H2SO4 + Zn + K3AsO4 = H2O + K2SO4 + ZnSO4 + AsH3

H_2SO_4 sulfuric acid + Zn zinc + K3AsO4 ⟶ H_2O water + K_2SO_4 potassium sulfate + ZnSO_4 zinc sulfate + AsH_3 arsine

Balance the chemical equation algebraically: H_2SO_4 + Zn + K3AsO4 ⟶ H_2O + K_2SO_4 + ZnSO_4 + AsH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn + c_3 K3AsO4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 ZnSO_4 + c_7 AsH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Zn, K and As: H: | 2 c_1 = 2 c_4 + 3 c_7 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 + c_6 Zn: | c_2 = c_6 K: | 3 c_3 = 2 c_5 As: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 11/2 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 3/2 c_6 = 4 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 11 c_2 = 8 c_3 = 2 c_4 = 8 c_5 = 3 c_6 = 8 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 H_2SO_4 + 8 Zn + 2 K3AsO4 ⟶ 8 H_2O + 3 K_2SO_4 + 8 ZnSO_4 + 2 AsH_3

+ + K3AsO4 ⟶ + + +

sulfuric acid + zinc + K3AsO4 ⟶ water + potassium sulfate + zinc sulfate + arsine

Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn + K3AsO4 ⟶ H_2O + K_2SO_4 + ZnSO_4 + AsH_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: 11 H_2SO_4 + 8 Zn + 2 K3AsO4 ⟶ 8 H_2O + 3 K_2SO_4 + 8 ZnSO_4 + 2 AsH_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 H_2SO_4 | 11 | -11 Zn | 8 | -8 K3AsO4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 3 | 3 ZnSO_4 | 8 | 8 AsH_3 | 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 | 11 | -11 | ([H2SO4])^(-11) Zn | 8 | -8 | ([Zn])^(-8) K3AsO4 | 2 | -2 | ([K3AsO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 3 | 3 | ([K2SO4])^3 ZnSO_4 | 8 | 8 | ([ZnSO4])^8 AsH_3 | 2 | 2 | ([AsH3])^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])^(-11) ([Zn])^(-8) ([K3AsO4])^(-2) ([H2O])^8 ([K2SO4])^3 ([ZnSO4])^8 ([AsH3])^2 = (([H2O])^8 ([K2SO4])^3 ([ZnSO4])^8 ([AsH3])^2)/(([H2SO4])^11 ([Zn])^8 ([K3AsO4])^2)

Construct the rate of reaction expression for: H_2SO_4 + Zn + K3AsO4 ⟶ H_2O + K_2SO_4 + ZnSO_4 + AsH_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: 11 H_2SO_4 + 8 Zn + 2 K3AsO4 ⟶ 8 H_2O + 3 K_2SO_4 + 8 ZnSO_4 + 2 AsH_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 H_2SO_4 | 11 | -11 Zn | 8 | -8 K3AsO4 | 2 | -2 H_2O | 8 | 8 K_2SO_4 | 3 | 3 ZnSO_4 | 8 | 8 AsH_3 | 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 | 11 | -11 | -1/11 (Δ[H2SO4])/(Δt) Zn | 8 | -8 | -1/8 (Δ[Zn])/(Δt) K3AsO4 | 2 | -2 | -1/2 (Δ[K3AsO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) ZnSO_4 | 8 | 8 | 1/8 (Δ[ZnSO4])/(Δt) AsH_3 | 2 | 2 | 1/2 (Δ[AsH3])/(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 = -1/11 (Δ[H2SO4])/(Δt) = -1/8 (Δ[Zn])/(Δt) = -1/2 (Δ[K3AsO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/8 (Δ[ZnSO4])/(Δt) = 1/2 (Δ[AsH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | zinc | K3AsO4 | water | potassium sulfate | zinc sulfate | arsine formula | H_2SO_4 | Zn | K3AsO4 | H_2O | K_2SO_4 | ZnSO_4 | AsH_3 Hill formula | H_2O_4S | Zn | AsK3O4 | H_2O | K_2O_4S | O_4SZn | AsH_3 name | sulfuric acid | zinc | | water | potassium sulfate | zinc sulfate | arsine IUPAC name | sulfuric acid | zinc | | water | dipotassium sulfate | zinc sulfate | arsane

| sulfuric acid | zinc | K3AsO4 | water | potassium sulfate | zinc sulfate | arsine molar mass | 98.07 g/mol | 65.38 g/mol | 256.212 g/mol | 18.015 g/mol | 174.25 g/mol | 161.4 g/mol | 77.946 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | | gas (at STP) melting point | 10.371 °C | 420 °C | | 0 °C | | | -111.2 °C boiling point | 279.6 °C | 907 °C | | 99.9839 °C | | | -62.5 °C density | 1.8305 g/cm^3 | 7.14 g/cm^3 | | 1 g/cm^3 | | 1.005 g/cm^3 | 0.003186 g/cm^3 (at 25 °C) 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) | | | 1.47×10^-5 Pa s (at 0 °C) odor | odorless | odorless | | odorless | | odorless |