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Ba(OH)2 + Na3PO4 = NaOH + Ba3(PO4)2

Input interpretation

Ba(OH)_2 barium hydroxide + Na_3PO_4 trisodium phosphate ⟶ NaOH sodium hydroxide + Ba3(PO4)2
Ba(OH)_2 barium hydroxide + Na_3PO_4 trisodium phosphate ⟶ NaOH sodium hydroxide + Ba3(PO4)2

Balanced equation

Balance the chemical equation algebraically: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ba(OH)_2 + c_2 Na_3PO_4 ⟶ c_3 NaOH + c_4 Ba3(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, H, O, Na and P: Ba: | c_1 = 3 c_4 H: | 2 c_1 = c_3 O: | 2 c_1 + 4 c_2 = c_3 + 8 c_4 Na: | 3 c_2 = c_3 P: | 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2
Balance the chemical equation algebraically: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ba(OH)_2 + c_2 Na_3PO_4 ⟶ c_3 NaOH + c_4 Ba3(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, H, O, Na and P: Ba: | c_1 = 3 c_4 H: | 2 c_1 = c_3 O: | 2 c_1 + 4 c_2 = c_3 + 8 c_4 Na: | 3 c_2 = c_3 P: | 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2

Structures

+ ⟶ + Ba3(PO4)2
+ ⟶ + Ba3(PO4)2

Names

barium hydroxide + trisodium phosphate ⟶ sodium hydroxide + Ba3(PO4)2
barium hydroxide + trisodium phosphate ⟶ sodium hydroxide + Ba3(PO4)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2 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 Ba(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ba3(PO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ba(OH)_2 | 3 | -3 | ([Ba(OH)2])^(-3) Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) NaOH | 6 | 6 | ([NaOH])^6 Ba3(PO4)2 | 1 | 1 | [Ba3(PO4)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 = ([Ba(OH)2])^(-3) ([Na3PO4])^(-2) ([NaOH])^6 [Ba3(PO4)2] = (([NaOH])^6 [Ba3(PO4)2])/(([Ba(OH)2])^3 ([Na3PO4])^2)
Construct the equilibrium constant, K, expression for: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2 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 Ba(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ba3(PO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ba(OH)_2 | 3 | -3 | ([Ba(OH)2])^(-3) Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) NaOH | 6 | 6 | ([NaOH])^6 Ba3(PO4)2 | 1 | 1 | [Ba3(PO4)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 = ([Ba(OH)2])^(-3) ([Na3PO4])^(-2) ([NaOH])^6 [Ba3(PO4)2] = (([NaOH])^6 [Ba3(PO4)2])/(([Ba(OH)2])^3 ([Na3PO4])^2)

Rate of reaction

Construct the rate of reaction expression for: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2 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 Ba(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ba3(PO4)2 | 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 Ba(OH)_2 | 3 | -3 | -1/3 (Δ[Ba(OH)2])/(Δt) Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) NaOH | 6 | 6 | 1/6 (Δ[NaOH])/(Δt) Ba3(PO4)2 | 1 | 1 | (Δ[Ba3(PO4)2])/(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[Ba(OH)2])/(Δt) = -1/2 (Δ[Na3PO4])/(Δt) = 1/6 (Δ[NaOH])/(Δt) = (Δ[Ba3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Ba(OH)_2 + Na_3PO_4 ⟶ NaOH + Ba3(PO4)2 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 Ba(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ba3(PO4)2 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 Ba(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ba3(PO4)2 | 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 Ba(OH)_2 | 3 | -3 | -1/3 (Δ[Ba(OH)2])/(Δt) Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) NaOH | 6 | 6 | 1/6 (Δ[NaOH])/(Δt) Ba3(PO4)2 | 1 | 1 | (Δ[Ba3(PO4)2])/(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[Ba(OH)2])/(Δt) = -1/2 (Δ[Na3PO4])/(Δt) = 1/6 (Δ[NaOH])/(Δt) = (Δ[Ba3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| barium hydroxide | trisodium phosphate | sodium hydroxide | Ba3(PO4)2 formula | Ba(OH)_2 | Na_3PO_4 | NaOH | Ba3(PO4)2 Hill formula | BaH_2O_2 | Na_3O_4P | HNaO | Ba3O8P2 name | barium hydroxide | trisodium phosphate | sodium hydroxide | IUPAC name | barium(+2) cation dihydroxide | trisodium phosphate | sodium hydroxide |
| barium hydroxide | trisodium phosphate | sodium hydroxide | Ba3(PO4)2 formula | Ba(OH)_2 | Na_3PO_4 | NaOH | Ba3(PO4)2 Hill formula | BaH_2O_2 | Na_3O_4P | HNaO | Ba3O8P2 name | barium hydroxide | trisodium phosphate | sodium hydroxide | IUPAC name | barium(+2) cation dihydroxide | trisodium phosphate | sodium hydroxide |

Substance properties

| barium hydroxide | trisodium phosphate | sodium hydroxide | Ba3(PO4)2 molar mass | 171.34 g/mol | 163.94 g/mol | 39.997 g/mol | 601.92 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 300 °C | 75 °C | 323 °C | boiling point | | | 1390 °C | density | 2.2 g/cm^3 | 2.536 g/cm^3 | 2.13 g/cm^3 | solubility in water | | soluble | soluble | surface tension | | | 0.07435 N/m | dynamic viscosity | | | 0.004 Pa s (at 350 °C) | odor | | odorless | |
| barium hydroxide | trisodium phosphate | sodium hydroxide | Ba3(PO4)2 molar mass | 171.34 g/mol | 163.94 g/mol | 39.997 g/mol | 601.92 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 300 °C | 75 °C | 323 °C | boiling point | | | 1390 °C | density | 2.2 g/cm^3 | 2.536 g/cm^3 | 2.13 g/cm^3 | solubility in water | | soluble | soluble | surface tension | | | 0.07435 N/m | dynamic viscosity | | | 0.004 Pa s (at 350 °C) | odor | | odorless | |

Units

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