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H2SeO4 + Pr(OH)3 = H2O + Pr2(SeO4)3

Input interpretation

H_2SeO_4 selenic acid + Pr(OH)_3 praseodymium(III) hydroxide ⟶ H_2O water + Pr2(SeO4)3
H_2SeO_4 selenic acid + Pr(OH)_3 praseodymium(III) hydroxide ⟶ H_2O water + Pr2(SeO4)3

Balanced equation

Balance the chemical equation algebraically: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SeO_4 + c_2 Pr(OH)_3 ⟶ c_3 H_2O + c_4 Pr2(SeO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Se and Pr: H: | 2 c_1 + 3 c_2 = 2 c_3 O: | 4 c_1 + 3 c_2 = c_3 + 12 c_4 Se: | c_1 = 3 c_4 Pr: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3
Balance the chemical equation algebraically: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SeO_4 + c_2 Pr(OH)_3 ⟶ c_3 H_2O + c_4 Pr2(SeO4)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Se and Pr: H: | 2 c_1 + 3 c_2 = 2 c_3 O: | 4 c_1 + 3 c_2 = c_3 + 12 c_4 Se: | c_1 = 3 c_4 Pr: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3

Structures

+ ⟶ + Pr2(SeO4)3
+ ⟶ + Pr2(SeO4)3

Names

selenic acid + praseodymium(III) hydroxide ⟶ water + Pr2(SeO4)3
selenic acid + praseodymium(III) hydroxide ⟶ water + Pr2(SeO4)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 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: 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3 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 H_2SeO_4 | 3 | -3 Pr(OH)_3 | 2 | -2 H_2O | 6 | 6 Pr2(SeO4)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SeO_4 | 3 | -3 | ([H2SeO4])^(-3) Pr(OH)_3 | 2 | -2 | ([Pr(OH)3])^(-2) H_2O | 6 | 6 | ([H2O])^6 Pr2(SeO4)3 | 1 | 1 | [Pr2(SeO4)3] 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 = ([H2SeO4])^(-3) ([Pr(OH)3])^(-2) ([H2O])^6 [Pr2(SeO4)3] = (([H2O])^6 [Pr2(SeO4)3])/(([H2SeO4])^3 ([Pr(OH)3])^2)
Construct the equilibrium constant, K, expression for: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 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: 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3 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 H_2SeO_4 | 3 | -3 Pr(OH)_3 | 2 | -2 H_2O | 6 | 6 Pr2(SeO4)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SeO_4 | 3 | -3 | ([H2SeO4])^(-3) Pr(OH)_3 | 2 | -2 | ([Pr(OH)3])^(-2) H_2O | 6 | 6 | ([H2O])^6 Pr2(SeO4)3 | 1 | 1 | [Pr2(SeO4)3] 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 = ([H2SeO4])^(-3) ([Pr(OH)3])^(-2) ([H2O])^6 [Pr2(SeO4)3] = (([H2O])^6 [Pr2(SeO4)3])/(([H2SeO4])^3 ([Pr(OH)3])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 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: 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3 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 H_2SeO_4 | 3 | -3 Pr(OH)_3 | 2 | -2 H_2O | 6 | 6 Pr2(SeO4)3 | 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 H_2SeO_4 | 3 | -3 | -1/3 (Δ[H2SeO4])/(Δt) Pr(OH)_3 | 2 | -2 | -1/2 (Δ[Pr(OH)3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Pr2(SeO4)3 | 1 | 1 | (Δ[Pr2(SeO4)3])/(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 = -1/3 (Δ[H2SeO4])/(Δt) = -1/2 (Δ[Pr(OH)3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[Pr2(SeO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SeO_4 + Pr(OH)_3 ⟶ H_2O + Pr2(SeO4)3 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: 3 H_2SeO_4 + 2 Pr(OH)_3 ⟶ 6 H_2O + Pr2(SeO4)3 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 H_2SeO_4 | 3 | -3 Pr(OH)_3 | 2 | -2 H_2O | 6 | 6 Pr2(SeO4)3 | 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 H_2SeO_4 | 3 | -3 | -1/3 (Δ[H2SeO4])/(Δt) Pr(OH)_3 | 2 | -2 | -1/2 (Δ[Pr(OH)3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) Pr2(SeO4)3 | 1 | 1 | (Δ[Pr2(SeO4)3])/(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 = -1/3 (Δ[H2SeO4])/(Δt) = -1/2 (Δ[Pr(OH)3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[Pr2(SeO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| selenic acid | praseodymium(III) hydroxide | water | Pr2(SeO4)3 formula | H_2SeO_4 | Pr(OH)_3 | H_2O | Pr2(SeO4)3 Hill formula | H_2O_4Se | H_3O_3Pr | H_2O | O12Pr2Se3 name | selenic acid | praseodymium(III) hydroxide | water | IUPAC name | selenic acid | praseodymium(+3) cation trihydroxide | water |
| selenic acid | praseodymium(III) hydroxide | water | Pr2(SeO4)3 formula | H_2SeO_4 | Pr(OH)_3 | H_2O | Pr2(SeO4)3 Hill formula | H_2O_4Se | H_3O_3Pr | H_2O | O12Pr2Se3 name | selenic acid | praseodymium(III) hydroxide | water | IUPAC name | selenic acid | praseodymium(+3) cation trihydroxide | water |

Substance properties

| selenic acid | praseodymium(III) hydroxide | water | Pr2(SeO4)3 molar mass | 144.98 g/mol | 191.93 g/mol | 18.015 g/mol | 710.72 g/mol phase | | | liquid (at STP) | melting point | | | 0 °C | boiling point | | | 99.9839 °C | density | 2.511 g/cm^3 | | 1 g/cm^3 | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |
| selenic acid | praseodymium(III) hydroxide | water | Pr2(SeO4)3 molar mass | 144.98 g/mol | 191.93 g/mol | 18.015 g/mol | 710.72 g/mol phase | | | liquid (at STP) | melting point | | | 0 °C | boiling point | | | 99.9839 °C | density | 2.511 g/cm^3 | | 1 g/cm^3 | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |

Units

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