S + P = P2S3

S mixed sulfur + P red phosphorus ⟶ P_2S_3 phosphorus trisulfide

Balance the chemical equation algebraically: S + P ⟶ P_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 P ⟶ c_3 P_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S and P: S: | c_1 = 3 c_3 P: | 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 = 3 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 S + 2 P ⟶ P_2S_3

+ ⟶

mixed sulfur + red phosphorus ⟶ phosphorus trisulfide

Construct the equilibrium constant, K, expression for: S + P ⟶ P_2S_3 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 S + 2 P ⟶ P_2S_3 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 S | 3 | -3 P | 2 | -2 P_2S_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 3 | -3 | ([S])^(-3) P | 2 | -2 | ([P])^(-2) P_2S_3 | 1 | 1 | [P2S3] 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 = ([S])^(-3) ([P])^(-2) [P2S3] = ([P2S3])/(([S])^3 ([P])^2)

Construct the rate of reaction expression for: S + P ⟶ P_2S_3 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 S + 2 P ⟶ P_2S_3 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 S | 3 | -3 P | 2 | -2 P_2S_3 | 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 S | 3 | -3 | -1/3 (Δ[S])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) P_2S_3 | 1 | 1 | (Δ[P2S3])/(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[S])/(Δt) = -1/2 (Δ[P])/(Δt) = (Δ[P2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | red phosphorus | phosphorus trisulfide formula | S | P | P_2S_3 name | mixed sulfur | red phosphorus | phosphorus trisulfide IUPAC name | sulfur | phosphorus |

| mixed sulfur | red phosphorus | phosphorus trisulfide molar mass | 32.06 g/mol | 30.973761998 g/mol | 158.1 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 579.2 °C | boiling point | 444.7 °C | | density | 2.07 g/cm^3 | 2.16 g/cm^3 | solubility in water | | insoluble | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) |