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H3PO4 + Ba(OH)2 = H2O + BaHPO4

Input interpretation

H_3PO_4 phosphoric acid + Ba(OH)_2 barium hydroxide ⟶ H_2O water + BaHPO_4 barium hydrogen phosphate
H_3PO_4 phosphoric acid + Ba(OH)_2 barium hydroxide ⟶ H_2O water + BaHPO_4 barium hydrogen phosphate

Balanced equation

Balance the chemical equation algebraically: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Ba(OH)_2 ⟶ c_3 H_2O + c_4 BaHPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Ba: H: | 3 c_1 + 2 c_2 = 2 c_3 + c_4 O: | 4 c_1 + 2 c_2 = c_3 + 4 c_4 P: | c_1 = c_4 Ba: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_4
Balance the chemical equation algebraically: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Ba(OH)_2 ⟶ c_3 H_2O + c_4 BaHPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Ba: H: | 3 c_1 + 2 c_2 = 2 c_3 + c_4 O: | 4 c_1 + 2 c_2 = c_3 + 4 c_4 P: | c_1 = c_4 Ba: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_4

Structures

+ ⟶ +
+ ⟶ +

Names

phosphoric acid + barium hydroxide ⟶ water + barium hydrogen phosphate
phosphoric acid + barium hydroxide ⟶ water + barium hydrogen phosphate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_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: H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_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 H_3PO_4 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 2 | 2 BaHPO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 BaHPO_4 | 1 | 1 | [BaHPO4] 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 = ([H3PO4])^(-1) ([Ba(OH)2])^(-1) ([H2O])^2 [BaHPO4] = (([H2O])^2 [BaHPO4])/([H3PO4] [Ba(OH)2])
Construct the equilibrium constant, K, expression for: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_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: H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_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 H_3PO_4 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 2 | 2 BaHPO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) Ba(OH)_2 | 1 | -1 | ([Ba(OH)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 BaHPO_4 | 1 | 1 | [BaHPO4] 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 = ([H3PO4])^(-1) ([Ba(OH)2])^(-1) ([H2O])^2 [BaHPO4] = (([H2O])^2 [BaHPO4])/([H3PO4] [Ba(OH)2])

Rate of reaction

Construct the rate of reaction expression for: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_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: H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_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 H_3PO_4 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 2 | 2 BaHPO_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 H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) BaHPO_4 | 1 | 1 | (Δ[BaHPO4])/(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 = -(Δ[H3PO4])/(Δt) = -(Δ[Ba(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[BaHPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_3PO_4 + Ba(OH)_2 ⟶ H_2O + BaHPO_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: H_3PO_4 + Ba(OH)_2 ⟶ 2 H_2O + BaHPO_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 H_3PO_4 | 1 | -1 Ba(OH)_2 | 1 | -1 H_2O | 2 | 2 BaHPO_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 H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) Ba(OH)_2 | 1 | -1 | -(Δ[Ba(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) BaHPO_4 | 1 | 1 | (Δ[BaHPO4])/(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 = -(Δ[H3PO4])/(Δt) = -(Δ[Ba(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[BaHPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| phosphoric acid | barium hydroxide | water | barium hydrogen phosphate formula | H_3PO_4 | Ba(OH)_2 | H_2O | BaHPO_4 Hill formula | H_3O_4P | BaH_2O_2 | H_2O | BaHO_4P name | phosphoric acid | barium hydroxide | water | barium hydrogen phosphate IUPAC name | phosphoric acid | barium(+2) cation dihydroxide | water |
| phosphoric acid | barium hydroxide | water | barium hydrogen phosphate formula | H_3PO_4 | Ba(OH)_2 | H_2O | BaHPO_4 Hill formula | H_3O_4P | BaH_2O_2 | H_2O | BaHO_4P name | phosphoric acid | barium hydroxide | water | barium hydrogen phosphate IUPAC name | phosphoric acid | barium(+2) cation dihydroxide | water |

Substance properties

| phosphoric acid | barium hydroxide | water | barium hydrogen phosphate molar mass | 97.994 g/mol | 171.34 g/mol | 18.015 g/mol | 233.3 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 42.4 °C | 300 °C | 0 °C | boiling point | 158 °C | | 99.9839 °C | density | 1.685 g/cm^3 | 2.2 g/cm^3 | 1 g/cm^3 | solubility in water | very soluble | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |
| phosphoric acid | barium hydroxide | water | barium hydrogen phosphate molar mass | 97.994 g/mol | 171.34 g/mol | 18.015 g/mol | 233.3 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 42.4 °C | 300 °C | 0 °C | boiling point | 158 °C | | 99.9839 °C | density | 1.685 g/cm^3 | 2.2 g/cm^3 | 1 g/cm^3 | solubility in water | very soluble | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |

Units

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