HCl + Mg = H2 + Mg2Cl

HCl hydrogen chloride + Mg magnesium ⟶ H_2 hydrogen + Mg2Cl

Balance the chemical equation algebraically: HCl + Mg ⟶ H_2 + Mg2Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Mg ⟶ c_3 H_2 + c_4 Mg2Cl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and Mg: Cl: | c_1 = c_4 H: | c_1 = 2 c_3 Mg: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 4 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + 4 Mg ⟶ H_2 + 2 Mg2Cl

+ ⟶ + Mg2Cl

hydrogen chloride + magnesium ⟶ hydrogen + Mg2Cl

Construct the equilibrium constant, K, expression for: HCl + Mg ⟶ H_2 + Mg2Cl 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 + 4 Mg ⟶ H_2 + 2 Mg2Cl 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 | 4 | -4 H_2 | 1 | 1 Mg2Cl | 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) Mg | 4 | -4 | ([Mg])^(-4) H_2 | 1 | 1 | [H2] Mg2Cl | 2 | 2 | ([Mg2Cl])^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) ([Mg])^(-4) [H2] ([Mg2Cl])^2 = ([H2] ([Mg2Cl])^2)/(([HCl])^2 ([Mg])^4)

Construct the rate of reaction expression for: HCl + Mg ⟶ H_2 + Mg2Cl 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 + 4 Mg ⟶ H_2 + 2 Mg2Cl 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 | 4 | -4 H_2 | 1 | 1 Mg2Cl | 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) Mg | 4 | -4 | -1/4 (Δ[Mg])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Mg2Cl | 2 | 2 | 1/2 (Δ[Mg2Cl])/(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) = -1/4 (Δ[Mg])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[Mg2Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | magnesium | hydrogen | Mg2Cl formula | HCl | Mg | H_2 | Mg2Cl Hill formula | ClH | Mg | H_2 | ClMg2 name | hydrogen chloride | magnesium | hydrogen | IUPAC name | hydrogen chloride | magnesium | molecular hydrogen |

| hydrogen chloride | magnesium | hydrogen | Mg2Cl molar mass | 36.46 g/mol | 24.305 g/mol | 2.016 g/mol | 84.06 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | melting point | -114.17 °C | 648 °C | -259.2 °C | boiling point | -85 °C | 1090 °C | -252.8 °C | density | 0.00149 g/cm^3 (at 25 °C) | 1.738 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | miscible | reacts | | dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |