NaOH + BaSO4 = Na2SO4 + Ba(OH)2

NaOH sodium hydroxide + BaSO_4 barium sulfate ⟶ Na_2SO_4 sodium sulfate + Ba(OH)_2 barium hydroxide

Balance the chemical equation algebraically: NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 BaSO_4 ⟶ c_3 Na_2SO_4 + c_4 Ba(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Ba and S: H: | c_1 = 2 c_4 Na: | c_1 = 2 c_3 O: | c_1 + 4 c_2 = 4 c_3 + 2 c_4 Ba: | c_2 = c_4 S: | c_2 = 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_2

+ ⟶ +

sodium hydroxide + barium sulfate ⟶ sodium sulfate + barium hydroxide

| sodium hydroxide | barium sulfate | sodium sulfate | barium hydroxide molecular enthalpy | -425.8 kJ/mol | -1473 kJ/mol | -1387 kJ/mol | -944.7 kJ/mol total enthalpy | -851.6 kJ/mol | -1473 kJ/mol | -1387 kJ/mol | -944.7 kJ/mol | H_initial = -2325 kJ/mol | | H_final = -2332 kJ/mol | ΔH_rxn^0 | -2332 kJ/mol - -2325 kJ/mol = -7 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_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: 2 NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_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 NaOH | 2 | -2 BaSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 Ba(OH)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) BaSO_4 | 1 | -1 | ([BaSO4])^(-1) Na_2SO_4 | 1 | 1 | [Na2SO4] Ba(OH)_2 | 1 | 1 | [Ba(OH)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 = ([NaOH])^(-2) ([BaSO4])^(-1) [Na2SO4] [Ba(OH)2] = ([Na2SO4] [Ba(OH)2])/(([NaOH])^2 [BaSO4])

Construct the rate of reaction expression for: NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_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: 2 NaOH + BaSO_4 ⟶ Na_2SO_4 + Ba(OH)_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 NaOH | 2 | -2 BaSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 Ba(OH)_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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) BaSO_4 | 1 | -1 | -(Δ[BaSO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) Ba(OH)_2 | 1 | 1 | (Δ[Ba(OH)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 = -1/2 (Δ[NaOH])/(Δt) = -(Δ[BaSO4])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[Ba(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | barium sulfate | sodium sulfate | barium hydroxide formula | NaOH | BaSO_4 | Na_2SO_4 | Ba(OH)_2 Hill formula | HNaO | BaO_4S | Na_2O_4S | BaH_2O_2 name | sodium hydroxide | barium sulfate | sodium sulfate | barium hydroxide IUPAC name | sodium hydroxide | barium(+2) cation sulfate | disodium sulfate | barium(+2) cation dihydroxide

| sodium hydroxide | barium sulfate | sodium sulfate | barium hydroxide molar mass | 39.997 g/mol | 233.38 g/mol | 142.04 g/mol | 171.34 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | 1345 °C | 884 °C | 300 °C boiling point | 1390 °C | | 1429 °C | density | 2.13 g/cm^3 | 4.5 g/cm^3 | 2.68 g/cm^3 | 2.2 g/cm^3 solubility in water | soluble | insoluble | soluble | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | |