S + In = In2S3

S mixed sulfur + In indium ⟶ In_2S_3 indium(III) sulfide red

Balance the chemical equation algebraically: S + In ⟶ In_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 In ⟶ c_3 In_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S and In: S: | c_1 = 3 c_3 In: | 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 In ⟶ In_2S_3

+ ⟶

mixed sulfur + indium ⟶ indium(III) sulfide red

Construct the equilibrium constant, K, expression for: S + In ⟶ In_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 In ⟶ In_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 In | 2 | -2 In_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) In | 2 | -2 | ([In])^(-2) In_2S_3 | 1 | 1 | [In2S3] 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) ([In])^(-2) [In2S3] = ([In2S3])/(([S])^3 ([In])^2)

Construct the rate of reaction expression for: S + In ⟶ In_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 In ⟶ In_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 In | 2 | -2 In_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) In | 2 | -2 | -1/2 (Δ[In])/(Δt) In_2S_3 | 1 | 1 | (Δ[In2S3])/(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[In])/(Δt) = (Δ[In2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | indium | indium(III) sulfide red formula | S | In | In_2S_3 name | mixed sulfur | indium | indium(III) sulfide red IUPAC name | sulfur | indium | thioxo-(thioxoindiganylthio)indigane