C + S8 = CS2

C activated charcoal + S_8 rhombic sulfur ⟶ CS_2 carbon disulfide

Balance the chemical equation algebraically: C + S_8 ⟶ CS_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 S_8 ⟶ c_3 CS_2 Set the number of atoms in the reactants equal to the number of atoms in the products for C and S: C: | c_1 = c_3 S: | 8 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 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 C + S_8 ⟶ 4 CS_2

+ ⟶

activated charcoal + rhombic sulfur ⟶ carbon disulfide

Construct the equilibrium constant, K, expression for: C + S_8 ⟶ 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 C + S_8 ⟶ 4 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 C | 4 | -4 S_8 | 1 | -1 CS_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 4 | -4 | ([C])^(-4) S_8 | 1 | -1 | ([S8])^(-1) CS_2 | 4 | 4 | ([CS2])^4 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 = ([C])^(-4) ([S8])^(-1) ([CS2])^4 = ([CS2])^4/(([C])^4 [S8])

Construct the rate of reaction expression for: C + S_8 ⟶ 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 C + S_8 ⟶ 4 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 C | 4 | -4 S_8 | 1 | -1 CS_2 | 4 | 4 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 C | 4 | -4 | -1/4 (Δ[C])/(Δt) S_8 | 1 | -1 | -(Δ[S8])/(Δt) CS_2 | 4 | 4 | 1/4 (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[C])/(Δt) = -(Δ[S8])/(Δt) = 1/4 (Δ[CS2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | rhombic sulfur | carbon disulfide formula | C | S_8 | CS_2 name | activated charcoal | rhombic sulfur | carbon disulfide IUPAC name | carbon | octathiocane | methanedithione

| activated charcoal | rhombic sulfur | carbon disulfide molar mass | 12.011 g/mol | 256.5 g/mol | 76.13 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) melting point | 3550 °C | | -111.5 °C boiling point | 4027 °C | | 46 °C density | 2.26 g/cm^3 | 2.07 g/cm^3 | 1.266 g/cm^3 solubility in water | insoluble | | slightly soluble surface tension | | | 0.03225 N/m dynamic viscosity | | | 3.52×10^-4 Pa s (at 25 °C)