HNO3 + C = H2O + CO2 + N2

HNO_3 nitric acid + C activated charcoal ⟶ H_2O water + CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: HNO_3 + C ⟶ H_2O + CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 C ⟶ c_3 H_2O + c_4 CO_2 + c_5 N_2 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 = 2 c_3 N: | c_1 = 2 c_5 O: | 3 c_1 = c_3 + 2 c_4 C: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 5/2 c_3 = 1 c_4 = 5/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 5 c_3 = 2 c_4 = 5 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + 5 C ⟶ 2 H_2O + 5 CO_2 + 2 N_2

+ ⟶ + +

nitric acid + activated charcoal ⟶ water + carbon dioxide + nitrogen

Construct the equilibrium constant, K, expression for: HNO_3 + C ⟶ H_2O + CO_2 + N_2 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: 4 HNO_3 + 5 C ⟶ 2 H_2O + 5 CO_2 + 2 N_2 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 | 4 | -4 C | 5 | -5 H_2O | 2 | 2 CO_2 | 5 | 5 N_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 4 | -4 | ([HNO3])^(-4) C | 5 | -5 | ([C])^(-5) H_2O | 2 | 2 | ([H2O])^2 CO_2 | 5 | 5 | ([CO2])^5 N_2 | 2 | 2 | ([N2])^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 = ([HNO3])^(-4) ([C])^(-5) ([H2O])^2 ([CO2])^5 ([N2])^2 = (([H2O])^2 ([CO2])^5 ([N2])^2)/(([HNO3])^4 ([C])^5)

Construct the rate of reaction expression for: HNO_3 + C ⟶ H_2O + CO_2 + N_2 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: 4 HNO_3 + 5 C ⟶ 2 H_2O + 5 CO_2 + 2 N_2 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 | 4 | -4 C | 5 | -5 H_2O | 2 | 2 CO_2 | 5 | 5 N_2 | 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 HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) C | 5 | -5 | -1/5 (Δ[C])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) N_2 | 2 | 2 | 1/2 (Δ[N2])/(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 = -1/4 (Δ[HNO3])/(Δt) = -1/5 (Δ[C])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/2 (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | activated charcoal | water | carbon dioxide | nitrogen formula | HNO_3 | C | H_2O | CO_2 | N_2 name | nitric acid | activated charcoal | water | carbon dioxide | nitrogen IUPAC name | nitric acid | carbon | water | carbon dioxide | molecular nitrogen