟶ 4 NaOH + 4 NaAu(CN)_2

+ + + ⟶ +

Names

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water + oxygen + gold + sodium cyanide ⟶ sodium hydroxide + sodium dicyanoaurate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + O_2 + Au + NaCN ⟶ NaOH + NaAu(CN)_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: 2 H_2O + O_2 + 4 Au + 8 NaCN ⟶ 4 NaOH + 4 NaAu(CN)_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 H_2O | 2 | -2 O_2 | 1 | -1 Au | 4 | -4 NaCN | 8 | -8 NaOH | 4 | 4 NaAu(CN)_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) Au | 4 | -4 | ([Au])^(-4) NaCN | 8 | -8 | ([NaCN])^(-8) NaOH | 4 | 4 | ([NaOH])^4 NaAu(CN)_2 | 4 | 4 | ([NaAu(CN)2])^4 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 = ([H2O])^(-2) ([O2])^(-1) ([Au])^(-4) ([NaCN])^(-8) ([NaOH])^4 ([NaAu(CN)2])^4 = (([NaOH])^4 ([NaAu(CN)2])^4)/(([H2O])^2 [O2] ([Au])^4 ([NaCN])^8)

Rate of reaction

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Construct the rate of reaction expression for: H_2O + O_2 + Au + NaCN ⟶ NaOH + NaAu(CN)_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: 2 H_2O + O_2 + 4 Au + 8 NaCN ⟶ 4 NaOH + 4 NaAu(CN)_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 H_2O | 2 | -2 O_2 | 1 | -1 Au | 4 | -4 NaCN | 8 | -8 NaOH | 4 | 4 NaAu(CN)_2 | 4 | 4 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Au | 4 | -4 | -1/4 (Δ[Au])/(Δt) NaCN | 8 | -8 | -1/8 (Δ[NaCN])/(Δt) NaOH | 4 | 4 | 1/4 (Δ[NaOH])/(Δt) NaAu(CN)_2 | 4 | 4 | 1/4 (Δ[NaAu(CN)2])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[O2])/(Δt) = -1/4 (Δ[Au])/(Δt) = -1/8 (Δ[NaCN])/(Δt) = 1/4 (Δ[NaOH])/(Δt) = 1/4 (Δ[NaAu(CN)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)