H2O + NaOH + Zn + KClO3 = KCl + Na2Zn(OH)4

Input interpretation

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H_2O water + NaOH sodium hydroxide + Zn zinc + KClO_3 potassium chlorate ⟶ KCl potassium chloride + Na2Zn(OH)4

Balanced equation

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Balance the chemical equation algebraically: H_2O + NaOH + Zn + KClO_3 ⟶ KCl + Na2Zn(OH)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOH + c_3 Zn + c_4 KClO_3 ⟶ c_5 KCl + c_6 Na2Zn(OH)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na, Zn, Cl and K: H: | 2 c_1 + c_2 = 4 c_6 O: | c_1 + c_2 + 3 c_4 = 4 c_6 Na: | c_2 = 2 c_6 Zn: | c_3 = c_6 Cl: | c_4 = c_5 K: | c_4 = c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 6 c_3 = 3 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 6 NaOH + 3 Zn + KClO_3 ⟶ KCl + 3 Na2Zn(OH)4

+ + + ⟶ + Na2Zn(OH)4

Names

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water + sodium hydroxide + zinc + potassium chlorate ⟶ potassium chloride + Na2Zn(OH)4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + NaOH + Zn + KClO_3 ⟶ KCl + Na2Zn(OH)4 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 H_2O + 6 NaOH + 3 Zn + KClO_3 ⟶ KCl + 3 Na2Zn(OH)4 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 | 3 | -3 NaOH | 6 | -6 Zn | 3 | -3 KClO_3 | 1 | -1 KCl | 1 | 1 Na2Zn(OH)4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) NaOH | 6 | -6 | ([NaOH])^(-6) Zn | 3 | -3 | ([Zn])^(-3) KClO_3 | 1 | -1 | ([KClO3])^(-1) KCl | 1 | 1 | [KCl] Na2Zn(OH)4 | 3 | 3 | ([Na2Zn(OH)4])^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 = ([H2O])^(-3) ([NaOH])^(-6) ([Zn])^(-3) ([KClO3])^(-1) [KCl] ([Na2Zn(OH)4])^3 = ([KCl] ([Na2Zn(OH)4])^3)/(([H2O])^3 ([NaOH])^6 ([Zn])^3 [KClO3])

Rate of reaction

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Construct the rate of reaction expression for: H_2O + NaOH + Zn + KClO_3 ⟶ KCl + Na2Zn(OH)4 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 H_2O + 6 NaOH + 3 Zn + KClO_3 ⟶ KCl + 3 Na2Zn(OH)4 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 | 3 | -3 NaOH | 6 | -6 Zn | 3 | -3 KClO_3 | 1 | -1 KCl | 1 | 1 Na2Zn(OH)4 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) Na2Zn(OH)4 | 3 | 3 | 1/3 (Δ[Na2Zn(OH)4])/(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[H2O])/(Δt) = -1/6 (Δ[NaOH])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -(Δ[KClO3])/(Δt) = (Δ[KCl])/(Δt) = 1/3 (Δ[Na2Zn(OH)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)