hydrochloric acid + calcium hydroxide -> calcium chloride + water

HCl hydrogen chloride + Ca(OH)_2 calcium hydroxide ⟶ CaCl_2 calcium chloride + H_2O water

Balance the chemical equation algebraically: HCl + Ca(OH)_2 ⟶ CaCl_2 + H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Ca(OH)_2 ⟶ c_3 CaCl_2 + c_4 H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Ca and O: Cl: | c_1 = 2 c_3 H: | c_1 + 2 c_2 = 2 c_4 Ca: | c_2 = c_3 O: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + Ca(OH)_2 ⟶ CaCl_2 + 2 H_2O

+ ⟶ +

hydrogen chloride + calcium hydroxide ⟶ calcium chloride + water

| hydrogen chloride | calcium hydroxide | calcium chloride | water molecular enthalpy | -92.3 kJ/mol | -985.2 kJ/mol | -795.4 kJ/mol | -285.8 kJ/mol total enthalpy | -184.6 kJ/mol | -985.2 kJ/mol | -795.4 kJ/mol | -571.7 kJ/mol | H_initial = -1170 kJ/mol | | H_final = -1367 kJ/mol | ΔH_rxn^0 | -1367 kJ/mol - -1170 kJ/mol = -197.3 kJ/mol (exothermic) | | |

| hydrogen chloride | calcium hydroxide | calcium chloride | water molecular free energy | -95.3 kJ/mol | -897.5 kJ/mol | -748.8 kJ/mol | -237.1 kJ/mol total free energy | -190.6 kJ/mol | -897.5 kJ/mol | -748.8 kJ/mol | -474.2 kJ/mol | G_initial = -1088 kJ/mol | | G_final = -1223 kJ/mol | ΔG_rxn^0 | -1223 kJ/mol - -1088 kJ/mol = -134.9 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: HCl + Ca(OH)_2 ⟶ CaCl_2 + H_2O 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 HCl + Ca(OH)_2 ⟶ CaCl_2 + 2 H_2O 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 | 2 | -2 Ca(OH)_2 | 1 | -1 CaCl_2 | 1 | 1 H_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) Ca(OH)_2 | 1 | -1 | ([Ca(OH)2])^(-1) CaCl_2 | 1 | 1 | [CaCl2] H_2O | 2 | 2 | ([H2O])^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 = ([HCl])^(-2) ([Ca(OH)2])^(-1) [CaCl2] ([H2O])^2 = ([CaCl2] ([H2O])^2)/(([HCl])^2 [Ca(OH)2])

Construct the rate of reaction expression for: HCl + Ca(OH)_2 ⟶ CaCl_2 + H_2O 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 HCl + Ca(OH)_2 ⟶ CaCl_2 + 2 H_2O 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 | 2 | -2 Ca(OH)_2 | 1 | -1 CaCl_2 | 1 | 1 H_2O | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) Ca(OH)_2 | 1 | -1 | -(Δ[Ca(OH)2])/(Δt) CaCl_2 | 1 | 1 | (Δ[CaCl2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(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[HCl])/(Δt) = -(Δ[Ca(OH)2])/(Δt) = (Δ[CaCl2])/(Δt) = 1/2 (Δ[H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | calcium hydroxide | calcium chloride | water formula | HCl | Ca(OH)_2 | CaCl_2 | H_2O Hill formula | ClH | CaH_2O_2 | CaCl_2 | H_2O name | hydrogen chloride | calcium hydroxide | calcium chloride | water IUPAC name | hydrogen chloride | calcium dihydroxide | calcium dichloride | water

| hydrogen chloride | calcium hydroxide | calcium chloride | water molar mass | 36.46 g/mol | 74.092 g/mol | 111 g/mol | 18.015 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) melting point | -114.17 °C | 550 °C | 772 °C | 0 °C boiling point | -85 °C | | | 99.9839 °C density | 0.00149 g/cm^3 (at 25 °C) | 2.24 g/cm^3 | 2.15 g/cm^3 | 1 g/cm^3 solubility in water | miscible | slightly soluble | soluble | surface tension | | | | 0.0728 N/m dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) odor | | odorless | | odorless