HCl + NaBiO3 = H2O + Cl2 + NaCl + BiCl3

Input interpretation

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HCl hydrogen chloride + NaBiO_3 sodium bismuthate ⟶ H_2O water + Cl_2 chlorine + NaCl sodium chloride + BiCl_3 bismuth chloride

Balanced equation

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Balance the chemical equation algebraically: HCl + NaBiO_3 ⟶ H_2O + Cl_2 + NaCl + BiCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 NaBiO_3 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 NaCl + c_6 BiCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Bi, Na and O: Cl: | c_1 = 2 c_4 + c_5 + 3 c_6 H: | c_1 = 2 c_3 Bi: | c_2 = c_6 Na: | c_2 = c_5 O: | 3 c_2 = c_3 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 = 3 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + NaBiO_3 ⟶ 3 H_2O + Cl_2 + NaCl + BiCl_3

+ ⟶ + + +

Names

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hydrogen chloride + sodium bismuthate ⟶ water + chlorine + sodium chloride + bismuth chloride

Equilibrium constant

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Construct the equilibrium constant, K, expression for: HCl + NaBiO_3 ⟶ H_2O + Cl_2 + NaCl + BiCl_3 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 HCl + NaBiO_3 ⟶ 3 H_2O + Cl_2 + NaCl + BiCl_3 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 HCl | 6 | -6 NaBiO_3 | 1 | -1 H_2O | 3 | 3 Cl_2 | 1 | 1 NaCl | 1 | 1 BiCl_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) NaBiO_3 | 1 | -1 | ([NaBiO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 Cl_2 | 1 | 1 | [Cl2] NaCl | 1 | 1 | [NaCl] BiCl_3 | 1 | 1 | [BiCl3] 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 = ([HCl])^(-6) ([NaBiO3])^(-1) ([H2O])^3 [Cl2] [NaCl] [BiCl3] = (([H2O])^3 [Cl2] [NaCl] [BiCl3])/(([HCl])^6 [NaBiO3])

Rate of reaction

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Construct the rate of reaction expression for: HCl + NaBiO_3 ⟶ H_2O + Cl_2 + NaCl + BiCl_3 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 HCl + NaBiO_3 ⟶ 3 H_2O + Cl_2 + NaCl + BiCl_3 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 HCl | 6 | -6 NaBiO_3 | 1 | -1 H_2O | 3 | 3 Cl_2 | 1 | 1 NaCl | 1 | 1 BiCl_3 | 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) NaBiO_3 | 1 | -1 | -(Δ[NaBiO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(Δt) BiCl_3 | 1 | 1 | (Δ[BiCl3])/(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[HCl])/(Δt) = -(Δ[NaBiO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Cl2])/(Δt) = (Δ[NaCl])/(Δt) = (Δ[BiCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)