Ca + P4 = Ca3P2

Ca calcium + P_4 white phosphorus ⟶ Ca_3P_2 calcium phosphide

Balance the chemical equation algebraically: Ca + P_4 ⟶ Ca_3P_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca + c_2 P_4 ⟶ c_3 Ca_3P_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca and P: Ca: | 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 Ca + P_4 ⟶ 2 Ca_3P_2

+ ⟶

calcium + white phosphorus ⟶ calcium phosphide

Construct the equilibrium constant, K, expression for: Ca + P_4 ⟶ Ca_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 Ca + P_4 ⟶ 2 Ca_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 Ca | 6 | -6 P_4 | 1 | -1 Ca_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 Ca | 6 | -6 | ([Ca])^(-6) P_4 | 1 | -1 | ([P4])^(-1) Ca_3P_2 | 2 | 2 | ([Ca3P2])^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 = ([Ca])^(-6) ([P4])^(-1) ([Ca3P2])^2 = ([Ca3P2])^2/(([Ca])^6 [P4])

Construct the rate of reaction expression for: Ca + P_4 ⟶ Ca_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 Ca + P_4 ⟶ 2 Ca_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 Ca | 6 | -6 P_4 | 1 | -1 Ca_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 Ca | 6 | -6 | -1/6 (Δ[Ca])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) Ca_3P_2 | 2 | 2 | 1/2 (Δ[Ca3P2])/(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[Ca])/(Δt) = -(Δ[P4])/(Δt) = 1/2 (Δ[Ca3P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium | white phosphorus | calcium phosphide formula | Ca | P_4 | Ca_3P_2 name | calcium | white phosphorus | calcium phosphide IUPAC name | calcium | tetraphosphorus | calcium phosphanidylidenecalcium

| calcium | white phosphorus | calcium phosphide molar mass | 40.078 g/mol | 123.89504799 g/mol | 182.18 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) melting point | 850 °C | 44.15 °C | 0.16 °C boiling point | 1484 °C | 280.5 °C | density | 1.54 g/cm^3 | 1.823 g/cm^3 | 2.51 g/cm^3 solubility in water | decomposes | insoluble | decomposes dynamic viscosity | | 0.00169 Pa s (at 50 °C) | odor | | odorless |