HCl + NH4OH = H2O + NH4Cl

HCl (hydrogen chloride) + NH_4OH (ammonium hydroxide) ⟶ H_2O (water) + NH_4Cl (ammonium chloride)

Balance the chemical equation algebraically: HCl + NH_4OH ⟶ H_2O + NH_4Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 NH_4OH ⟶ c_3 H_2O + c_4 NH_4Cl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N and O: Cl: | c_1 = c_4 H: | c_1 + 5 c_2 = 2 c_3 + 4 c_4 N: | 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HCl + NH_4OH ⟶ H_2O + NH_4Cl

+ ⟶ +

hydrogen chloride + ammonium hydroxide ⟶ water + ammonium chloride

Construct the equilibrium constant, K, expression for: HCl + NH_4OH ⟶ H_2O + NH_4Cl 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: HCl + NH_4OH ⟶ H_2O + NH_4Cl 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 HCl | 1 | -1 NH_4OH | 1 | -1 H_2O | 1 | 1 NH_4Cl | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 1 | -1 | ([HCl])^(-1) NH_4OH | 1 | -1 | ([NH4OH])^(-1) H_2O | 1 | 1 | [H2O] NH_4Cl | 1 | 1 | [NH4Cl] 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 = ([HCl])^(-1) ([NH4OH])^(-1) [H2O] [NH4Cl] = ([H2O] [NH4Cl])/([HCl] [NH4OH])

Construct the rate of reaction expression for: HCl + NH_4OH ⟶ H_2O + NH_4Cl 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: HCl + NH_4OH ⟶ H_2O + NH_4Cl 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 HCl | 1 | -1 NH_4OH | 1 | -1 H_2O | 1 | 1 NH_4Cl | 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 HCl | 1 | -1 | -(Δ[HCl])/(Δt) NH_4OH | 1 | -1 | -(Δ[NH4OH])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_4Cl | 1 | 1 | (Δ[NH4Cl])/(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[HCl])/(Δt) = -(Δ[NH4OH])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NH4Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | ammonium hydroxide | water | ammonium chloride formula | HCl | NH_4OH | H_2O | NH_4Cl Hill formula | ClH | H_5NO | H_2O | ClH_4N name | hydrogen chloride | ammonium hydroxide | water | ammonium chloride

| hydrogen chloride | ammonium hydroxide | water | ammonium chloride molar mass | 36.46 g/mol | 35.046 g/mol | 18.015 g/mol | 53.49 g/mol phase | gas (at STP) | aqueous (at STP) | liquid (at STP) | solid (at STP) melting point | -114.17 °C | -57.5 °C | 0 °C | 340 °C boiling point | -85 °C | 36 °C | 99.9839 °C | density | 0.00149 g/cm^3 (at 25 °C) | 0.9 g/cm^3 | 1 g/cm^3 | 1.5256 g/cm^3 solubility in water | miscible | very soluble | | soluble surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |