H2SO4 + Zn + NaVO3 = H2O + Na2SO4 + ZnSO4 + VSO4

H_2SO_4 sulfuric acid + Zn zinc + NaVO_3 sodium metavanadate ⟶ H_2O water + Na_2SO_4 sodium sulfate + ZnSO_4 zinc sulfate + VSO4

Balance the chemical equation algebraically: H_2SO_4 + Zn + NaVO_3 ⟶ H_2O + Na_2SO_4 + ZnSO_4 + VSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn + c_3 NaVO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 ZnSO_4 + c_7 VSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Zn, Na and V: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_6 + c_7 Zn: | c_2 = c_6 Na: | c_3 = 2 c_5 V: | c_3 = c_7 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 3 c_3 = 2 c_4 = 6 c_5 = 1 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + 3 Zn + 2 NaVO_3 ⟶ 6 H_2O + Na_2SO_4 + 3 ZnSO_4 + 2 VSO4

+ + ⟶ + + + VSO4

sulfuric acid + zinc + sodium metavanadate ⟶ water + sodium sulfate + zinc sulfate + VSO4

Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + NaVO_3 ⟶ H_2O + Na_2SO_4 + ZnSO_4 + VSO4 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_2SO_4 + 3 Zn + 2 NaVO_3 ⟶ 6 H_2O + Na_2SO_4 + 3 ZnSO_4 + 2 VSO4 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_2SO_4 | 6 | -6 Zn | 3 | -3 NaVO_3 | 2 | -2 H_2O | 6 | 6 Na_2SO_4 | 1 | 1 ZnSO_4 | 3 | 3 VSO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 6 | -6 | ([H2SO4])^(-6) Zn | 3 | -3 | ([Zn])^(-3) NaVO_3 | 2 | -2 | ([NaVO3])^(-2) H_2O | 6 | 6 | ([H2O])^6 Na_2SO_4 | 1 | 1 | [Na2SO4] ZnSO_4 | 3 | 3 | ([ZnSO4])^3 VSO4 | 2 | 2 | ([VSO4])^2 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 = ([H2SO4])^(-6) ([Zn])^(-3) ([NaVO3])^(-2) ([H2O])^6 [Na2SO4] ([ZnSO4])^3 ([VSO4])^2 = (([H2O])^6 [Na2SO4] ([ZnSO4])^3 ([VSO4])^2)/(([H2SO4])^6 ([Zn])^3 ([NaVO3])^2)

Construct the rate of reaction expression for: H_2SO_4 + Zn + NaVO_3 ⟶ H_2O + Na_2SO_4 + ZnSO_4 + VSO4 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_2SO_4 + 3 Zn + 2 NaVO_3 ⟶ 6 H_2O + Na_2SO_4 + 3 ZnSO_4 + 2 VSO4 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_2SO_4 | 6 | -6 Zn | 3 | -3 NaVO_3 | 2 | -2 H_2O | 6 | 6 Na_2SO_4 | 1 | 1 ZnSO_4 | 3 | 3 VSO4 | 2 | 2 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_2SO_4 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) NaVO_3 | 2 | -2 | -1/2 (Δ[NaVO3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) ZnSO_4 | 3 | 3 | 1/3 (Δ[ZnSO4])/(Δt) VSO4 | 2 | 2 | 1/2 (Δ[VSO4])/(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[H2SO4])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -1/2 (Δ[NaVO3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[Na2SO4])/(Δt) = 1/3 (Δ[ZnSO4])/(Δt) = 1/2 (Δ[VSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | zinc | sodium metavanadate | water | sodium sulfate | zinc sulfate | VSO4 formula | H_2SO_4 | Zn | NaVO_3 | H_2O | Na_2SO_4 | ZnSO_4 | VSO4 Hill formula | H_2O_4S | Zn | NaO_3V | H_2O | Na_2O_4S | O_4SZn | O4SV name | sulfuric acid | zinc | sodium metavanadate | water | sodium sulfate | zinc sulfate | IUPAC name | sulfuric acid | zinc | sodium oxido-dioxovanadium | water | disodium sulfate | zinc sulfate |

| sulfuric acid | zinc | sodium metavanadate | water | sodium sulfate | zinc sulfate | VSO4 molar mass | 98.07 g/mol | 65.38 g/mol | 121.93 g/mol | 18.015 g/mol | 142.04 g/mol | 161.4 g/mol | 147 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | | melting point | 10.371 °C | 420 °C | 630 °C | 0 °C | 884 °C | | boiling point | 279.6 °C | 907 °C | | 99.9839 °C | 1429 °C | | density | 1.8305 g/cm^3 | 7.14 g/cm^3 | 5.15 g/cm^3 | 1 g/cm^3 | 2.68 g/cm^3 | 1.005 g/cm^3 | solubility in water | very soluble | insoluble | | | soluble | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | odorless |