KOH + Na2SO4 = NaOH + K2SO4

KOH potassium hydroxide + Na_2SO_4 sodium sulfate ⟶ NaOH sodium hydroxide + K_2SO_4 potassium sulfate

Balance the chemical equation algebraically: KOH + Na_2SO_4 ⟶ NaOH + K_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Na_2SO_4 ⟶ c_3 NaOH + c_4 K_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Na and S: H: | c_1 = c_3 K: | c_1 = 2 c_4 O: | c_1 + 4 c_2 = c_3 + 4 c_4 Na: | 2 c_2 = c_3 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + Na_2SO_4 ⟶ 2 NaOH + K_2SO_4

+ ⟶ +

potassium hydroxide + sodium sulfate ⟶ sodium hydroxide + potassium sulfate

Construct the equilibrium constant, K, expression for: KOH + Na_2SO_4 ⟶ NaOH + K_2SO_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: 2 KOH + Na_2SO_4 ⟶ 2 NaOH + K_2SO_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 KOH | 2 | -2 Na_2SO_4 | 1 | -1 NaOH | 2 | 2 K_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) NaOH | 2 | 2 | ([NaOH])^2 K_2SO_4 | 1 | 1 | [K2SO4] 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 = ([KOH])^(-2) ([Na2SO4])^(-1) ([NaOH])^2 [K2SO4] = (([NaOH])^2 [K2SO4])/(([KOH])^2 [Na2SO4])

Construct the rate of reaction expression for: KOH + Na_2SO_4 ⟶ NaOH + K_2SO_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: 2 KOH + Na_2SO_4 ⟶ 2 NaOH + K_2SO_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 KOH | 2 | -2 Na_2SO_4 | 1 | -1 NaOH | 2 | 2 K_2SO_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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(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[KOH])/(Δt) = -(Δ[Na2SO4])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = (Δ[K2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | sodium sulfate | sodium hydroxide | potassium sulfate formula | KOH | Na_2SO_4 | NaOH | K_2SO_4 Hill formula | HKO | Na_2O_4S | HNaO | K_2O_4S name | potassium hydroxide | sodium sulfate | sodium hydroxide | potassium sulfate IUPAC name | potassium hydroxide | disodium sulfate | sodium hydroxide | dipotassium sulfate

| potassium hydroxide | sodium sulfate | sodium hydroxide | potassium sulfate molar mass | 56.105 g/mol | 142.04 g/mol | 39.997 g/mol | 174.25 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 406 °C | 884 °C | 323 °C | boiling point | 1327 °C | 1429 °C | 1390 °C | density | 2.044 g/cm^3 | 2.68 g/cm^3 | 2.13 g/cm^3 | solubility in water | soluble | soluble | soluble | soluble surface tension | | | 0.07435 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 0.004 Pa s (at 350 °C) |