P + Sn = Sn3P4

P red phosphorus + Sn white tin ⟶ Sn3P4

Balance the chemical equation algebraically: P + Sn ⟶ Sn3P4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 Sn ⟶ c_3 Sn3P4 Set the number of atoms in the reactants equal to the number of atoms in the products for P and Sn: P: | c_1 = 4 c_3 Sn: | 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 = 4 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 P + 3 Sn ⟶ Sn3P4

+ ⟶ Sn3P4

red phosphorus + white tin ⟶ Sn3P4

Construct the equilibrium constant, K, expression for: P + Sn ⟶ Sn3P4 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: 4 P + 3 Sn ⟶ Sn3P4 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 | 4 | -4 Sn | 3 | -3 Sn3P4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 4 | -4 | ([P])^(-4) Sn | 3 | -3 | ([Sn])^(-3) Sn3P4 | 1 | 1 | [Sn3P4] 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])^(-4) ([Sn])^(-3) [Sn3P4] = ([Sn3P4])/(([P])^4 ([Sn])^3)

Construct the rate of reaction expression for: P + Sn ⟶ Sn3P4 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: 4 P + 3 Sn ⟶ Sn3P4 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 | 4 | -4 Sn | 3 | -3 Sn3P4 | 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 | 4 | -4 | -1/4 (Δ[P])/(Δt) Sn | 3 | -3 | -1/3 (Δ[Sn])/(Δt) Sn3P4 | 1 | 1 | (Δ[Sn3P4])/(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 = -1/4 (Δ[P])/(Δt) = -1/3 (Δ[Sn])/(Δt) = (Δ[Sn3P4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | white tin | Sn3P4 formula | P | Sn | Sn3P4 Hill formula | P | Sn | P4Sn3 name | red phosphorus | white tin | IUPAC name | phosphorus | tin |

| red phosphorus | white tin | Sn3P4 molar mass | 30.973761998 g/mol | 118.71 g/mol | 480.025 g/mol phase | solid (at STP) | solid (at STP) | melting point | 579.2 °C | 231.9 °C | boiling point | | 2602 °C | density | 2.16 g/cm^3 | 7.31 g/cm^3 | solubility in water | insoluble | insoluble | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | 0.001 Pa s (at 600 °C) | odor | | odorless |