Mg + P4 = Mg3P2

Mg magnesium + P_4 white phosphorus ⟶ Mg_3P_2 magnesium phosphide

Balance the chemical equation algebraically: Mg + P_4 ⟶ Mg_3P_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 P_4 ⟶ c_3 Mg_3P_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg and P: Mg: | c_1 = 3 c_3 P: | 4 c_2 = 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 = 6 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Mg + P_4 ⟶ 2 Mg_3P_2

+ ⟶

magnesium + white phosphorus ⟶ magnesium phosphide

Construct the equilibrium constant, K, expression for: Mg + P_4 ⟶ Mg_3P_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: 6 Mg + P_4 ⟶ 2 Mg_3P_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 Mg | 6 | -6 P_4 | 1 | -1 Mg_3P_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 6 | -6 | ([Mg])^(-6) P_4 | 1 | -1 | ([P4])^(-1) Mg_3P_2 | 2 | 2 | ([Mg3P2])^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 = ([Mg])^(-6) ([P4])^(-1) ([Mg3P2])^2 = ([Mg3P2])^2/(([Mg])^6 [P4])

Construct the rate of reaction expression for: Mg + P_4 ⟶ Mg_3P_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: 6 Mg + P_4 ⟶ 2 Mg_3P_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 Mg | 6 | -6 P_4 | 1 | -1 Mg_3P_2 | 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 Mg | 6 | -6 | -1/6 (Δ[Mg])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) Mg_3P_2 | 2 | 2 | 1/2 (Δ[Mg3P2])/(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[Mg])/(Δt) = -(Δ[P4])/(Δt) = 1/2 (Δ[Mg3P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | white phosphorus | magnesium phosphide formula | Mg | P_4 | Mg_3P_2 name | magnesium | white phosphorus | magnesium phosphide IUPAC name | magnesium | tetraphosphorus | trimagnesium phosphorus(-3) anion

| magnesium | white phosphorus | magnesium phosphide molar mass | 24.305 g/mol | 123.89504799 g/mol | 134.86 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 44.15 °C | 750 °C boiling point | 1090 °C | 280.5 °C | density | 1.738 g/cm^3 | 1.823 g/cm^3 | 2.055 g/cm^3 solubility in water | reacts | insoluble | reacts dynamic viscosity | | 0.00169 Pa s (at 50 °C) | odor | | odorless |