Input interpretation
NaOH sodium hydroxide + Al aluminum ⟶ Na sodium + Al(OH)_3 aluminum hydroxide
Balanced equation
Balance the chemical equation algebraically: NaOH + Al ⟶ Na + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Al ⟶ c_3 Na + c_4 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and Al: H: | c_1 = 3 c_4 Na: | c_1 = c_3 O: | c_1 = 3 c_4 Al: | 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 NaOH + Al ⟶ 3 Na + Al(OH)_3
Structures
+ ⟶ +
Names
sodium hydroxide + aluminum ⟶ sodium + aluminum hydroxide
Equilibrium constant
![Construct the equilibrium constant, K, expression for: NaOH + Al ⟶ Na + 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: 3 NaOH + Al ⟶ 3 Na + 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 | 3 | -3 Al | 1 | -1 Na | 3 | 3 Al(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 3 | -3 | ([NaOH])^(-3) Al | 1 | -1 | ([Al])^(-1) Na | 3 | 3 | ([Na])^3 Al(OH)_3 | 1 | 1 | [Al(OH)3] 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])^(-3) ([Al])^(-1) ([Na])^3 [Al(OH)3] = (([Na])^3 [Al(OH)3])/(([NaOH])^3 [Al])](../image_source/e75073c3f5ce86eeaa9e0efacd09ff77.png)
Construct the equilibrium constant, K, expression for: NaOH + Al ⟶ Na + 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: 3 NaOH + Al ⟶ 3 Na + 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 | 3 | -3 Al | 1 | -1 Na | 3 | 3 Al(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 3 | -3 | ([NaOH])^(-3) Al | 1 | -1 | ([Al])^(-1) Na | 3 | 3 | ([Na])^3 Al(OH)_3 | 1 | 1 | [Al(OH)3] 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])^(-3) ([Al])^(-1) ([Na])^3 [Al(OH)3] = (([Na])^3 [Al(OH)3])/(([NaOH])^3 [Al])
Rate of reaction
![Construct the rate of reaction expression for: NaOH + Al ⟶ Na + 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: 3 NaOH + Al ⟶ 3 Na + 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 | 3 | -3 Al | 1 | -1 Na | 3 | 3 Al(OH)_3 | 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 | 3 | -3 | -1/3 (Δ[NaOH])/(Δt) Al | 1 | -1 | -(Δ[Al])/(Δt) Na | 3 | 3 | 1/3 (Δ[Na])/(Δt) Al(OH)_3 | 1 | 1 | (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 = -1/3 (Δ[NaOH])/(Δt) = -(Δ[Al])/(Δt) = 1/3 (Δ[Na])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/37ffd58e4788ba95f195bf5c1fbad5f8.png)
Construct the rate of reaction expression for: NaOH + Al ⟶ Na + 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: 3 NaOH + Al ⟶ 3 Na + 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 | 3 | -3 Al | 1 | -1 Na | 3 | 3 Al(OH)_3 | 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 | 3 | -3 | -1/3 (Δ[NaOH])/(Δt) Al | 1 | -1 | -(Δ[Al])/(Δt) Na | 3 | 3 | 1/3 (Δ[Na])/(Δt) Al(OH)_3 | 1 | 1 | (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 = -1/3 (Δ[NaOH])/(Δt) = -(Δ[Al])/(Δt) = 1/3 (Δ[Na])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium hydroxide | aluminum | sodium | aluminum hydroxide formula | NaOH | Al | Na | Al(OH)_3 Hill formula | HNaO | Al | Na | AlH_3O_3 name | sodium hydroxide | aluminum | sodium | aluminum hydroxide