H2O + NH3 = NH4OH

H_2O (water) + NH_3 (ammonia) ⟶ NH_4OH (ammonium hydroxide)

Balance the chemical equation algebraically: H_2O + NH_3 ⟶ NH_4OH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_3 ⟶ c_3 NH_4OH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and N: H: | 2 c_1 + 3 c_2 = 5 c_3 O: | c_1 = c_3 N: | 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + NH_3 ⟶ NH_4OH

+ ⟶

water + ammonia ⟶ ammonium hydroxide

Construct the equilibrium constant, K, expression for: H_2O + NH_3 ⟶ NH_4OH 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_2O + NH_3 ⟶ NH_4OH 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 | 1 | -1 NH_3 | 1 | -1 NH_4OH | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) NH_3 | 1 | -1 | ([NH3])^(-1) NH_4OH | 1 | 1 | [NH4OH] 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])^(-1) ([NH3])^(-1) [NH4OH] = ([NH4OH])/([H2O] [NH3])

Construct the rate of reaction expression for: H_2O + NH_3 ⟶ NH_4OH 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_2O + NH_3 ⟶ NH_4OH 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 | 1 | -1 NH_3 | 1 | -1 NH_4OH | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) NH_3 | 1 | -1 | -(Δ[NH3])/(Δt) NH_4OH | 1 | 1 | (Δ[NH4OH])/(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[H2O])/(Δt) = -(Δ[NH3])/(Δt) = (Δ[NH4OH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | ammonia | ammonium hydroxide formula | H_2O | NH_3 | NH_4OH Hill formula | H_2O | H_3N | H_5NO name | water | ammonia | ammonium hydroxide

| water | ammonia | ammonium hydroxide molar mass | 18.015 g/mol | 17.031 g/mol | 35.046 g/mol phase | liquid (at STP) | gas (at STP) | aqueous (at STP) melting point | 0 °C | -77.73 °C | -57.5 °C boiling point | 99.9839 °C | -33.33 °C | 36 °C density | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 0.9 g/cm^3 solubility in water | | | very soluble surface tension | 0.0728 N/m | 0.0234 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | odor | odorless | |