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NH4OH + CH2O + [Ag(NH3)2]NO3 = H2O + NH3 + Ag + NH4NO3 + HCOOH

Input interpretation

NH_4OH ammonium hydroxide + HCHO formaldehyde + Ag(NH3)2NO3 ⟶ H_2O water + NH_3 ammonia + Ag silver + NH_4NO_3 ammonium nitrate + HCOOH formic acid
NH_4OH ammonium hydroxide + HCHO formaldehyde + Ag(NH3)2NO3 ⟶ H_2O water + NH_3 ammonia + Ag silver + NH_4NO_3 ammonium nitrate + HCOOH formic acid

Balanced equation

Balance the chemical equation algebraically: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4OH + c_2 HCHO + c_3 Ag(NH3)2NO3 ⟶ c_4 H_2O + c_5 NH_3 + c_6 Ag + c_7 NH_4NO_3 + c_8 HCOOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, C and Ag: H: | 5 c_1 + 2 c_2 + 6 c_3 = 2 c_4 + 3 c_5 + 4 c_7 + 2 c_8 N: | c_1 + 3 c_3 = c_5 + 2 c_7 O: | c_1 + c_2 + 3 c_3 = c_4 + 3 c_7 + 2 c_8 C: | c_2 = c_8 Ag: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_3 = -8/3 + (8 c_1)/3 - (2 c_2)/3 c_4 = 1 c_5 = 3 c_1 - 2 c_6 = -8/3 + (8 c_1)/3 - (2 c_2)/3 c_7 = -3 + 3 c_1 - c_2 c_8 = c_2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 7 and c_2 = 9 and solve for the remaining coefficients: c_1 = 7 c_2 = 9 c_3 = 10 c_4 = 1 c_5 = 19 c_6 = 10 c_7 = 9 c_8 = 9 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH
Balance the chemical equation algebraically: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4OH + c_2 HCHO + c_3 Ag(NH3)2NO3 ⟶ c_4 H_2O + c_5 NH_3 + c_6 Ag + c_7 NH_4NO_3 + c_8 HCOOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, C and Ag: H: | 5 c_1 + 2 c_2 + 6 c_3 = 2 c_4 + 3 c_5 + 4 c_7 + 2 c_8 N: | c_1 + 3 c_3 = c_5 + 2 c_7 O: | c_1 + c_2 + 3 c_3 = c_4 + 3 c_7 + 2 c_8 C: | c_2 = c_8 Ag: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_3 = -8/3 + (8 c_1)/3 - (2 c_2)/3 c_4 = 1 c_5 = 3 c_1 - 2 c_6 = -8/3 + (8 c_1)/3 - (2 c_2)/3 c_7 = -3 + 3 c_1 - c_2 c_8 = c_2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 7 and c_2 = 9 and solve for the remaining coefficients: c_1 = 7 c_2 = 9 c_3 = 10 c_4 = 1 c_5 = 19 c_6 = 10 c_7 = 9 c_8 = 9 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH

Structures

+ + Ag(NH3)2NO3 ⟶ + + + +
+ + Ag(NH3)2NO3 ⟶ + + + +

Names

ammonium hydroxide + formaldehyde + Ag(NH3)2NO3 ⟶ water + ammonia + silver + ammonium nitrate + formic acid
ammonium hydroxide + formaldehyde + Ag(NH3)2NO3 ⟶ water + ammonia + silver + ammonium nitrate + formic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH 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: 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH 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 NH_4OH | 7 | -7 HCHO | 9 | -9 Ag(NH3)2NO3 | 10 | -10 H_2O | 1 | 1 NH_3 | 19 | 19 Ag | 10 | 10 NH_4NO_3 | 9 | 9 HCOOH | 9 | 9 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4OH | 7 | -7 | ([NH4OH])^(-7) HCHO | 9 | -9 | ([HCHO])^(-9) Ag(NH3)2NO3 | 10 | -10 | ([Ag(NH3)2NO3])^(-10) H_2O | 1 | 1 | [H2O] NH_3 | 19 | 19 | ([NH3])^19 Ag | 10 | 10 | ([Ag])^10 NH_4NO_3 | 9 | 9 | ([NH4NO3])^9 HCOOH | 9 | 9 | ([HCOOH])^9 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 = ([NH4OH])^(-7) ([HCHO])^(-9) ([Ag(NH3)2NO3])^(-10) [H2O] ([NH3])^19 ([Ag])^10 ([NH4NO3])^9 ([HCOOH])^9 = ([H2O] ([NH3])^19 ([Ag])^10 ([NH4NO3])^9 ([HCOOH])^9)/(([NH4OH])^7 ([HCHO])^9 ([Ag(NH3)2NO3])^10)
Construct the equilibrium constant, K, expression for: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH 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: 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH 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 NH_4OH | 7 | -7 HCHO | 9 | -9 Ag(NH3)2NO3 | 10 | -10 H_2O | 1 | 1 NH_3 | 19 | 19 Ag | 10 | 10 NH_4NO_3 | 9 | 9 HCOOH | 9 | 9 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4OH | 7 | -7 | ([NH4OH])^(-7) HCHO | 9 | -9 | ([HCHO])^(-9) Ag(NH3)2NO3 | 10 | -10 | ([Ag(NH3)2NO3])^(-10) H_2O | 1 | 1 | [H2O] NH_3 | 19 | 19 | ([NH3])^19 Ag | 10 | 10 | ([Ag])^10 NH_4NO_3 | 9 | 9 | ([NH4NO3])^9 HCOOH | 9 | 9 | ([HCOOH])^9 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 = ([NH4OH])^(-7) ([HCHO])^(-9) ([Ag(NH3)2NO3])^(-10) [H2O] ([NH3])^19 ([Ag])^10 ([NH4NO3])^9 ([HCOOH])^9 = ([H2O] ([NH3])^19 ([Ag])^10 ([NH4NO3])^9 ([HCOOH])^9)/(([NH4OH])^7 ([HCHO])^9 ([Ag(NH3)2NO3])^10)

Rate of reaction

Construct the rate of reaction expression for: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH 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: 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH 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 NH_4OH | 7 | -7 HCHO | 9 | -9 Ag(NH3)2NO3 | 10 | -10 H_2O | 1 | 1 NH_3 | 19 | 19 Ag | 10 | 10 NH_4NO_3 | 9 | 9 HCOOH | 9 | 9 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 NH_4OH | 7 | -7 | -1/7 (Δ[NH4OH])/(Δt) HCHO | 9 | -9 | -1/9 (Δ[HCHO])/(Δt) Ag(NH3)2NO3 | 10 | -10 | -1/10 (Δ[Ag(NH3)2NO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_3 | 19 | 19 | 1/19 (Δ[NH3])/(Δt) Ag | 10 | 10 | 1/10 (Δ[Ag])/(Δt) NH_4NO_3 | 9 | 9 | 1/9 (Δ[NH4NO3])/(Δt) HCOOH | 9 | 9 | 1/9 (Δ[HCOOH])/(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 = -1/7 (Δ[NH4OH])/(Δt) = -1/9 (Δ[HCHO])/(Δt) = -1/10 (Δ[Ag(NH3)2NO3])/(Δt) = (Δ[H2O])/(Δt) = 1/19 (Δ[NH3])/(Δt) = 1/10 (Δ[Ag])/(Δt) = 1/9 (Δ[NH4NO3])/(Δt) = 1/9 (Δ[HCOOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NH_4OH + HCHO + Ag(NH3)2NO3 ⟶ H_2O + NH_3 + Ag + NH_4NO_3 + HCOOH 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: 7 NH_4OH + 9 HCHO + 10 Ag(NH3)2NO3 ⟶ H_2O + 19 NH_3 + 10 Ag + 9 NH_4NO_3 + 9 HCOOH 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 NH_4OH | 7 | -7 HCHO | 9 | -9 Ag(NH3)2NO3 | 10 | -10 H_2O | 1 | 1 NH_3 | 19 | 19 Ag | 10 | 10 NH_4NO_3 | 9 | 9 HCOOH | 9 | 9 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 NH_4OH | 7 | -7 | -1/7 (Δ[NH4OH])/(Δt) HCHO | 9 | -9 | -1/9 (Δ[HCHO])/(Δt) Ag(NH3)2NO3 | 10 | -10 | -1/10 (Δ[Ag(NH3)2NO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_3 | 19 | 19 | 1/19 (Δ[NH3])/(Δt) Ag | 10 | 10 | 1/10 (Δ[Ag])/(Δt) NH_4NO_3 | 9 | 9 | 1/9 (Δ[NH4NO3])/(Δt) HCOOH | 9 | 9 | 1/9 (Δ[HCOOH])/(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 = -1/7 (Δ[NH4OH])/(Δt) = -1/9 (Δ[HCHO])/(Δt) = -1/10 (Δ[Ag(NH3)2NO3])/(Δt) = (Δ[H2O])/(Δt) = 1/19 (Δ[NH3])/(Δt) = 1/10 (Δ[Ag])/(Δt) = 1/9 (Δ[NH4NO3])/(Δt) = 1/9 (Δ[HCOOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| ammonium hydroxide | formaldehyde | Ag(NH3)2NO3 | water | ammonia | silver | ammonium nitrate | formic acid formula | NH_4OH | HCHO | Ag(NH3)2NO3 | H_2O | NH_3 | Ag | NH_4NO_3 | HCOOH Hill formula | H_5NO | CH_2O | H6AgN3O3 | H_2O | H_3N | Ag | H_4N_2O_3 | CH_2O_2 name | ammonium hydroxide | formaldehyde | | water | ammonia | silver | ammonium nitrate | formic acid
| ammonium hydroxide | formaldehyde | Ag(NH3)2NO3 | water | ammonia | silver | ammonium nitrate | formic acid formula | NH_4OH | HCHO | Ag(NH3)2NO3 | H_2O | NH_3 | Ag | NH_4NO_3 | HCOOH Hill formula | H_5NO | CH_2O | H6AgN3O3 | H_2O | H_3N | Ag | H_4N_2O_3 | CH_2O_2 name | ammonium hydroxide | formaldehyde | | water | ammonia | silver | ammonium nitrate | formic acid

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