H2O + Na = H2 + NaOH

H_2O (water) + Na (sodium) ⟶ H_2 (hydrogen) + NaOH (sodium hydroxide)

Balance the chemical equation algebraically: H_2O + Na ⟶ H_2 + NaOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na ⟶ c_3 H_2 + c_4 NaOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Na: H: | 2 c_1 = 2 c_3 + c_4 O: | c_1 = c_4 Na: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 Na ⟶ H_2 + 2 NaOH

+ ⟶ +

water + sodium ⟶ hydrogen + sodium hydroxide

| water | sodium | hydrogen | sodium hydroxide molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | 0 kJ/mol | -425.8 kJ/mol total enthalpy | -571.7 kJ/mol | 0 kJ/mol | 0 kJ/mol | -851.6 kJ/mol | H_initial = -571.7 kJ/mol | | H_final = -851.6 kJ/mol | ΔH_rxn^0 | -851.6 kJ/mol - -571.7 kJ/mol = -279.9 kJ/mol (exothermic) | | |

| water | sodium | hydrogen | sodium hydroxide molecular entropy | 69.91 J/(mol K) | 51 J/(mol K) | 115 J/(mol K) | 64 J/(mol K) total entropy | 139.8 J/(mol K) | 102 J/(mol K) | 115 J/(mol K) | 128 J/(mol K) | S_initial = 241.8 J/(mol K) | | S_final = 243 J/(mol K) | ΔS_rxn^0 | 243 J/(mol K) - 241.8 J/(mol K) = 1.18 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2O + Na ⟶ H_2 + NaOH 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 H_2O + 2 Na ⟶ H_2 + 2 NaOH 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 H_2O | 2 | -2 Na | 2 | -2 H_2 | 1 | 1 NaOH | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) Na | 2 | -2 | ([Na])^(-2) H_2 | 1 | 1 | [H2] NaOH | 2 | 2 | ([NaOH])^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 = ([H2O])^(-2) ([Na])^(-2) [H2] ([NaOH])^2 = ([H2] ([NaOH])^2)/(([H2O])^2 ([Na])^2)

Construct the rate of reaction expression for: H_2O + Na ⟶ H_2 + NaOH 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 H_2O + 2 Na ⟶ H_2 + 2 NaOH 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 H_2O | 2 | -2 Na | 2 | -2 H_2 | 1 | 1 NaOH | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(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[H2O])/(Δt) = -1/2 (Δ[Na])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[NaOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium | hydrogen | sodium hydroxide formula | H_2O | Na | H_2 | NaOH Hill formula | H_2O | Na | H_2 | HNaO name | water | sodium | hydrogen | sodium hydroxide IUPAC name | water | sodium | molecular hydrogen | sodium hydroxide