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HNO3 + Fe(CrO2)2 = H2O + NO + Fe(NO3)3 + H2CrO4

Input interpretation

HNO_3 nitric acid + Fe(CrO2)2 ⟶ H_2O water + NO nitric oxide + Fe(NO_3)_3 ferric nitrate + H_2CrO_4 chromic acid
HNO_3 nitric acid + Fe(CrO2)2 ⟶ H_2O water + NO nitric oxide + Fe(NO_3)_3 ferric nitrate + H_2CrO_4 chromic acid

Balanced equation

Balance the chemical equation algebraically: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Fe(CrO2)2 ⟶ c_3 H_2O + c_4 NO + c_5 Fe(NO_3)_3 + c_6 H_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Fe and Cr: H: | c_1 = 2 c_3 + 2 c_6 N: | c_1 = c_4 + 3 c_5 O: | 3 c_1 + 4 c_2 = c_3 + c_4 + 9 c_5 + 4 c_6 Fe: | c_2 = c_5 Cr: | 2 c_2 = 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 = 8 c_2 = 3/2 c_3 = 1 c_4 = 7/2 c_5 = 3/2 c_6 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 3 c_3 = 2 c_4 = 7 c_5 = 3 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4
Balance the chemical equation algebraically: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Fe(CrO2)2 ⟶ c_3 H_2O + c_4 NO + c_5 Fe(NO_3)_3 + c_6 H_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Fe and Cr: H: | c_1 = 2 c_3 + 2 c_6 N: | c_1 = c_4 + 3 c_5 O: | 3 c_1 + 4 c_2 = c_3 + c_4 + 9 c_5 + 4 c_6 Fe: | c_2 = c_5 Cr: | 2 c_2 = 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 = 8 c_2 = 3/2 c_3 = 1 c_4 = 7/2 c_5 = 3/2 c_6 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 3 c_3 = 2 c_4 = 7 c_5 = 3 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4

Structures

+ Fe(CrO2)2 ⟶ + + +
+ Fe(CrO2)2 ⟶ + + +

Names

nitric acid + Fe(CrO2)2 ⟶ water + nitric oxide + ferric nitrate + chromic acid
nitric acid + Fe(CrO2)2 ⟶ water + nitric oxide + ferric nitrate + chromic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 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: 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4 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 HNO_3 | 16 | -16 Fe(CrO2)2 | 3 | -3 H_2O | 2 | 2 NO | 7 | 7 Fe(NO_3)_3 | 3 | 3 H_2CrO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 16 | -16 | ([HNO3])^(-16) Fe(CrO2)2 | 3 | -3 | ([Fe(CrO2)2])^(-3) H_2O | 2 | 2 | ([H2O])^2 NO | 7 | 7 | ([NO])^7 Fe(NO_3)_3 | 3 | 3 | ([Fe(NO3)3])^3 H_2CrO_4 | 6 | 6 | ([H2CrO4])^6 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 = ([HNO3])^(-16) ([Fe(CrO2)2])^(-3) ([H2O])^2 ([NO])^7 ([Fe(NO3)3])^3 ([H2CrO4])^6 = (([H2O])^2 ([NO])^7 ([Fe(NO3)3])^3 ([H2CrO4])^6)/(([HNO3])^16 ([Fe(CrO2)2])^3)
Construct the equilibrium constant, K, expression for: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 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: 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4 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 HNO_3 | 16 | -16 Fe(CrO2)2 | 3 | -3 H_2O | 2 | 2 NO | 7 | 7 Fe(NO_3)_3 | 3 | 3 H_2CrO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 16 | -16 | ([HNO3])^(-16) Fe(CrO2)2 | 3 | -3 | ([Fe(CrO2)2])^(-3) H_2O | 2 | 2 | ([H2O])^2 NO | 7 | 7 | ([NO])^7 Fe(NO_3)_3 | 3 | 3 | ([Fe(NO3)3])^3 H_2CrO_4 | 6 | 6 | ([H2CrO4])^6 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 = ([HNO3])^(-16) ([Fe(CrO2)2])^(-3) ([H2O])^2 ([NO])^7 ([Fe(NO3)3])^3 ([H2CrO4])^6 = (([H2O])^2 ([NO])^7 ([Fe(NO3)3])^3 ([H2CrO4])^6)/(([HNO3])^16 ([Fe(CrO2)2])^3)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 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: 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4 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 HNO_3 | 16 | -16 Fe(CrO2)2 | 3 | -3 H_2O | 2 | 2 NO | 7 | 7 Fe(NO_3)_3 | 3 | 3 H_2CrO_4 | 6 | 6 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 HNO_3 | 16 | -16 | -1/16 (Δ[HNO3])/(Δt) Fe(CrO2)2 | 3 | -3 | -1/3 (Δ[Fe(CrO2)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 7 | 7 | 1/7 (Δ[NO])/(Δt) Fe(NO_3)_3 | 3 | 3 | 1/3 (Δ[Fe(NO3)3])/(Δt) H_2CrO_4 | 6 | 6 | 1/6 (Δ[H2CrO4])/(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 = -1/16 (Δ[HNO3])/(Δt) = -1/3 (Δ[Fe(CrO2)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/7 (Δ[NO])/(Δt) = 1/3 (Δ[Fe(NO3)3])/(Δt) = 1/6 (Δ[H2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + Fe(CrO2)2 ⟶ H_2O + NO + Fe(NO_3)_3 + H_2CrO_4 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: 16 HNO_3 + 3 Fe(CrO2)2 ⟶ 2 H_2O + 7 NO + 3 Fe(NO_3)_3 + 6 H_2CrO_4 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 HNO_3 | 16 | -16 Fe(CrO2)2 | 3 | -3 H_2O | 2 | 2 NO | 7 | 7 Fe(NO_3)_3 | 3 | 3 H_2CrO_4 | 6 | 6 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 HNO_3 | 16 | -16 | -1/16 (Δ[HNO3])/(Δt) Fe(CrO2)2 | 3 | -3 | -1/3 (Δ[Fe(CrO2)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 7 | 7 | 1/7 (Δ[NO])/(Δt) Fe(NO_3)_3 | 3 | 3 | 1/3 (Δ[Fe(NO3)3])/(Δt) H_2CrO_4 | 6 | 6 | 1/6 (Δ[H2CrO4])/(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 = -1/16 (Δ[HNO3])/(Δt) = -1/3 (Δ[Fe(CrO2)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/7 (Δ[NO])/(Δt) = 1/3 (Δ[Fe(NO3)3])/(Δt) = 1/6 (Δ[H2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | Fe(CrO2)2 | water | nitric oxide | ferric nitrate | chromic acid formula | HNO_3 | Fe(CrO2)2 | H_2O | NO | Fe(NO_3)_3 | H_2CrO_4 Hill formula | HNO_3 | Cr2FeO4 | H_2O | NO | FeN_3O_9 | CrH_2O_4 name | nitric acid | | water | nitric oxide | ferric nitrate | chromic acid IUPAC name | nitric acid | | water | nitric oxide | iron(+3) cation trinitrate | dihydroxy-dioxo-chromium
| nitric acid | Fe(CrO2)2 | water | nitric oxide | ferric nitrate | chromic acid formula | HNO_3 | Fe(CrO2)2 | H_2O | NO | Fe(NO_3)_3 | H_2CrO_4 Hill formula | HNO_3 | Cr2FeO4 | H_2O | NO | FeN_3O_9 | CrH_2O_4 name | nitric acid | | water | nitric oxide | ferric nitrate | chromic acid IUPAC name | nitric acid | | water | nitric oxide | iron(+3) cation trinitrate | dihydroxy-dioxo-chromium

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