P + Ca = Ca2P2

P red phosphorus + Ca calcium ⟶ Ca2P2

Balance the chemical equation algebraically: P + Ca ⟶ Ca2P2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 Ca ⟶ c_3 Ca2P2 Set the number of atoms in the reactants equal to the number of atoms in the products for P and Ca: P: | c_1 = 2 c_3 Ca: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 P + 2 Ca ⟶ Ca2P2

+ ⟶ Ca2P2

red phosphorus + calcium ⟶ Ca2P2

Construct the equilibrium constant, K, expression for: P + Ca ⟶ Ca2P2 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 P + 2 Ca ⟶ Ca2P2 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 P | 2 | -2 Ca | 2 | -2 Ca2P2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 2 | -2 | ([P])^(-2) Ca | 2 | -2 | ([Ca])^(-2) Ca2P2 | 1 | 1 | [Ca2P2] 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 = ([P])^(-2) ([Ca])^(-2) [Ca2P2] = ([Ca2P2])/(([P])^2 ([Ca])^2)

Construct the rate of reaction expression for: P + Ca ⟶ Ca2P2 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 P + 2 Ca ⟶ Ca2P2 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 P | 2 | -2 Ca | 2 | -2 Ca2P2 | 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 P | 2 | -2 | -1/2 (Δ[P])/(Δt) Ca | 2 | -2 | -1/2 (Δ[Ca])/(Δt) Ca2P2 | 1 | 1 | (Δ[Ca2P2])/(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[P])/(Δt) = -1/2 (Δ[Ca])/(Δt) = (Δ[Ca2P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | calcium | Ca2P2 formula | P | Ca | Ca2P2 name | red phosphorus | calcium | IUPAC name | phosphorus | calcium |

| red phosphorus | calcium | Ca2P2 molar mass | 30.973761998 g/mol | 40.078 g/mol | 142.1 g/mol phase | solid (at STP) | solid (at STP) | melting point | 579.2 °C | 850 °C | boiling point | | 1484 °C | density | 2.16 g/cm^3 | 1.54 g/cm^3 | solubility in water | insoluble | decomposes | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | |