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H2O + AgNO3 + AsH3 = HNO3 + Ag + H3AsO3

Input interpretation

H_2O (water) + AgNO_3 (silver nitrate) + AsH_3 (arsine) ⟶ HNO_3 (nitric acid) + Ag (silver) + As(OH)_3 (arsenious acid)
H_2O (water) + AgNO_3 (silver nitrate) + AsH_3 (arsine) ⟶ HNO_3 (nitric acid) + Ag (silver) + As(OH)_3 (arsenious acid)

Balanced equation

Balance the chemical equation algebraically: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AgNO_3 + c_3 AsH_3 ⟶ c_4 HNO_3 + c_5 Ag + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag, N and As: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_6 O: | c_1 + 3 c_2 = 3 c_4 + 3 c_6 Ag: | c_2 = c_5 N: | c_2 = c_4 As: | c_3 = c_6 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 = 3 c_2 = 6 c_3 = 1 c_4 = 6 c_5 = 6 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_3
Balance the chemical equation algebraically: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AgNO_3 + c_3 AsH_3 ⟶ c_4 HNO_3 + c_5 Ag + c_6 As(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag, N and As: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_6 O: | c_1 + 3 c_2 = 3 c_4 + 3 c_6 Ag: | c_2 = c_5 N: | c_2 = c_4 As: | c_3 = c_6 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 = 3 c_2 = 6 c_3 = 1 c_4 = 6 c_5 = 6 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + silver nitrate + arsine ⟶ nitric acid + silver + arsenious acid
water + silver nitrate + arsine ⟶ nitric acid + silver + arsenious acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_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: 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_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_2O | 3 | -3 AgNO_3 | 6 | -6 AsH_3 | 1 | -1 HNO_3 | 6 | 6 Ag | 6 | 6 As(OH)_3 | 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 | 3 | -3 | ([H2O])^(-3) AgNO_3 | 6 | -6 | ([AgNO3])^(-6) AsH_3 | 1 | -1 | ([AsH3])^(-1) HNO_3 | 6 | 6 | ([HNO3])^6 Ag | 6 | 6 | ([Ag])^6 As(OH)_3 | 1 | 1 | [As(OH)3] 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])^(-3) ([AgNO3])^(-6) ([AsH3])^(-1) ([HNO3])^6 ([Ag])^6 [As(OH)3] = (([HNO3])^6 ([Ag])^6 [As(OH)3])/(([H2O])^3 ([AgNO3])^6 [AsH3])
Construct the equilibrium constant, K, expression for: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_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: 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_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_2O | 3 | -3 AgNO_3 | 6 | -6 AsH_3 | 1 | -1 HNO_3 | 6 | 6 Ag | 6 | 6 As(OH)_3 | 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 | 3 | -3 | ([H2O])^(-3) AgNO_3 | 6 | -6 | ([AgNO3])^(-6) AsH_3 | 1 | -1 | ([AsH3])^(-1) HNO_3 | 6 | 6 | ([HNO3])^6 Ag | 6 | 6 | ([Ag])^6 As(OH)_3 | 1 | 1 | [As(OH)3] 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])^(-3) ([AgNO3])^(-6) ([AsH3])^(-1) ([HNO3])^6 ([Ag])^6 [As(OH)3] = (([HNO3])^6 ([Ag])^6 [As(OH)3])/(([H2O])^3 ([AgNO3])^6 [AsH3])

Rate of reaction

Construct the rate of reaction expression for: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_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: 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_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_2O | 3 | -3 AgNO_3 | 6 | -6 AsH_3 | 1 | -1 HNO_3 | 6 | 6 Ag | 6 | 6 As(OH)_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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) AgNO_3 | 6 | -6 | -1/6 (Δ[AgNO3])/(Δt) AsH_3 | 1 | -1 | -(Δ[AsH3])/(Δt) HNO_3 | 6 | 6 | 1/6 (Δ[HNO3])/(Δt) Ag | 6 | 6 | 1/6 (Δ[Ag])/(Δt) As(OH)_3 | 1 | 1 | (Δ[As(OH)3])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/6 (Δ[AgNO3])/(Δt) = -(Δ[AsH3])/(Δt) = 1/6 (Δ[HNO3])/(Δt) = 1/6 (Δ[Ag])/(Δt) = (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + AgNO_3 + AsH_3 ⟶ HNO_3 + Ag + As(OH)_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: 3 H_2O + 6 AgNO_3 + AsH_3 ⟶ 6 HNO_3 + 6 Ag + As(OH)_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_2O | 3 | -3 AgNO_3 | 6 | -6 AsH_3 | 1 | -1 HNO_3 | 6 | 6 Ag | 6 | 6 As(OH)_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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) AgNO_3 | 6 | -6 | -1/6 (Δ[AgNO3])/(Δt) AsH_3 | 1 | -1 | -(Δ[AsH3])/(Δt) HNO_3 | 6 | 6 | 1/6 (Δ[HNO3])/(Δt) Ag | 6 | 6 | 1/6 (Δ[Ag])/(Δt) As(OH)_3 | 1 | 1 | (Δ[As(OH)3])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/6 (Δ[AgNO3])/(Δt) = -(Δ[AsH3])/(Δt) = 1/6 (Δ[HNO3])/(Δt) = 1/6 (Δ[Ag])/(Δt) = (Δ[As(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | silver nitrate | arsine | nitric acid | silver | arsenious acid formula | H_2O | AgNO_3 | AsH_3 | HNO_3 | Ag | As(OH)_3 Hill formula | H_2O | AgNO_3 | AsH_3 | HNO_3 | Ag | AsH_3O_3 name | water | silver nitrate | arsine | nitric acid | silver | arsenious acid IUPAC name | water | silver nitrate | arsane | nitric acid | silver | arsorous acid
| water | silver nitrate | arsine | nitric acid | silver | arsenious acid formula | H_2O | AgNO_3 | AsH_3 | HNO_3 | Ag | As(OH)_3 Hill formula | H_2O | AgNO_3 | AsH_3 | HNO_3 | Ag | AsH_3O_3 name | water | silver nitrate | arsine | nitric acid | silver | arsenious acid IUPAC name | water | silver nitrate | arsane | nitric acid | silver | arsorous acid

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