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NH2OH + Rh2(SO4)3 = H2O + H2SO4 + N2O + RhSO4

Input interpretation

NH_2OH hydroxylamine + Rh_2(SO_4)_3 rhodium(III) sulfate ⟶ H_2O water + H_2SO_4 sulfuric acid + N_2O nitrous oxide + RhSO4
NH_2OH hydroxylamine + Rh_2(SO_4)_3 rhodium(III) sulfate ⟶ H_2O water + H_2SO_4 sulfuric acid + N_2O nitrous oxide + RhSO4

Balanced equation

Balance the chemical equation algebraically: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_2OH + c_2 Rh_2(SO_4)_3 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 N_2O + c_6 RhSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Rh and S: H: | 3 c_1 = 2 c_3 + 2 c_4 N: | c_1 = 2 c_5 O: | c_1 + 12 c_2 = c_3 + 4 c_4 + c_5 + 4 c_6 Rh: | 2 c_2 = c_6 S: | 3 c_2 = c_4 + 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 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4
Balance the chemical equation algebraically: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_2OH + c_2 Rh_2(SO_4)_3 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 N_2O + c_6 RhSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Rh and S: H: | 3 c_1 = 2 c_3 + 2 c_4 N: | c_1 = 2 c_5 O: | c_1 + 12 c_2 = c_3 + 4 c_4 + c_5 + 4 c_6 Rh: | 2 c_2 = c_6 S: | 3 c_2 = c_4 + 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 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4

Structures

+ ⟶ + + + RhSO4
+ ⟶ + + + RhSO4

Names

hydroxylamine + rhodium(III) sulfate ⟶ water + sulfuric acid + nitrous oxide + RhSO4
hydroxylamine + rhodium(III) sulfate ⟶ water + sulfuric acid + nitrous oxide + RhSO4

Equilibrium constant

Construct the equilibrium constant, K, expression for: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 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: 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4 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 NH_2OH | 2 | -2 Rh_2(SO_4)_3 | 2 | -2 H_2O | 1 | 1 H_2SO_4 | 2 | 2 N_2O | 1 | 1 RhSO4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_2OH | 2 | -2 | ([NH2OH])^(-2) Rh_2(SO_4)_3 | 2 | -2 | ([Rh2(SO4)3])^(-2) H_2O | 1 | 1 | [H2O] H_2SO_4 | 2 | 2 | ([H2SO4])^2 N_2O | 1 | 1 | [N2O] RhSO4 | 4 | 4 | ([RhSO4])^4 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 = ([NH2OH])^(-2) ([Rh2(SO4)3])^(-2) [H2O] ([H2SO4])^2 [N2O] ([RhSO4])^4 = ([H2O] ([H2SO4])^2 [N2O] ([RhSO4])^4)/(([NH2OH])^2 ([Rh2(SO4)3])^2)
Construct the equilibrium constant, K, expression for: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 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: 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4 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 NH_2OH | 2 | -2 Rh_2(SO_4)_3 | 2 | -2 H_2O | 1 | 1 H_2SO_4 | 2 | 2 N_2O | 1 | 1 RhSO4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_2OH | 2 | -2 | ([NH2OH])^(-2) Rh_2(SO_4)_3 | 2 | -2 | ([Rh2(SO4)3])^(-2) H_2O | 1 | 1 | [H2O] H_2SO_4 | 2 | 2 | ([H2SO4])^2 N_2O | 1 | 1 | [N2O] RhSO4 | 4 | 4 | ([RhSO4])^4 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 = ([NH2OH])^(-2) ([Rh2(SO4)3])^(-2) [H2O] ([H2SO4])^2 [N2O] ([RhSO4])^4 = ([H2O] ([H2SO4])^2 [N2O] ([RhSO4])^4)/(([NH2OH])^2 ([Rh2(SO4)3])^2)

Rate of reaction

Construct the rate of reaction expression for: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 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: 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4 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 NH_2OH | 2 | -2 Rh_2(SO_4)_3 | 2 | -2 H_2O | 1 | 1 H_2SO_4 | 2 | 2 N_2O | 1 | 1 RhSO4 | 4 | 4 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 NH_2OH | 2 | -2 | -1/2 (Δ[NH2OH])/(Δt) Rh_2(SO_4)_3 | 2 | -2 | -1/2 (Δ[Rh2(SO4)3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(Δt) RhSO4 | 4 | 4 | 1/4 (Δ[RhSO4])/(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 = -1/2 (Δ[NH2OH])/(Δt) = -1/2 (Δ[Rh2(SO4)3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = (Δ[N2O])/(Δt) = 1/4 (Δ[RhSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NH_2OH + Rh_2(SO_4)_3 ⟶ H_2O + H_2SO_4 + N_2O + RhSO4 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: 2 NH_2OH + 2 Rh_2(SO_4)_3 ⟶ H_2O + 2 H_2SO_4 + N_2O + 4 RhSO4 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 NH_2OH | 2 | -2 Rh_2(SO_4)_3 | 2 | -2 H_2O | 1 | 1 H_2SO_4 | 2 | 2 N_2O | 1 | 1 RhSO4 | 4 | 4 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 NH_2OH | 2 | -2 | -1/2 (Δ[NH2OH])/(Δt) Rh_2(SO_4)_3 | 2 | -2 | -1/2 (Δ[Rh2(SO4)3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(Δt) RhSO4 | 4 | 4 | 1/4 (Δ[RhSO4])/(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 = -1/2 (Δ[NH2OH])/(Δt) = -1/2 (Δ[Rh2(SO4)3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = (Δ[N2O])/(Δt) = 1/4 (Δ[RhSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydroxylamine | rhodium(III) sulfate | water | sulfuric acid | nitrous oxide | RhSO4 formula | NH_2OH | Rh_2(SO_4)_3 | H_2O | H_2SO_4 | N_2O | RhSO4 Hill formula | H_3NO | O_12Rh_2S_3 | H_2O | H_2O_4S | N_2O | O4RhS name | hydroxylamine | rhodium(III) sulfate | water | sulfuric acid | nitrous oxide |
| hydroxylamine | rhodium(III) sulfate | water | sulfuric acid | nitrous oxide | RhSO4 formula | NH_2OH | Rh_2(SO_4)_3 | H_2O | H_2SO_4 | N_2O | RhSO4 Hill formula | H_3NO | O_12Rh_2S_3 | H_2O | H_2O_4S | N_2O | O4RhS name | hydroxylamine | rhodium(III) sulfate | water | sulfuric acid | nitrous oxide |

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