NaOH + Zn + KNO3 = H2O + NH3 + Na2ZnO2 + KNaZnO2

Input interpretation

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NaOH sodium hydroxide + Zn zinc + KNO_3 potassium nitrate ⟶ H_2O water + NH_3 ammonia + Na2ZnO2 + KNaZnO2

Balanced equation

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Balance the chemical equation algebraically: NaOH + Zn + KNO_3 ⟶ H_2O + NH_3 + Na2ZnO2 + KNaZnO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Zn + c_3 KNO_3 ⟶ c_4 H_2O + c_5 NH_3 + c_6 Na2ZnO2 + c_7 KNaZnO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Zn, K and N: H: | c_1 = 2 c_4 + 3 c_5 Na: | c_1 = 2 c_6 + c_7 O: | c_1 + 3 c_3 = c_4 + 2 c_6 + 2 c_7 Zn: | c_2 = c_6 + c_7 K: | c_3 = c_7 N: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 4 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 3 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 NaOH + 4 Zn + KNO_3 ⟶ 2 H_2O + NH_3 + 3 Na2ZnO2 + KNaZnO2

+ + ⟶ + + Na2ZnO2 + KNaZnO2

Names

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sodium hydroxide + zinc + potassium nitrate ⟶ water + ammonia + Na2ZnO2 + KNaZnO2

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + Zn + KNO_3 ⟶ H_2O + NH_3 + Na2ZnO2 + KNaZnO2 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: 7 NaOH + 4 Zn + KNO_3 ⟶ 2 H_2O + NH_3 + 3 Na2ZnO2 + KNaZnO2 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 NaOH | 7 | -7 Zn | 4 | -4 KNO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 1 | 1 Na2ZnO2 | 3 | 3 KNaZnO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 7 | -7 | ([NaOH])^(-7) Zn | 4 | -4 | ([Zn])^(-4) KNO_3 | 1 | -1 | ([KNO3])^(-1) H_2O | 2 | 2 | ([H2O])^2 NH_3 | 1 | 1 | [NH3] Na2ZnO2 | 3 | 3 | ([Na2ZnO2])^3 KNaZnO2 | 1 | 1 | [KNaZnO2] 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 = ([NaOH])^(-7) ([Zn])^(-4) ([KNO3])^(-1) ([H2O])^2 [NH3] ([Na2ZnO2])^3 [KNaZnO2] = (([H2O])^2 [NH3] ([Na2ZnO2])^3 [KNaZnO2])/(([NaOH])^7 ([Zn])^4 [KNO3])

Rate of reaction

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Construct the rate of reaction expression for: NaOH + Zn + KNO_3 ⟶ H_2O + NH_3 + Na2ZnO2 + KNaZnO2 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: 7 NaOH + 4 Zn + KNO_3 ⟶ 2 H_2O + NH_3 + 3 Na2ZnO2 + KNaZnO2 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 NaOH | 7 | -7 Zn | 4 | -4 KNO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 1 | 1 Na2ZnO2 | 3 | 3 KNaZnO2 | 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 NaOH | 7 | -7 | -1/7 (Δ[NaOH])/(Δt) Zn | 4 | -4 | -1/4 (Δ[Zn])/(Δt) KNO_3 | 1 | -1 | -(Δ[KNO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) Na2ZnO2 | 3 | 3 | 1/3 (Δ[Na2ZnO2])/(Δt) KNaZnO2 | 1 | 1 | (Δ[KNaZnO2])/(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 = -1/7 (Δ[NaOH])/(Δt) = -1/4 (Δ[Zn])/(Δt) = -(Δ[KNO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[NH3])/(Δt) = 1/3 (Δ[Na2ZnO2])/(Δt) = (Δ[KNaZnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)