HCl + Mg3P2 = MgCl2 + PH3

HCl hydrogen chloride + Mg_3P_2 magnesium phosphide ⟶ MgCl_2 magnesium chloride + PH_3 phosphine

Balance the chemical equation algebraically: HCl + Mg_3P_2 ⟶ MgCl_2 + PH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Mg_3P_2 ⟶ c_3 MgCl_2 + c_4 PH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mg and P: Cl: | c_1 = 2 c_3 H: | c_1 = 3 c_4 Mg: | 3 c_2 = c_3 P: | 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 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + Mg_3P_2 ⟶ 3 MgCl_2 + 2 PH_3

+ ⟶ +

hydrogen chloride + magnesium phosphide ⟶ magnesium chloride + phosphine

Construct the equilibrium constant, K, expression for: HCl + Mg_3P_2 ⟶ MgCl_2 + PH_3 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: 6 HCl + Mg_3P_2 ⟶ 3 MgCl_2 + 2 PH_3 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 | 6 | -6 Mg_3P_2 | 1 | -1 MgCl_2 | 3 | 3 PH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) Mg_3P_2 | 1 | -1 | ([Mg3P2])^(-1) MgCl_2 | 3 | 3 | ([MgCl2])^3 PH_3 | 2 | 2 | ([PH3])^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])^(-6) ([Mg3P2])^(-1) ([MgCl2])^3 ([PH3])^2 = (([MgCl2])^3 ([PH3])^2)/(([HCl])^6 [Mg3P2])

Construct the rate of reaction expression for: HCl + Mg_3P_2 ⟶ MgCl_2 + PH_3 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: 6 HCl + Mg_3P_2 ⟶ 3 MgCl_2 + 2 PH_3 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 | 6 | -6 Mg_3P_2 | 1 | -1 MgCl_2 | 3 | 3 PH_3 | 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) Mg_3P_2 | 1 | -1 | -(Δ[Mg3P2])/(Δt) MgCl_2 | 3 | 3 | 1/3 (Δ[MgCl2])/(Δt) PH_3 | 2 | 2 | 1/2 (Δ[PH3])/(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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[Mg3P2])/(Δt) = 1/3 (Δ[MgCl2])/(Δt) = 1/2 (Δ[PH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | magnesium phosphide | magnesium chloride | phosphine formula | HCl | Mg_3P_2 | MgCl_2 | PH_3 Hill formula | ClH | Mg_3P_2 | Cl_2Mg | H_3P name | hydrogen chloride | magnesium phosphide | magnesium chloride | phosphine IUPAC name | hydrogen chloride | trimagnesium phosphorus(-3) anion | magnesium dichloride | phosphine

| hydrogen chloride | magnesium phosphide | magnesium chloride | phosphine molar mass | 36.46 g/mol | 134.86 g/mol | 95.2 g/mol | 33.998 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) melting point | -114.17 °C | 750 °C | 714 °C | -132.8 °C boiling point | -85 °C | | | -87.5 °C density | 0.00149 g/cm^3 (at 25 °C) | 2.055 g/cm^3 | 2.32 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) solubility in water | miscible | reacts | soluble | slightly soluble dynamic viscosity | | | | 1.1×10^-5 Pa s (at 0 °C)