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HF + Sc2(SO4)3 = H2SO4 + ScF3

Input interpretation

HF hydrogen fluoride + Sc2(SO4)3 ⟶ H_2SO_4 sulfuric acid + ScF_3 scandium fluoride
HF hydrogen fluoride + Sc2(SO4)3 ⟶ H_2SO_4 sulfuric acid + ScF_3 scandium fluoride

Balanced equation

Balance the chemical equation algebraically: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HF + c_2 Sc2(SO4)3 ⟶ c_3 H_2SO_4 + c_4 ScF_3 Set the number of atoms in the reactants equal to the number of atoms in the products for F, H, Sc, S and O: F: | c_1 = 3 c_4 H: | c_1 = 2 c_3 Sc: | 2 c_2 = c_4 S: | 3 c_2 = c_3 O: | 12 c_2 = 4 c_3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: |   | 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_3
Balance the chemical equation algebraically: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HF + c_2 Sc2(SO4)3 ⟶ c_3 H_2SO_4 + c_4 ScF_3 Set the number of atoms in the reactants equal to the number of atoms in the products for F, H, Sc, S and O: F: | c_1 = 3 c_4 H: | c_1 = 2 c_3 Sc: | 2 c_2 = c_4 S: | 3 c_2 = c_3 O: | 12 c_2 = 4 c_3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_3

Structures

 + Sc2(SO4)3 ⟶ +
+ Sc2(SO4)3 ⟶ +

Names

hydrogen fluoride + Sc2(SO4)3 ⟶ sulfuric acid + scandium fluoride
hydrogen fluoride + Sc2(SO4)3 ⟶ sulfuric acid + scandium fluoride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_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: 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_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 HF | 6 | -6 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 ScF_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HF | 6 | -6 | ([HF])^(-6) Sc2(SO4)3 | 1 | -1 | ([Sc2(SO4)3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 ScF_3 | 2 | 2 | ([ScF3])^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 = ([HF])^(-6) ([Sc2(SO4)3])^(-1) ([H2SO4])^3 ([ScF3])^2 = (([H2SO4])^3 ([ScF3])^2)/(([HF])^6 [Sc2(SO4)3])
Construct the equilibrium constant, K, expression for: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_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: 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_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 HF | 6 | -6 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 ScF_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HF | 6 | -6 | ([HF])^(-6) Sc2(SO4)3 | 1 | -1 | ([Sc2(SO4)3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 ScF_3 | 2 | 2 | ([ScF3])^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 = ([HF])^(-6) ([Sc2(SO4)3])^(-1) ([H2SO4])^3 ([ScF3])^2 = (([H2SO4])^3 ([ScF3])^2)/(([HF])^6 [Sc2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_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: 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_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 HF | 6 | -6 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 ScF_3 | 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 HF | 6 | -6 | -1/6 (Δ[HF])/(Δt) Sc2(SO4)3 | 1 | -1 | -(Δ[Sc2(SO4)3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) ScF_3 | 2 | 2 | 1/2 (Δ[ScF3])/(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 = -1/6 (Δ[HF])/(Δt) = -(Δ[Sc2(SO4)3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[ScF3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HF + Sc2(SO4)3 ⟶ H_2SO_4 + ScF_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: 6 HF + Sc2(SO4)3 ⟶ 3 H_2SO_4 + 2 ScF_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 HF | 6 | -6 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 ScF_3 | 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 HF | 6 | -6 | -1/6 (Δ[HF])/(Δt) Sc2(SO4)3 | 1 | -1 | -(Δ[Sc2(SO4)3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) ScF_3 | 2 | 2 | 1/2 (Δ[ScF3])/(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 = -1/6 (Δ[HF])/(Δt) = -(Δ[Sc2(SO4)3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[ScF3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

 | hydrogen fluoride | Sc2(SO4)3 | sulfuric acid | scandium fluoride formula | HF | Sc2(SO4)3 | H_2SO_4 | ScF_3 Hill formula | FH | O12S3Sc2 | H_2O_4S | F_3Sc name | hydrogen fluoride | | sulfuric acid | scandium fluoride
| hydrogen fluoride | Sc2(SO4)3 | sulfuric acid | scandium fluoride formula | HF | Sc2(SO4)3 | H_2SO_4 | ScF_3 Hill formula | FH | O12S3Sc2 | H_2O_4S | F_3Sc name | hydrogen fluoride | | sulfuric acid | scandium fluoride

Substance properties

 | hydrogen fluoride | Sc2(SO4)3 | sulfuric acid | scandium fluoride molar mass | 20.006 g/mol | 378.1 g/mol | 98.07 g/mol | 101.95112 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) melting point | -83.36 °C | | 10.371 °C | 1150 °C boiling point | 19.5 °C | | 279.6 °C | 1527 °C density | 8.18×10^-4 g/cm^3 (at 25 °C) | | 1.8305 g/cm^3 | 2.52 g/cm^3 solubility in water | miscible | | very soluble |  surface tension | | | 0.0735 N/m |  dynamic viscosity | 1.2571×10^-5 Pa s (at 20 °C) | | 0.021 Pa s (at 25 °C) |  odor | | | odorless |
| hydrogen fluoride | Sc2(SO4)3 | sulfuric acid | scandium fluoride molar mass | 20.006 g/mol | 378.1 g/mol | 98.07 g/mol | 101.95112 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) melting point | -83.36 °C | | 10.371 °C | 1150 °C boiling point | 19.5 °C | | 279.6 °C | 1527 °C density | 8.18×10^-4 g/cm^3 (at 25 °C) | | 1.8305 g/cm^3 | 2.52 g/cm^3 solubility in water | miscible | | very soluble | surface tension | | | 0.0735 N/m | dynamic viscosity | 1.2571×10^-5 Pa s (at 20 °C) | | 0.021 Pa s (at 25 °C) | odor | | | odorless |

Units