NaOH + Al + NaNO3 = H2O + NH3 + Na2AlO2

NaOH sodium hydroxide + Al aluminum + NaNO_3 sodium nitrate ⟶ H_2O water + NH_3 ammonia + Na2AlO2

Balance the chemical equation algebraically: NaOH + Al + NaNO_3 ⟶ H_2O + NH_3 + Na2AlO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Al + c_3 NaNO_3 ⟶ c_4 H_2O + c_5 NH_3 + c_6 Na2AlO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Al and N: H: | c_1 = 2 c_4 + 3 c_5 Na: | c_1 + c_3 = 2 c_6 O: | c_1 + 3 c_3 = c_4 + 2 c_6 Al: | c_2 = c_6 N: | c_3 = c_5 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 = 7 c_2 = 4 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 NaOH + 4 Al + NaNO_3 ⟶ 2 H_2O + NH_3 + 4 Na2AlO2

+ + ⟶ + + Na2AlO2

sodium hydroxide + aluminum + sodium nitrate ⟶ water + ammonia + Na2AlO2

Construct the equilibrium constant, K, expression for: NaOH + Al + NaNO_3 ⟶ H_2O + NH_3 + Na2AlO2 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: 7 NaOH + 4 Al + NaNO_3 ⟶ 2 H_2O + NH_3 + 4 Na2AlO2 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 | 7 | -7 Al | 4 | -4 NaNO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 1 | 1 Na2AlO2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 7 | -7 | ([NaOH])^(-7) Al | 4 | -4 | ([Al])^(-4) NaNO_3 | 1 | -1 | ([NaNO3])^(-1) H_2O | 2 | 2 | ([H2O])^2 NH_3 | 1 | 1 | [NH3] Na2AlO2 | 4 | 4 | ([Na2AlO2])^4 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])^(-7) ([Al])^(-4) ([NaNO3])^(-1) ([H2O])^2 [NH3] ([Na2AlO2])^4 = (([H2O])^2 [NH3] ([Na2AlO2])^4)/(([NaOH])^7 ([Al])^4 [NaNO3])

Construct the rate of reaction expression for: NaOH + Al + NaNO_3 ⟶ H_2O + NH_3 + Na2AlO2 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: 7 NaOH + 4 Al + NaNO_3 ⟶ 2 H_2O + NH_3 + 4 Na2AlO2 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 | 7 | -7 Al | 4 | -4 NaNO_3 | 1 | -1 H_2O | 2 | 2 NH_3 | 1 | 1 Na2AlO2 | 4 | 4 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 | 7 | -7 | -1/7 (Δ[NaOH])/(Δt) Al | 4 | -4 | -1/4 (Δ[Al])/(Δt) NaNO_3 | 1 | -1 | -(Δ[NaNO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) Na2AlO2 | 4 | 4 | 1/4 (Δ[Na2AlO2])/(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 = -1/7 (Δ[NaOH])/(Δt) = -1/4 (Δ[Al])/(Δt) = -(Δ[NaNO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[NH3])/(Δt) = 1/4 (Δ[Na2AlO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | aluminum | sodium nitrate | water | ammonia | Na2AlO2 formula | NaOH | Al | NaNO_3 | H_2O | NH_3 | Na2AlO2 Hill formula | HNaO | Al | NNaO_3 | H_2O | H_3N | AlNa2O2 name | sodium hydroxide | aluminum | sodium nitrate | water | ammonia |

| sodium hydroxide | aluminum | sodium nitrate | water | ammonia | Na2AlO2 molar mass | 39.997 g/mol | 26.9815385 g/mol | 84.994 g/mol | 18.015 g/mol | 17.031 g/mol | 104.959 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | 323 °C | 660.4 °C | 306 °C | 0 °C | -77.73 °C | boiling point | 1390 °C | 2460 °C | | 99.9839 °C | -33.33 °C | density | 2.13 g/cm^3 | 2.7 g/cm^3 | 2.26 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | solubility in water | soluble | insoluble | soluble | | | surface tension | 0.07435 N/m | 0.817 N/m | | 0.0728 N/m | 0.0234 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | 1.5×10^-4 Pa s (at 760 °C) | 0.003 Pa s (at 250 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | odor | | odorless | | odorless | |