Input interpretation
HNO_3 nitric acid + MoS_2 molybdenum disulfide ⟶ H_2O water + H_2SO_4 sulfuric acid + NO_2 nitrogen dioxide + H_2MoO_4 molybdic acid
Balanced equation
Balance the chemical equation algebraically: HNO_3 + MoS_2 ⟶ H_2O + H_2SO_4 + NO_2 + H_2MoO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 MoS_2 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 + c_6 H_2MoO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Mo and S: H: | c_1 = 2 c_3 + 2 c_4 + 2 c_6 N: | c_1 = c_5 O: | 3 c_1 = c_3 + 4 c_4 + 2 c_5 + 4 c_6 Mo: | c_2 = c_6 S: | 2 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 = 18 c_2 = 1 c_3 = 6 c_4 = 2 c_5 = 18 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 18 HNO_3 + MoS_2 ⟶ 6 H_2O + 2 H_2SO_4 + 18 NO_2 + H_2MoO_4
Structures
+ ⟶ + + +
Names
nitric acid + molybdenum disulfide ⟶ water + sulfuric acid + nitrogen dioxide + molybdic acid
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HNO_3 + MoS_2 ⟶ H_2O + H_2SO_4 + NO_2 + H_2MoO_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: 18 HNO_3 + MoS_2 ⟶ 6 H_2O + 2 H_2SO_4 + 18 NO_2 + H_2MoO_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 | 18 | -18 MoS_2 | 1 | -1 H_2O | 6 | 6 H_2SO_4 | 2 | 2 NO_2 | 18 | 18 H_2MoO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 18 | -18 | ([HNO3])^(-18) MoS_2 | 1 | -1 | ([MoS2])^(-1) H_2O | 6 | 6 | ([H2O])^6 H_2SO_4 | 2 | 2 | ([H2SO4])^2 NO_2 | 18 | 18 | ([NO2])^18 H_2MoO_4 | 1 | 1 | [H2MoO4] 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])^(-18) ([MoS2])^(-1) ([H2O])^6 ([H2SO4])^2 ([NO2])^18 [H2MoO4] = (([H2O])^6 ([H2SO4])^2 ([NO2])^18 [H2MoO4])/(([HNO3])^18 [MoS2])](../image_source/78dc41149ff960d7b06697ae4a42a605.png)
Construct the equilibrium constant, K, expression for: HNO_3 + MoS_2 ⟶ H_2O + H_2SO_4 + NO_2 + H_2MoO_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: 18 HNO_3 + MoS_2 ⟶ 6 H_2O + 2 H_2SO_4 + 18 NO_2 + H_2MoO_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 | 18 | -18 MoS_2 | 1 | -1 H_2O | 6 | 6 H_2SO_4 | 2 | 2 NO_2 | 18 | 18 H_2MoO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 18 | -18 | ([HNO3])^(-18) MoS_2 | 1 | -1 | ([MoS2])^(-1) H_2O | 6 | 6 | ([H2O])^6 H_2SO_4 | 2 | 2 | ([H2SO4])^2 NO_2 | 18 | 18 | ([NO2])^18 H_2MoO_4 | 1 | 1 | [H2MoO4] 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])^(-18) ([MoS2])^(-1) ([H2O])^6 ([H2SO4])^2 ([NO2])^18 [H2MoO4] = (([H2O])^6 ([H2SO4])^2 ([NO2])^18 [H2MoO4])/(([HNO3])^18 [MoS2])
Rate of reaction
![Construct the rate of reaction expression for: HNO_3 + MoS_2 ⟶ H_2O + H_2SO_4 + NO_2 + H_2MoO_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: 18 HNO_3 + MoS_2 ⟶ 6 H_2O + 2 H_2SO_4 + 18 NO_2 + H_2MoO_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 | 18 | -18 MoS_2 | 1 | -1 H_2O | 6 | 6 H_2SO_4 | 2 | 2 NO_2 | 18 | 18 H_2MoO_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 HNO_3 | 18 | -18 | -1/18 (Δ[HNO3])/(Δt) MoS_2 | 1 | -1 | -(Δ[MoS2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) NO_2 | 18 | 18 | 1/18 (Δ[NO2])/(Δt) H_2MoO_4 | 1 | 1 | (Δ[H2MoO4])/(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 = -1/18 (Δ[HNO3])/(Δt) = -(Δ[MoS2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/18 (Δ[NO2])/(Δt) = (Δ[H2MoO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/b9e169c7b35b9acc0269617879e1fdef.png)
Construct the rate of reaction expression for: HNO_3 + MoS_2 ⟶ H_2O + H_2SO_4 + NO_2 + H_2MoO_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: 18 HNO_3 + MoS_2 ⟶ 6 H_2O + 2 H_2SO_4 + 18 NO_2 + H_2MoO_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 | 18 | -18 MoS_2 | 1 | -1 H_2O | 6 | 6 H_2SO_4 | 2 | 2 NO_2 | 18 | 18 H_2MoO_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 HNO_3 | 18 | -18 | -1/18 (Δ[HNO3])/(Δt) MoS_2 | 1 | -1 | -(Δ[MoS2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) NO_2 | 18 | 18 | 1/18 (Δ[NO2])/(Δt) H_2MoO_4 | 1 | 1 | (Δ[H2MoO4])/(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 = -1/18 (Δ[HNO3])/(Δt) = -(Δ[MoS2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/18 (Δ[NO2])/(Δt) = (Δ[H2MoO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| nitric acid | molybdenum disulfide | water | sulfuric acid | nitrogen dioxide | molybdic acid formula | HNO_3 | MoS_2 | H_2O | H_2SO_4 | NO_2 | H_2MoO_4 Hill formula | HNO_3 | MoS_2 | H_2O | H_2O_4S | NO_2 | H_2MoO_4 name | nitric acid | molybdenum disulfide | water | sulfuric acid | nitrogen dioxide | molybdic acid IUPAC name | nitric acid | dithioxomolybdenum | water | sulfuric acid | Nitrogen dioxide | dihydroxy-dioxo-molybdenum