P + Ba = Ba3P2

P red phosphorus + Ba barium ⟶ Ba3P2

Balance the chemical equation algebraically: P + Ba ⟶ Ba3P2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 Ba ⟶ c_3 Ba3P2 Set the number of atoms in the reactants equal to the number of atoms in the products for P and Ba: P: | c_1 = 2 c_3 Ba: | c_2 = 3 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 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 P + 3 Ba ⟶ Ba3P2

+ ⟶ Ba3P2

red phosphorus + barium ⟶ Ba3P2

Construct the equilibrium constant, K, expression for: P + Ba ⟶ Ba3P2 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 + 3 Ba ⟶ Ba3P2 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 Ba | 3 | -3 Ba3P2 | 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) Ba | 3 | -3 | ([Ba])^(-3) Ba3P2 | 1 | 1 | [Ba3P2] 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) ([Ba])^(-3) [Ba3P2] = ([Ba3P2])/(([P])^2 ([Ba])^3)

Construct the rate of reaction expression for: P + Ba ⟶ Ba3P2 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 + 3 Ba ⟶ Ba3P2 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 Ba | 3 | -3 Ba3P2 | 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) Ba | 3 | -3 | -1/3 (Δ[Ba])/(Δt) Ba3P2 | 1 | 1 | (Δ[Ba3P2])/(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) = -1/3 (Δ[Ba])/(Δt) = (Δ[Ba3P2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | barium | Ba3P2 formula | P | Ba | Ba3P2 name | red phosphorus | barium | IUPAC name | phosphorus | barium |

| red phosphorus | barium | Ba3P2 molar mass | 30.973761998 g/mol | 137.327 g/mol | 473.929 g/mol phase | solid (at STP) | solid (at STP) | melting point | 579.2 °C | 725 °C | boiling point | | 1640 °C | density | 2.16 g/cm^3 | 3.6 g/cm^3 | solubility in water | insoluble | insoluble | surface tension | | 0.224 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | |