S + CH4 = H2S + CS2

S mixed sulfur + CH_4 methane ⟶ H_2S hydrogen sulfide + CS_2 carbon disulfide

Balance the chemical equation algebraically: S + CH_4 ⟶ H_2S + CS_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 CH_4 ⟶ c_3 H_2S + c_4 CS_2 Set the number of atoms in the reactants equal to the number of atoms in the products for S, C and H: S: | c_1 = c_3 + 2 c_4 C: | c_2 = c_4 H: | 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 S + CH_4 ⟶ 2 H_2S + CS_2

+ ⟶ +

mixed sulfur + methane ⟶ hydrogen sulfide + carbon disulfide

Construct the equilibrium constant, K, expression for: S + CH_4 ⟶ H_2S + CS_2 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 S + CH_4 ⟶ 2 H_2S + CS_2 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 | 4 | -4 CH_4 | 1 | -1 H_2S | 2 | 2 CS_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 4 | -4 | ([S])^(-4) CH_4 | 1 | -1 | ([CH4])^(-1) H_2S | 2 | 2 | ([H2S])^2 CS_2 | 1 | 1 | [CS2] 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])^(-4) ([CH4])^(-1) ([H2S])^2 [CS2] = (([H2S])^2 [CS2])/(([S])^4 [CH4])

Construct the rate of reaction expression for: S + CH_4 ⟶ H_2S + CS_2 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 S + CH_4 ⟶ 2 H_2S + CS_2 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 | 4 | -4 CH_4 | 1 | -1 H_2S | 2 | 2 CS_2 | 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 | 4 | -4 | -1/4 (Δ[S])/(Δt) CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) H_2S | 2 | 2 | 1/2 (Δ[H2S])/(Δt) CS_2 | 1 | 1 | (Δ[CS2])/(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[S])/(Δt) = -(Δ[CH4])/(Δt) = 1/2 (Δ[H2S])/(Δt) = (Δ[CS2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | methane | hydrogen sulfide | carbon disulfide formula | S | CH_4 | H_2S | CS_2 name | mixed sulfur | methane | hydrogen sulfide | carbon disulfide IUPAC name | sulfur | methane | hydrogen sulfide | methanedithione

| mixed sulfur | methane | hydrogen sulfide | carbon disulfide molar mass | 32.06 g/mol | 16.04 g/mol | 34.08 g/mol | 76.13 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) melting point | 112.8 °C | -182.47 °C | -85 °C | -111.5 °C boiling point | 444.7 °C | -161.48 °C | -60 °C | 46 °C density | 2.07 g/cm^3 | 6.67151×10^-4 g/cm^3 (at 20 °C) | 0.001393 g/cm^3 (at 25 °C) | 1.266 g/cm^3 solubility in water | | soluble | | slightly soluble surface tension | | 0.0137 N/m | | 0.03225 N/m dynamic viscosity | | 1.114×10^-5 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | 3.52×10^-4 Pa s (at 25 °C) odor | | odorless | |