HBr + Mg(OH)2 = H2O + MgBr2

HBr hydrogen bromide + Mg(OH)_2 magnesium hydroxide ⟶ H_2O water + MgBr_2 magnesium bromide

Balance the chemical equation algebraically: HBr + Mg(OH)_2 ⟶ H_2O + MgBr_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HBr + c_2 Mg(OH)_2 ⟶ c_3 H_2O + c_4 MgBr_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Br, H, Mg and O: Br: | c_1 = 2 c_4 H: | c_1 + 2 c_2 = 2 c_3 Mg: | c_2 = c_4 O: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HBr + Mg(OH)_2 ⟶ 2 H_2O + MgBr_2

+ ⟶ +

hydrogen bromide + magnesium hydroxide ⟶ water + magnesium bromide

| hydrogen bromide | magnesium hydroxide | water | magnesium bromide molecular enthalpy | -36.3 kJ/mol | -924.5 kJ/mol | -285.8 kJ/mol | -5243 kJ/mol total enthalpy | -72.6 kJ/mol | -924.5 kJ/mol | -571.7 kJ/mol | -5243 kJ/mol | H_initial = -997.1 kJ/mol | | H_final = -5815 kJ/mol | ΔH_rxn^0 | -5815 kJ/mol - -997.1 kJ/mol = -4818 kJ/mol (exothermic) | | |

| hydrogen bromide | magnesium hydroxide | water | magnesium bromide molecular free energy | -53.4 kJ/mol | -833.5 kJ/mol | -237.1 kJ/mol | -503.8 kJ/mol total free energy | -106.8 kJ/mol | -833.5 kJ/mol | -474.2 kJ/mol | -503.8 kJ/mol | G_initial = -940.3 kJ/mol | | G_final = -978 kJ/mol | ΔG_rxn^0 | -978 kJ/mol - -940.3 kJ/mol = -37.7 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: HBr + Mg(OH)_2 ⟶ H_2O + MgBr_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 HBr + Mg(OH)_2 ⟶ 2 H_2O + MgBr_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 HBr | 2 | -2 Mg(OH)_2 | 1 | -1 H_2O | 2 | 2 MgBr_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HBr | 2 | -2 | ([HBr])^(-2) Mg(OH)_2 | 1 | -1 | ([Mg(OH)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 MgBr_2 | 1 | 1 | [MgBr2] 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 = ([HBr])^(-2) ([Mg(OH)2])^(-1) ([H2O])^2 [MgBr2] = (([H2O])^2 [MgBr2])/(([HBr])^2 [Mg(OH)2])

Construct the rate of reaction expression for: HBr + Mg(OH)_2 ⟶ H_2O + MgBr_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 HBr + Mg(OH)_2 ⟶ 2 H_2O + MgBr_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 HBr | 2 | -2 Mg(OH)_2 | 1 | -1 H_2O | 2 | 2 MgBr_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 HBr | 2 | -2 | -1/2 (Δ[HBr])/(Δt) Mg(OH)_2 | 1 | -1 | -(Δ[Mg(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MgBr_2 | 1 | 1 | (Δ[MgBr2])/(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[HBr])/(Δt) = -(Δ[Mg(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[MgBr2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen bromide | magnesium hydroxide | water | magnesium bromide formula | HBr | Mg(OH)_2 | H_2O | MgBr_2 Hill formula | BrH | H_2MgO_2 | H_2O | Br_2Mg name | hydrogen bromide | magnesium hydroxide | water | magnesium bromide IUPAC name | hydrogen bromide | magnesium dihydroxide | water | magnesium dibromide

| hydrogen bromide | magnesium hydroxide | water | magnesium bromide molar mass | 80.912 g/mol | 58.319 g/mol | 18.015 g/mol | 184.11 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -86.8 °C | 350 °C | 0 °C | 711 °C boiling point | -66.38 °C | | 99.9839 °C | density | 0.003307 g/cm^3 (at 25 °C) | 2.3446 g/cm^3 | 1 g/cm^3 | 3.72 g/cm^3 solubility in water | miscible | insoluble | | soluble surface tension | 0.0271 N/m | | 0.0728 N/m | dynamic viscosity | 8.4×10^-4 Pa s (at -75 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |