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H2O + NH3 + Cr(NO3)3 = NH4NO3 + Cr(OH)3

Input interpretation

H_2O water + NH_3 ammonia + CrN_3O_9 chromium nitrate ⟶ NH_4NO_3 ammonium nitrate + Cr(OH)3
H_2O water + NH_3 ammonia + CrN_3O_9 chromium nitrate ⟶ NH_4NO_3 ammonium nitrate + Cr(OH)3

Balanced equation

Balance the chemical equation algebraically: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 CrN_3O_9 ⟶ c_4 NH_4NO_3 + c_5 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and Cr: H: | 2 c_1 + 3 c_2 = 4 c_4 + 3 c_5 O: | c_1 + 9 c_3 = 3 c_4 + 3 c_5 N: | c_2 + 3 c_3 = 2 c_4 Cr: | c_3 = c_5 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 = 3 c_3 = 1 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(OH)3
Balance the chemical equation algebraically: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 + c_3 CrN_3O_9 ⟶ c_4 NH_4NO_3 + c_5 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and Cr: H: | 2 c_1 + 3 c_2 = 4 c_4 + 3 c_5 O: | c_1 + 9 c_3 = 3 c_4 + 3 c_5 N: | c_2 + 3 c_3 = 2 c_4 Cr: | c_3 = c_5 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 = 3 c_3 = 1 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(OH)3

Structures

+ + ⟶ + Cr(OH)3
+ + ⟶ + Cr(OH)3

Names

water + ammonia + chromium nitrate ⟶ ammonium nitrate + Cr(OH)3
water + ammonia + chromium nitrate ⟶ ammonium nitrate + Cr(OH)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(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 + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(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 NH_3 | 3 | -3 CrN_3O_9 | 1 | -1 NH_4NO_3 | 3 | 3 Cr(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) NH_3 | 3 | -3 | ([NH3])^(-3) CrN_3O_9 | 1 | -1 | ([CrN3O9])^(-1) NH_4NO_3 | 3 | 3 | ([NH4NO3])^3 Cr(OH)3 | 1 | 1 | [Cr(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) ([NH3])^(-3) ([CrN3O9])^(-1) ([NH4NO3])^3 [Cr(OH)3] = (([NH4NO3])^3 [Cr(OH)3])/(([H2O])^3 ([NH3])^3 [CrN3O9])
Construct the equilibrium constant, K, expression for: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(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 + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(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 NH_3 | 3 | -3 CrN_3O_9 | 1 | -1 NH_4NO_3 | 3 | 3 Cr(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) NH_3 | 3 | -3 | ([NH3])^(-3) CrN_3O_9 | 1 | -1 | ([CrN3O9])^(-1) NH_4NO_3 | 3 | 3 | ([NH4NO3])^3 Cr(OH)3 | 1 | 1 | [Cr(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) ([NH3])^(-3) ([CrN3O9])^(-1) ([NH4NO3])^3 [Cr(OH)3] = (([NH4NO3])^3 [Cr(OH)3])/(([H2O])^3 ([NH3])^3 [CrN3O9])

Rate of reaction

Construct the rate of reaction expression for: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(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 + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(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 NH_3 | 3 | -3 CrN_3O_9 | 1 | -1 NH_4NO_3 | 3 | 3 Cr(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) NH_3 | 3 | -3 | -1/3 (Δ[NH3])/(Δt) CrN_3O_9 | 1 | -1 | -(Δ[CrN3O9])/(Δt) NH_4NO_3 | 3 | 3 | 1/3 (Δ[NH4NO3])/(Δt) Cr(OH)3 | 1 | 1 | (Δ[Cr(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) = -1/3 (Δ[NH3])/(Δt) = -(Δ[CrN3O9])/(Δt) = 1/3 (Δ[NH4NO3])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + NH_3 + CrN_3O_9 ⟶ NH_4NO_3 + Cr(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 + 3 NH_3 + CrN_3O_9 ⟶ 3 NH_4NO_3 + Cr(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 NH_3 | 3 | -3 CrN_3O_9 | 1 | -1 NH_4NO_3 | 3 | 3 Cr(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) NH_3 | 3 | -3 | -1/3 (Δ[NH3])/(Δt) CrN_3O_9 | 1 | -1 | -(Δ[CrN3O9])/(Δt) NH_4NO_3 | 3 | 3 | 1/3 (Δ[NH4NO3])/(Δt) Cr(OH)3 | 1 | 1 | (Δ[Cr(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) = -1/3 (Δ[NH3])/(Δt) = -(Δ[CrN3O9])/(Δt) = 1/3 (Δ[NH4NO3])/(Δt) = (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | ammonia | chromium nitrate | ammonium nitrate | Cr(OH)3 formula | H_2O | NH_3 | CrN_3O_9 | NH_4NO_3 | Cr(OH)3 Hill formula | H_2O | H_3N | CrN_3O_9 | H_4N_2O_3 | H3CrO3 name | water | ammonia | chromium nitrate | ammonium nitrate | IUPAC name | water | ammonia | chromium(+3) cation trinitrate | |
| water | ammonia | chromium nitrate | ammonium nitrate | Cr(OH)3 formula | H_2O | NH_3 | CrN_3O_9 | NH_4NO_3 | Cr(OH)3 Hill formula | H_2O | H_3N | CrN_3O_9 | H_4N_2O_3 | H3CrO3 name | water | ammonia | chromium nitrate | ammonium nitrate | IUPAC name | water | ammonia | chromium(+3) cation trinitrate | |

Substance properties

| water | ammonia | chromium nitrate | ammonium nitrate | Cr(OH)3 molar mass | 18.015 g/mol | 17.031 g/mol | 238.01 g/mol | 80.04 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | -77.73 °C | 66 °C | 169 °C | boiling point | 99.9839 °C | -33.33 °C | | 210 °C | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.8 g/cm^3 | 1.73 g/cm^3 | solubility in water | | | soluble | | surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | odorless |
| water | ammonia | chromium nitrate | ammonium nitrate | Cr(OH)3 molar mass | 18.015 g/mol | 17.031 g/mol | 238.01 g/mol | 80.04 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | -77.73 °C | 66 °C | 169 °C | boiling point | 99.9839 °C | -33.33 °C | | 210 °C | density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.8 g/cm^3 | 1.73 g/cm^3 | solubility in water | | | soluble | | surface tension | 0.0728 N/m | 0.0234 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | odorless |

Units

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