HCl + Mg(HCO3)2 = H2O + CO2 + MgCl2

HCl hydrogen chloride + Mg(HCO3)2 ⟶ H_2O water + CO_2 carbon dioxide + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: HCl + Mg(HCO3)2 ⟶ H_2O + CO_2 + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Mg(HCO3)2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mg, C and O: Cl: | c_1 = 2 c_5 H: | c_1 + 2 c_2 = 2 c_3 Mg: | c_2 = c_5 C: | 2 c_2 = c_4 O: | 6 c_2 = c_3 + 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 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + Mg(HCO3)2 ⟶ 2 H_2O + 2 CO_2 + MgCl_2

+ Mg(HCO3)2 ⟶ + +

hydrogen chloride + Mg(HCO3)2 ⟶ water + carbon dioxide + magnesium chloride

Construct the equilibrium constant, K, expression for: HCl + Mg(HCO3)2 ⟶ H_2O + CO_2 + MgCl_2 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 + Mg(HCO3)2 ⟶ 2 H_2O + 2 CO_2 + MgCl_2 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 Mg(HCO3)2 | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 MgCl_2 | 1 | 1 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) Mg(HCO3)2 | 1 | -1 | ([Mg(HCO3)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 CO_2 | 2 | 2 | ([CO2])^2 MgCl_2 | 1 | 1 | [MgCl2] 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) ([Mg(HCO3)2])^(-1) ([H2O])^2 ([CO2])^2 [MgCl2] = (([H2O])^2 ([CO2])^2 [MgCl2])/(([HCl])^2 [Mg(HCO3)2])

Construct the rate of reaction expression for: HCl + Mg(HCO3)2 ⟶ H_2O + CO_2 + MgCl_2 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 + Mg(HCO3)2 ⟶ 2 H_2O + 2 CO_2 + MgCl_2 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 Mg(HCO3)2 | 1 | -1 H_2O | 2 | 2 CO_2 | 2 | 2 MgCl_2 | 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 | 2 | -2 | -1/2 (Δ[HCl])/(Δt) Mg(HCO3)2 | 1 | -1 | -(Δ[Mg(HCO3)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) MgCl_2 | 1 | 1 | (Δ[MgCl2])/(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[Mg(HCO3)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | Mg(HCO3)2 | water | carbon dioxide | magnesium chloride formula | HCl | Mg(HCO3)2 | H_2O | CO_2 | MgCl_2 Hill formula | ClH | C2H2MgO6 | H_2O | CO_2 | Cl_2Mg name | hydrogen chloride | | water | carbon dioxide | magnesium chloride IUPAC name | hydrogen chloride | | water | carbon dioxide | magnesium dichloride

| hydrogen chloride | Mg(HCO3)2 | water | carbon dioxide | magnesium chloride molar mass | 36.46 g/mol | 146.34 g/mol | 18.015 g/mol | 44.009 g/mol | 95.2 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | -56.56 °C (at triple point) | 714 °C boiling point | -85 °C | | 99.9839 °C | -78.5 °C (at sublimation point) | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.32 g/cm^3 solubility in water | miscible | | | | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |