Input interpretation
HCl hydrogen chloride + HNO_3 nitric acid + Ti titanium ⟶ H_2O water + N_2O nitrous oxide + TiCl_4 titanium tetrachloride
Balanced equation
Balance the chemical equation algebraically: HCl + HNO_3 + Ti ⟶ H_2O + N_2O + TiCl_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 + c_3 Ti ⟶ c_4 H_2O + c_5 N_2O + c_6 TiCl_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, O and Ti: Cl: | c_1 = 4 c_6 H: | c_1 + c_2 = 2 c_4 N: | c_2 = 2 c_5 O: | 3 c_2 = c_4 + c_5 Ti: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 2 c_4 = 5 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 2 HNO_3 + 2 Ti ⟶ 5 H_2O + N_2O + 2 TiCl_4
Structures
+ + ⟶ + +
Names
hydrogen chloride + nitric acid + titanium ⟶ water + nitrous oxide + titanium tetrachloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + HNO_3 + Ti ⟶ H_2O + N_2O + TiCl_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: 8 HCl + 2 HNO_3 + 2 Ti ⟶ 5 H_2O + N_2O + 2 TiCl_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 | 8 | -8 HNO_3 | 2 | -2 Ti | 2 | -2 H_2O | 5 | 5 N_2O | 1 | 1 TiCl_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) HNO_3 | 2 | -2 | ([HNO3])^(-2) Ti | 2 | -2 | ([Ti])^(-2) H_2O | 5 | 5 | ([H2O])^5 N_2O | 1 | 1 | [N2O] TiCl_4 | 2 | 2 | ([TiCl4])^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 = ([HCl])^(-8) ([HNO3])^(-2) ([Ti])^(-2) ([H2O])^5 [N2O] ([TiCl4])^2 = (([H2O])^5 [N2O] ([TiCl4])^2)/(([HCl])^8 ([HNO3])^2 ([Ti])^2)](../image_source/ecea1163132cf74b17e636a4ff01e5d6.png)
Construct the equilibrium constant, K, expression for: HCl + HNO_3 + Ti ⟶ H_2O + N_2O + TiCl_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: 8 HCl + 2 HNO_3 + 2 Ti ⟶ 5 H_2O + N_2O + 2 TiCl_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 | 8 | -8 HNO_3 | 2 | -2 Ti | 2 | -2 H_2O | 5 | 5 N_2O | 1 | 1 TiCl_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) HNO_3 | 2 | -2 | ([HNO3])^(-2) Ti | 2 | -2 | ([Ti])^(-2) H_2O | 5 | 5 | ([H2O])^5 N_2O | 1 | 1 | [N2O] TiCl_4 | 2 | 2 | ([TiCl4])^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 = ([HCl])^(-8) ([HNO3])^(-2) ([Ti])^(-2) ([H2O])^5 [N2O] ([TiCl4])^2 = (([H2O])^5 [N2O] ([TiCl4])^2)/(([HCl])^8 ([HNO3])^2 ([Ti])^2)
Rate of reaction
![Construct the rate of reaction expression for: HCl + HNO_3 + Ti ⟶ H_2O + N_2O + TiCl_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: 8 HCl + 2 HNO_3 + 2 Ti ⟶ 5 H_2O + N_2O + 2 TiCl_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 | 8 | -8 HNO_3 | 2 | -2 Ti | 2 | -2 H_2O | 5 | 5 N_2O | 1 | 1 TiCl_4 | 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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Ti | 2 | -2 | -1/2 (Δ[Ti])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(Δt) TiCl_4 | 2 | 2 | 1/2 (Δ[TiCl4])/(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 = -1/8 (Δ[HCl])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/2 (Δ[Ti])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[N2O])/(Δt) = 1/2 (Δ[TiCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/2d3229c385c54b16b9f5fd99b40b07d9.png)
Construct the rate of reaction expression for: HCl + HNO_3 + Ti ⟶ H_2O + N_2O + TiCl_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: 8 HCl + 2 HNO_3 + 2 Ti ⟶ 5 H_2O + N_2O + 2 TiCl_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 | 8 | -8 HNO_3 | 2 | -2 Ti | 2 | -2 H_2O | 5 | 5 N_2O | 1 | 1 TiCl_4 | 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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Ti | 2 | -2 | -1/2 (Δ[Ti])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(Δt) TiCl_4 | 2 | 2 | 1/2 (Δ[TiCl4])/(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 = -1/8 (Δ[HCl])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/2 (Δ[Ti])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[N2O])/(Δt) = 1/2 (Δ[TiCl4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| hydrogen chloride | nitric acid | titanium | water | nitrous oxide | titanium tetrachloride formula | HCl | HNO_3 | Ti | H_2O | N_2O | TiCl_4 Hill formula | ClH | HNO_3 | Ti | H_2O | N_2O | Cl_4Ti name | hydrogen chloride | nitric acid | titanium | water | nitrous oxide | titanium tetrachloride IUPAC name | hydrogen chloride | nitric acid | titanium | water | nitrous oxide | tetrachlorotitanium