Ca + S8 = CaS

Ca calcium + S_8 rhombic sulfur ⟶ CaS calcium sulfide

Balance the chemical equation algebraically: Ca + S_8 ⟶ CaS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca + c_2 S_8 ⟶ c_3 CaS Set the number of atoms in the reactants equal to the number of atoms in the products for Ca and S: Ca: | c_1 = c_3 S: | 8 c_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 = 8 c_2 = 1 c_3 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Ca + S_8 ⟶ 8 CaS

+ ⟶

calcium + rhombic sulfur ⟶ calcium sulfide

| calcium | rhombic sulfur | calcium sulfide molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -482.4 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -3859 kJ/mol | H_initial = 0 kJ/mol | | H_final = -3859 kJ/mol ΔH_rxn^0 | -3859 kJ/mol - 0 kJ/mol = -3859 kJ/mol (exothermic) | |

Construct the equilibrium constant, K, expression for: Ca + S_8 ⟶ CaS 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: 8 Ca + S_8 ⟶ 8 CaS 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 Ca | 8 | -8 S_8 | 1 | -1 CaS | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca | 8 | -8 | ([Ca])^(-8) S_8 | 1 | -1 | ([S8])^(-1) CaS | 8 | 8 | ([CaS])^8 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 = ([Ca])^(-8) ([S8])^(-1) ([CaS])^8 = ([CaS])^8/(([Ca])^8 [S8])

Construct the rate of reaction expression for: Ca + S_8 ⟶ CaS 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: 8 Ca + S_8 ⟶ 8 CaS 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 Ca | 8 | -8 S_8 | 1 | -1 CaS | 8 | 8 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 Ca | 8 | -8 | -1/8 (Δ[Ca])/(Δt) S_8 | 1 | -1 | -(Δ[S8])/(Δt) CaS | 8 | 8 | 1/8 (Δ[CaS])/(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 = -1/8 (Δ[Ca])/(Δt) = -(Δ[S8])/(Δt) = 1/8 (Δ[CaS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium | rhombic sulfur | calcium sulfide formula | Ca | S_8 | CaS name | calcium | rhombic sulfur | calcium sulfide IUPAC name | calcium | octathiocane | thioxocalcium

| calcium | rhombic sulfur | calcium sulfide molar mass | 40.078 g/mol | 256.5 g/mol | 72.14 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 850 °C | | 2450 °C boiling point | 1484 °C | | density | 1.54 g/cm^3 | 2.07 g/cm^3 | 2.5 g/cm^3 solubility in water | decomposes | | decomposes