H2O + Ca(ClO3)2 + Na2S = NaOH + S + CaCl2

Input interpretation

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H_2O water + CaCl_2O_6 calcium chlorate + Na_2S sodium sulfide ⟶ NaOH sodium hydroxide + S mixed sulfur + CaCl_2 calcium chloride

Balanced equation

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Balance the chemical equation algebraically: H_2O + CaCl_2O_6 + Na_2S ⟶ NaOH + S + CaCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CaCl_2O_6 + c_3 Na_2S ⟶ c_4 NaOH + c_5 S + c_6 CaCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ca, Cl, Na and S: H: | 2 c_1 = c_4 O: | c_1 + 6 c_2 = c_4 Ca: | c_2 = c_6 Cl: | 2 c_2 = 2 c_6 Na: | 2 c_3 = c_4 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 6 c_4 = 12 c_5 = 6 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + CaCl_2O_6 + 6 Na_2S ⟶ 12 NaOH + 6 S + CaCl_2

+ + ⟶ + +

Names

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water + calcium chlorate + sodium sulfide ⟶ sodium hydroxide + mixed sulfur + calcium chloride

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + CaCl_2O_6 + Na_2S ⟶ NaOH + S + CaCl_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: 6 H_2O + CaCl_2O_6 + 6 Na_2S ⟶ 12 NaOH + 6 S + CaCl_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 | 6 | -6 CaCl_2O_6 | 1 | -1 Na_2S | 6 | -6 NaOH | 12 | 12 S | 6 | 6 CaCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) CaCl_2O_6 | 1 | -1 | ([CaCl2O6])^(-1) Na_2S | 6 | -6 | ([Na2S])^(-6) NaOH | 12 | 12 | ([NaOH])^12 S | 6 | 6 | ([S])^6 CaCl_2 | 1 | 1 | [CaCl2] 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])^(-6) ([CaCl2O6])^(-1) ([Na2S])^(-6) ([NaOH])^12 ([S])^6 [CaCl2] = (([NaOH])^12 ([S])^6 [CaCl2])/(([H2O])^6 [CaCl2O6] ([Na2S])^6)

Rate of reaction

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Construct the rate of reaction expression for: H_2O + CaCl_2O_6 + Na_2S ⟶ NaOH + S + CaCl_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: 6 H_2O + CaCl_2O_6 + 6 Na_2S ⟶ 12 NaOH + 6 S + CaCl_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 | 6 | -6 CaCl_2O_6 | 1 | -1 Na_2S | 6 | -6 NaOH | 12 | 12 S | 6 | 6 CaCl_2 | 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 H_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) CaCl_2O_6 | 1 | -1 | -(Δ[CaCl2O6])/(Δt) Na_2S | 6 | -6 | -1/6 (Δ[Na2S])/(Δt) NaOH | 12 | 12 | 1/12 (Δ[NaOH])/(Δt) S | 6 | 6 | 1/6 (Δ[S])/(Δt) CaCl_2 | 1 | 1 | (Δ[CaCl2])/(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 = -1/6 (Δ[H2O])/(Δt) = -(Δ[CaCl2O6])/(Δt) = -1/6 (Δ[Na2S])/(Δt) = 1/12 (Δ[NaOH])/(Δt) = 1/6 (Δ[S])/(Δt) = (Δ[CaCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)