HCl + HNO3 + V = H2O + NO2 + VCl4

Input interpretation

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HCl hydrogen chloride + HNO_3 nitric acid + V vanadium ⟶ H_2O water + NO_2 nitrogen dioxide + VCl_4 vanadium tetrachloride

Balanced equation

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Balance the chemical equation algebraically: HCl + HNO_3 + V ⟶ H_2O + NO_2 + VCl_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 + c_3 V ⟶ c_4 H_2O + c_5 NO_2 + c_6 VCl_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, O and V: Cl: | c_1 = 4 c_6 H: | c_1 + c_2 = 2 c_4 N: | c_2 = c_5 O: | 3 c_2 = c_4 + 2 c_5 V: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HCl + 4 HNO_3 + V ⟶ 4 H_2O + 4 NO_2 + VCl_4

+ + ⟶ + +

Names

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hydrogen chloride + nitric acid + vanadium ⟶ water + nitrogen dioxide + vanadium tetrachloride

Equilibrium constant

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Construct the equilibrium constant, K, expression for: HCl + HNO_3 + V ⟶ H_2O + NO_2 + VCl_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: 4 HCl + 4 HNO_3 + V ⟶ 4 H_2O + 4 NO_2 + VCl_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 HCl | 4 | -4 HNO_3 | 4 | -4 V | 1 | -1 H_2O | 4 | 4 NO_2 | 4 | 4 VCl_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 4 | -4 | ([HCl])^(-4) HNO_3 | 4 | -4 | ([HNO3])^(-4) V | 1 | -1 | ([V])^(-1) H_2O | 4 | 4 | ([H2O])^4 NO_2 | 4 | 4 | ([NO2])^4 VCl_4 | 1 | 1 | [VCl4] 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 = ([HCl])^(-4) ([HNO3])^(-4) ([V])^(-1) ([H2O])^4 ([NO2])^4 [VCl4] = (([H2O])^4 ([NO2])^4 [VCl4])/(([HCl])^4 ([HNO3])^4 [V])

Rate of reaction

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Construct the rate of reaction expression for: HCl + HNO_3 + V ⟶ H_2O + NO_2 + VCl_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: 4 HCl + 4 HNO_3 + V ⟶ 4 H_2O + 4 NO_2 + VCl_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 HCl | 4 | -4 HNO_3 | 4 | -4 V | 1 | -1 H_2O | 4 | 4 NO_2 | 4 | 4 VCl_4 | 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 HCl | 4 | -4 | -1/4 (Δ[HCl])/(Δt) HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) V | 1 | -1 | -(Δ[V])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO_2 | 4 | 4 | 1/4 (Δ[NO2])/(Δt) VCl_4 | 1 | 1 | (Δ[VCl4])/(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[HCl])/(Δt) = -1/4 (Δ[HNO3])/(Δt) = -(Δ[V])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[NO2])/(Δt) = (Δ[VCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)