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NaOH + KAl(SO4)2 = K2SO4 + Na2SO4 + Al(OH)3

Input interpretation

NaOH sodium hydroxide + AlKO_8S_2 potassium alum ⟶ K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + Al(OH)_3 aluminum hydroxide
NaOH sodium hydroxide + AlKO_8S_2 potassium alum ⟶ K_2SO_4 potassium sulfate + Na_2SO_4 sodium sulfate + Al(OH)_3 aluminum hydroxide

Balanced equation

Balance the chemical equation algebraically: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 AlKO_8S_2 ⟶ c_3 K_2SO_4 + c_4 Na_2SO_4 + c_5 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Al, K and S: H: | c_1 = 3 c_5 Na: | c_1 = 2 c_4 O: | c_1 + 8 c_2 = 4 c_3 + 4 c_4 + 3 c_5 Al: | c_2 = c_5 K: | c_2 = 2 c_3 S: | 2 c_2 = c_3 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_3
Balance the chemical equation algebraically: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 AlKO_8S_2 ⟶ c_3 K_2SO_4 + c_4 Na_2SO_4 + c_5 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Al, K and S: H: | c_1 = 3 c_5 Na: | c_1 = 2 c_4 O: | c_1 + 8 c_2 = 4 c_3 + 4 c_4 + 3 c_5 Al: | c_2 = c_5 K: | c_2 = 2 c_3 S: | 2 c_2 = c_3 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_3

Structures

+ ⟶ + +
+ ⟶ + +

Names

sodium hydroxide + potassium alum ⟶ potassium sulfate + sodium sulfate + aluminum hydroxide
sodium hydroxide + potassium alum ⟶ potassium sulfate + sodium sulfate + aluminum hydroxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_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 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_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 NaOH | 6 | -6 AlKO_8S_2 | 2 | -2 K_2SO_4 | 1 | 1 Na_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) AlKO_8S_2 | 2 | -2 | ([AlKO8S2])^(-2) K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Al(OH)_3 | 2 | 2 | ([Al(OH)3])^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])^(-6) ([AlKO8S2])^(-2) [K2SO4] ([Na2SO4])^3 ([Al(OH)3])^2 = ([K2SO4] ([Na2SO4])^3 ([Al(OH)3])^2)/(([NaOH])^6 ([AlKO8S2])^2)
Construct the equilibrium constant, K, expression for: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_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 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_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 NaOH | 6 | -6 AlKO_8S_2 | 2 | -2 K_2SO_4 | 1 | 1 Na_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) AlKO_8S_2 | 2 | -2 | ([AlKO8S2])^(-2) K_2SO_4 | 1 | 1 | [K2SO4] Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Al(OH)_3 | 2 | 2 | ([Al(OH)3])^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])^(-6) ([AlKO8S2])^(-2) [K2SO4] ([Na2SO4])^3 ([Al(OH)3])^2 = ([K2SO4] ([Na2SO4])^3 ([Al(OH)3])^2)/(([NaOH])^6 ([AlKO8S2])^2)

Rate of reaction

Construct the rate of reaction expression for: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_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 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_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 NaOH | 6 | -6 AlKO_8S_2 | 2 | -2 K_2SO_4 | 1 | 1 Na_2SO_4 | 3 | 3 Al(OH)_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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) AlKO_8S_2 | 2 | -2 | -1/2 (Δ[AlKO8S2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (Δ[Al(OH)3])/(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[NaOH])/(Δt) = -1/2 (Δ[AlKO8S2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: NaOH + AlKO_8S_2 ⟶ K_2SO_4 + Na_2SO_4 + Al(OH)_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 NaOH + 2 AlKO_8S_2 ⟶ K_2SO_4 + 3 Na_2SO_4 + 2 Al(OH)_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 NaOH | 6 | -6 AlKO_8S_2 | 2 | -2 K_2SO_4 | 1 | 1 Na_2SO_4 | 3 | 3 Al(OH)_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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) AlKO_8S_2 | 2 | -2 | -1/2 (Δ[AlKO8S2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (Δ[Al(OH)3])/(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[NaOH])/(Δt) = -1/2 (Δ[AlKO8S2])/(Δt) = (Δ[K2SO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide formula | NaOH | AlKO_8S_2 | K_2SO_4 | Na_2SO_4 | Al(OH)_3 Hill formula | HNaO | AlKO_8S_2 | K_2O_4S | Na_2O_4S | AlH_3O_3 name | sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide IUPAC name | sodium hydroxide | potassium aluminum(+3) cation disulfate | dipotassium sulfate | disodium sulfate | aluminum hydroxide
| sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide formula | NaOH | AlKO_8S_2 | K_2SO_4 | Na_2SO_4 | Al(OH)_3 Hill formula | HNaO | AlKO_8S_2 | K_2O_4S | Na_2O_4S | AlH_3O_3 name | sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide IUPAC name | sodium hydroxide | potassium aluminum(+3) cation disulfate | dipotassium sulfate | disodium sulfate | aluminum hydroxide

Substance properties

| sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide molar mass | 39.997 g/mol | 258.19 g/mol | 174.25 g/mol | 142.04 g/mol | 78.003 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) | melting point | 323 °C | 92.5 °C | | 884 °C | boiling point | 1390 °C | | | 1429 °C | density | 2.13 g/cm^3 | 1.725 g/cm^3 | | 2.68 g/cm^3 | solubility in water | soluble | | soluble | soluble | surface tension | 0.07435 N/m | | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | | odor | | odorless | | |
| sodium hydroxide | potassium alum | potassium sulfate | sodium sulfate | aluminum hydroxide molar mass | 39.997 g/mol | 258.19 g/mol | 174.25 g/mol | 142.04 g/mol | 78.003 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) | melting point | 323 °C | 92.5 °C | | 884 °C | boiling point | 1390 °C | | | 1429 °C | density | 2.13 g/cm^3 | 1.725 g/cm^3 | | 2.68 g/cm^3 | solubility in water | soluble | | soluble | soluble | surface tension | 0.07435 N/m | | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | | odor | | odorless | | |

Units

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