HCl + Mn = H2 + MnCl2

HCl hydrogen chloride + Mn manganese ⟶ H_2 hydrogen + MnCl_2 manganese(II) chloride

Balance the chemical equation algebraically: HCl + Mn ⟶ H_2 + MnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Mn ⟶ c_3 H_2 + c_4 MnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and Mn: Cl: | c_1 = 2 c_4 H: | c_1 = 2 c_3 Mn: | 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + Mn ⟶ H_2 + MnCl_2

+ ⟶ +

hydrogen chloride + manganese ⟶ hydrogen + manganese(II) chloride

| hydrogen chloride | manganese | hydrogen | manganese(II) chloride molecular enthalpy | -92.3 kJ/mol | 0 kJ/mol | 0 kJ/mol | -481.3 kJ/mol total enthalpy | -184.6 kJ/mol | 0 kJ/mol | 0 kJ/mol | -481.3 kJ/mol | H_initial = -184.6 kJ/mol | | H_final = -481.3 kJ/mol | ΔH_rxn^0 | -481.3 kJ/mol - -184.6 kJ/mol = -296.7 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: HCl + Mn ⟶ H_2 + MnCl_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 + Mn ⟶ H_2 + MnCl_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 Mn | 1 | -1 H_2 | 1 | 1 MnCl_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) Mn | 1 | -1 | ([Mn])^(-1) H_2 | 1 | 1 | [H2] MnCl_2 | 1 | 1 | [MnCl2] 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) ([Mn])^(-1) [H2] [MnCl2] = ([H2] [MnCl2])/(([HCl])^2 [Mn])

Construct the rate of reaction expression for: HCl + Mn ⟶ H_2 + MnCl_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 + Mn ⟶ H_2 + MnCl_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 Mn | 1 | -1 H_2 | 1 | 1 MnCl_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) Mn | 1 | -1 | -(Δ[Mn])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) MnCl_2 | 1 | 1 | (Δ[MnCl2])/(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[Mn])/(Δt) = (Δ[H2])/(Δt) = (Δ[MnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | manganese | hydrogen | manganese(II) chloride formula | HCl | Mn | H_2 | MnCl_2 Hill formula | ClH | Mn | H_2 | Cl_2Mn name | hydrogen chloride | manganese | hydrogen | manganese(II) chloride IUPAC name | hydrogen chloride | manganese | molecular hydrogen | dichloromanganese

| hydrogen chloride | manganese | hydrogen | manganese(II) chloride molar mass | 36.46 g/mol | 54.938044 g/mol | 2.016 g/mol | 125.8 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -114.17 °C | 1244 °C | -259.2 °C | 652 °C boiling point | -85 °C | 1962 °C | -252.8 °C | density | 0.00149 g/cm^3 (at 25 °C) | 7.3 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.98 g/cm^3 solubility in water | miscible | insoluble | | dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |