H2 + KOH = H2O + K

H_2 hydrogen + KOH potassium hydroxide ⟶ H_2O water + K potassium

Balance the chemical equation algebraically: H_2 + KOH ⟶ H_2O + K Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 KOH ⟶ c_3 H_2O + c_4 K Set the number of atoms in the reactants equal to the number of atoms in the products for H, K and O: H: | 2 c_1 + c_2 = 2 c_3 K: | c_2 = c_4 O: | c_2 = c_3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2 + 2 KOH ⟶ 2 H_2O + 2 K

+ ⟶ +

hydrogen + potassium hydroxide ⟶ water + potassium

| hydrogen | potassium hydroxide | water | potassium molecular entropy | 115 J/(mol K) | 79 J/(mol K) | 69.91 J/(mol K) | 64 J/(mol K) total entropy | 115 J/(mol K) | 158 J/(mol K) | 139.8 J/(mol K) | 128 J/(mol K) | S_initial = 273 J/(mol K) | | S_final = 267.8 J/(mol K) | ΔS_rxn^0 | 267.8 J/(mol K) - 273 J/(mol K) = -5.18 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2 + KOH ⟶ H_2O + K 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: H_2 + 2 KOH ⟶ 2 H_2O + 2 K 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_2 | 1 | -1 KOH | 2 | -2 H_2O | 2 | 2 K | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 1 | -1 | ([H2])^(-1) KOH | 2 | -2 | ([KOH])^(-2) H_2O | 2 | 2 | ([H2O])^2 K | 2 | 2 | ([K])^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 = ([H2])^(-1) ([KOH])^(-2) ([H2O])^2 ([K])^2 = (([H2O])^2 ([K])^2)/([H2] ([KOH])^2)

Construct the rate of reaction expression for: H_2 + KOH ⟶ H_2O + K 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: H_2 + 2 KOH ⟶ 2 H_2O + 2 K 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_2 | 1 | -1 KOH | 2 | -2 H_2O | 2 | 2 K | 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_2 | 1 | -1 | -(Δ[H2])/(Δt) KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K | 2 | 2 | 1/2 (Δ[K])/(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 = -(Δ[H2])/(Δt) = -1/2 (Δ[KOH])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[K])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | potassium hydroxide | water | potassium formula | H_2 | KOH | H_2O | K Hill formula | H_2 | HKO | H_2O | K name | hydrogen | potassium hydroxide | water | potassium IUPAC name | molecular hydrogen | potassium hydroxide | water | potassium

| hydrogen | potassium hydroxide | water | potassium molar mass | 2.016 g/mol | 56.105 g/mol | 18.015 g/mol | 39.0983 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 406 °C | 0 °C | 64 °C boiling point | -252.8 °C | 1327 °C | 99.9839 °C | 760 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.044 g/cm^3 | 1 g/cm^3 | 0.86 g/cm^3 solubility in water | | soluble | | reacts surface tension | | | 0.0728 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | 0.001 Pa s (at 550 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |