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HNO3 + C6H10O5 = H2O + CO2 + N2O3

Input interpretation

HNO_3 nitric acid + HOC(CH_3)(CH_2CO_2H)_2 3-hydroxy-3-methylglutaric acid ⟶ H_2O water + CO_2 carbon dioxide + N_2O_3 nitrogen trioxide
HNO_3 nitric acid + HOC(CH_3)(CH_2CO_2H)_2 3-hydroxy-3-methylglutaric acid ⟶ H_2O water + CO_2 carbon dioxide + N_2O_3 nitrogen trioxide

Balanced equation

Balance the chemical equation algebraically: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 HOC(CH_3)(CH_2CO_2H)_2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 N_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and C: H: | c_1 + 10 c_2 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 + 5 c_2 = c_3 + 2 c_4 + 3 c_5 C: | 6 c_2 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 1 c_3 = 11 c_4 = 6 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_3
Balance the chemical equation algebraically: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 HOC(CH_3)(CH_2CO_2H)_2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 N_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and C: H: | c_1 + 10 c_2 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 + 5 c_2 = c_3 + 2 c_4 + 3 c_5 C: | 6 c_2 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 1 c_3 = 11 c_4 = 6 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_3

Structures

+ ⟶ + +
+ ⟶ + +

Names

nitric acid + 3-hydroxy-3-methylglutaric acid ⟶ water + carbon dioxide + nitrogen trioxide
nitric acid + 3-hydroxy-3-methylglutaric acid ⟶ water + carbon dioxide + nitrogen trioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_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: 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_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 HNO_3 | 12 | -12 HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 H_2O | 11 | 11 CO_2 | 6 | 6 N_2O_3 | 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 | 12 | -12 | ([HNO3])^(-12) HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 | ([HOC(CH3)(CH2CO2H)2])^(-1) H_2O | 11 | 11 | ([H2O])^11 CO_2 | 6 | 6 | ([CO2])^6 N_2O_3 | 6 | 6 | ([N2O3])^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])^(-12) ([HOC(CH3)(CH2CO2H)2])^(-1) ([H2O])^11 ([CO2])^6 ([N2O3])^6 = (([H2O])^11 ([CO2])^6 ([N2O3])^6)/(([HNO3])^12 [HOC(CH3)(CH2CO2H)2])
Construct the equilibrium constant, K, expression for: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_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: 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_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 HNO_3 | 12 | -12 HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 H_2O | 11 | 11 CO_2 | 6 | 6 N_2O_3 | 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 | 12 | -12 | ([HNO3])^(-12) HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 | ([HOC(CH3)(CH2CO2H)2])^(-1) H_2O | 11 | 11 | ([H2O])^11 CO_2 | 6 | 6 | ([CO2])^6 N_2O_3 | 6 | 6 | ([N2O3])^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])^(-12) ([HOC(CH3)(CH2CO2H)2])^(-1) ([H2O])^11 ([CO2])^6 ([N2O3])^6 = (([H2O])^11 ([CO2])^6 ([N2O3])^6)/(([HNO3])^12 [HOC(CH3)(CH2CO2H)2])

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_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: 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_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 HNO_3 | 12 | -12 HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 H_2O | 11 | 11 CO_2 | 6 | 6 N_2O_3 | 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 | 12 | -12 | -1/12 (Δ[HNO3])/(Δt) HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 | -(Δ[HOC(CH3)(CH2CO2H)2])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) N_2O_3 | 6 | 6 | 1/6 (Δ[N2O3])/(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 = -1/12 (Δ[HNO3])/(Δt) = -(Δ[HOC(CH3)(CH2CO2H)2])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/6 (Δ[N2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ H_2O + CO_2 + N_2O_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: 12 HNO_3 + HOC(CH_3)(CH_2CO_2H)_2 ⟶ 11 H_2O + 6 CO_2 + 6 N_2O_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 HNO_3 | 12 | -12 HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 H_2O | 11 | 11 CO_2 | 6 | 6 N_2O_3 | 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 | 12 | -12 | -1/12 (Δ[HNO3])/(Δt) HOC(CH_3)(CH_2CO_2H)_2 | 1 | -1 | -(Δ[HOC(CH3)(CH2CO2H)2])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) N_2O_3 | 6 | 6 | 1/6 (Δ[N2O3])/(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 = -1/12 (Δ[HNO3])/(Δt) = -(Δ[HOC(CH3)(CH2CO2H)2])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/6 (Δ[N2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | 3-hydroxy-3-methylglutaric acid | water | carbon dioxide | nitrogen trioxide formula | HNO_3 | HOC(CH_3)(CH_2CO_2H)_2 | H_2O | CO_2 | N_2O_3 Hill formula | HNO_3 | C_6H_10O_5 | H_2O | CO_2 | N_2O_3 name | nitric acid | 3-hydroxy-3-methylglutaric acid | water | carbon dioxide | nitrogen trioxide IUPAC name | nitric acid | 3-hydroxy-3-methylpentanedioic acid | water | carbon dioxide | nitramide
| nitric acid | 3-hydroxy-3-methylglutaric acid | water | carbon dioxide | nitrogen trioxide formula | HNO_3 | HOC(CH_3)(CH_2CO_2H)_2 | H_2O | CO_2 | N_2O_3 Hill formula | HNO_3 | C_6H_10O_5 | H_2O | CO_2 | N_2O_3 name | nitric acid | 3-hydroxy-3-methylglutaric acid | water | carbon dioxide | nitrogen trioxide IUPAC name | nitric acid | 3-hydroxy-3-methylpentanedioic acid | water | carbon dioxide | nitramide

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