Mg + P = Mg3P

Mg magnesium + P red phosphorus ⟶ Mg3P

Balance the chemical equation algebraically: Mg + P ⟶ Mg3P Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 P ⟶ c_3 Mg3P 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: | 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 = 3 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Mg + P ⟶ Mg3P

+ ⟶ Mg3P

magnesium + red phosphorus ⟶ Mg3P

Construct the equilibrium constant, K, expression for: Mg + P ⟶ Mg3P 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: 3 Mg + P ⟶ Mg3P 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 | 3 | -3 P | 1 | -1 Mg3P | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 3 | -3 | ([Mg])^(-3) P | 1 | -1 | ([P])^(-1) Mg3P | 1 | 1 | [Mg3P] 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])^(-3) ([P])^(-1) [Mg3P] = ([Mg3P])/(([Mg])^3 [P])

Construct the rate of reaction expression for: Mg + P ⟶ Mg3P 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: 3 Mg + P ⟶ Mg3P 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 | 3 | -3 P | 1 | -1 Mg3P | 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 Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) P | 1 | -1 | -(Δ[P])/(Δt) Mg3P | 1 | 1 | (Δ[Mg3P])/(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 = -1/3 (Δ[Mg])/(Δt) = -(Δ[P])/(Δt) = (Δ[Mg3P])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | red phosphorus | Mg3P formula | Mg | P | Mg3P name | magnesium | red phosphorus | IUPAC name | magnesium | phosphorus |

| magnesium | red phosphorus | Mg3P molar mass | 24.305 g/mol | 30.973761998 g/mol | 103.89 g/mol phase | solid (at STP) | solid (at STP) | melting point | 648 °C | 579.2 °C | boiling point | 1090 °C | | density | 1.738 g/cm^3 | 2.16 g/cm^3 | solubility in water | reacts | insoluble | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) |