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H2O2 + AgNO3 + NH4OH = H2O + O2 + Ag + NH4NO3

Input interpretation

H_2O_2 hydrogen peroxide + AgNO_3 silver nitrate + NH_4OH ammonium hydroxide ⟶ H_2O water + O_2 oxygen + Ag silver + NH_4NO_3 ammonium nitrate
H_2O_2 hydrogen peroxide + AgNO_3 silver nitrate + NH_4OH ammonium hydroxide ⟶ H_2O water + O_2 oxygen + Ag silver + NH_4NO_3 ammonium nitrate

Balanced equation

Balance the chemical equation algebraically: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 AgNO_3 + c_3 NH_4OH ⟶ c_4 H_2O + c_5 O_2 + c_6 Ag + c_7 NH_4NO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag and N: H: | 2 c_1 + 5 c_3 = 2 c_4 + 4 c_7 O: | 2 c_1 + 3 c_2 + c_3 = c_4 + 2 c_5 + 3 c_7 Ag: | c_2 = c_6 N: | c_2 + c_3 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_4 = 1 - c_2 + (3 c_3)/2 c_5 = 1/2 + (5 c_2)/4 - c_3 c_6 = c_2 c_7 = c_2/2 + c_3/2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_2 = 2 and c_3 = 2 and solve for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_3
Balance the chemical equation algebraically: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 AgNO_3 + c_3 NH_4OH ⟶ c_4 H_2O + c_5 O_2 + c_6 Ag + c_7 NH_4NO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag and N: H: | 2 c_1 + 5 c_3 = 2 c_4 + 4 c_7 O: | 2 c_1 + 3 c_2 + c_3 = c_4 + 2 c_5 + 3 c_7 Ag: | c_2 = c_6 N: | c_2 + c_3 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_4 = 1 - c_2 + (3 c_3)/2 c_5 = 1/2 + (5 c_2)/4 - c_3 c_6 = c_2 c_7 = c_2/2 + c_3/2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_2 = 2 and c_3 = 2 and solve for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_3

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

hydrogen peroxide + silver nitrate + ammonium hydroxide ⟶ water + oxygen + silver + ammonium nitrate
hydrogen peroxide + silver nitrate + ammonium hydroxide ⟶ water + oxygen + silver + ammonium nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_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: H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_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_2 | 1 | -1 AgNO_3 | 2 | -2 NH_4OH | 2 | -2 H_2O | 2 | 2 O_2 | 1 | 1 Ag | 2 | 2 NH_4NO_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_2O_2 | 1 | -1 | ([H2O2])^(-1) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) NH_4OH | 2 | -2 | ([NH4OH])^(-2) H_2O | 2 | 2 | ([H2O])^2 O_2 | 1 | 1 | [O2] Ag | 2 | 2 | ([Ag])^2 NH_4NO_3 | 2 | 2 | ([NH4NO3])^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 = ([H2O2])^(-1) ([AgNO3])^(-2) ([NH4OH])^(-2) ([H2O])^2 [O2] ([Ag])^2 ([NH4NO3])^2 = (([H2O])^2 [O2] ([Ag])^2 ([NH4NO3])^2)/([H2O2] ([AgNO3])^2 ([NH4OH])^2)
Construct the equilibrium constant, K, expression for: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_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: H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_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_2 | 1 | -1 AgNO_3 | 2 | -2 NH_4OH | 2 | -2 H_2O | 2 | 2 O_2 | 1 | 1 Ag | 2 | 2 NH_4NO_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_2O_2 | 1 | -1 | ([H2O2])^(-1) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) NH_4OH | 2 | -2 | ([NH4OH])^(-2) H_2O | 2 | 2 | ([H2O])^2 O_2 | 1 | 1 | [O2] Ag | 2 | 2 | ([Ag])^2 NH_4NO_3 | 2 | 2 | ([NH4NO3])^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 = ([H2O2])^(-1) ([AgNO3])^(-2) ([NH4OH])^(-2) ([H2O])^2 [O2] ([Ag])^2 ([NH4NO3])^2 = (([H2O])^2 [O2] ([Ag])^2 ([NH4NO3])^2)/([H2O2] ([AgNO3])^2 ([NH4OH])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_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: H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_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_2 | 1 | -1 AgNO_3 | 2 | -2 NH_4OH | 2 | -2 H_2O | 2 | 2 O_2 | 1 | 1 Ag | 2 | 2 NH_4NO_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_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Ag | 2 | 2 | 1/2 (Δ[Ag])/(Δt) NH_4NO_3 | 2 | 2 | 1/2 (Δ[NH4NO3])/(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 = -(Δ[H2O2])/(Δt) = -1/2 (Δ[AgNO3])/(Δt) = -1/2 (Δ[NH4OH])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[Ag])/(Δt) = 1/2 (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O_2 + AgNO_3 + NH_4OH ⟶ H_2O + O_2 + Ag + NH_4NO_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: H_2O_2 + 2 AgNO_3 + 2 NH_4OH ⟶ 2 H_2O + O_2 + 2 Ag + 2 NH_4NO_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_2 | 1 | -1 AgNO_3 | 2 | -2 NH_4OH | 2 | -2 H_2O | 2 | 2 O_2 | 1 | 1 Ag | 2 | 2 NH_4NO_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_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Ag | 2 | 2 | 1/2 (Δ[Ag])/(Δt) NH_4NO_3 | 2 | 2 | 1/2 (Δ[NH4NO3])/(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 = -(Δ[H2O2])/(Δt) = -1/2 (Δ[AgNO3])/(Δt) = -1/2 (Δ[NH4OH])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[Ag])/(Δt) = 1/2 (Δ[NH4NO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen peroxide | silver nitrate | ammonium hydroxide | water | oxygen | silver | ammonium nitrate formula | H_2O_2 | AgNO_3 | NH_4OH | H_2O | O_2 | Ag | NH_4NO_3 Hill formula | H_2O_2 | AgNO_3 | H_5NO | H_2O | O_2 | Ag | H_4N_2O_3 name | hydrogen peroxide | silver nitrate | ammonium hydroxide | water | oxygen | silver | ammonium nitrate IUPAC name | hydrogen peroxide | silver nitrate | ammonium hydroxide | water | molecular oxygen | silver |
| hydrogen peroxide | silver nitrate | ammonium hydroxide | water | oxygen | silver | ammonium nitrate formula | H_2O_2 | AgNO_3 | NH_4OH | H_2O | O_2 | Ag | NH_4NO_3 Hill formula | H_2O_2 | AgNO_3 | H_5NO | H_2O | O_2 | Ag | H_4N_2O_3 name | hydrogen peroxide | silver nitrate | ammonium hydroxide | water | oxygen | silver | ammonium nitrate IUPAC name | hydrogen peroxide | silver nitrate | ammonium hydroxide | water | molecular oxygen | silver |

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