S + K = K2S

S mixed sulfur + K potassium ⟶ K2S

Balance the chemical equation algebraically: S + K ⟶ K2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 K ⟶ c_3 K2S Set the number of atoms in the reactants equal to the number of atoms in the products for S and K: S: | c_1 = c_3 K: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + 2 K ⟶ K2S

+ ⟶ K2S

mixed sulfur + potassium ⟶ K2S

Construct the equilibrium constant, K, expression for: S + K ⟶ K2S 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: S + 2 K ⟶ K2S 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 | 1 | -1 K | 2 | -2 K2S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 1 | -1 | ([S])^(-1) K | 2 | -2 | ([K])^(-2) K2S | 1 | 1 | [K2S] 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])^(-1) ([K])^(-2) [K2S] = ([K2S])/([S] ([K])^2)

Construct the rate of reaction expression for: S + K ⟶ K2S 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: S + 2 K ⟶ K2S 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 | 1 | -1 K | 2 | -2 K2S | 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 | 1 | -1 | -(Δ[S])/(Δt) K | 2 | -2 | -1/2 (Δ[K])/(Δt) K2S | 1 | 1 | (Δ[K2S])/(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 = -(Δ[S])/(Δt) = -1/2 (Δ[K])/(Δt) = (Δ[K2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | potassium | K2S formula | S | K | K2S name | mixed sulfur | potassium | IUPAC name | sulfur | potassium |

| mixed sulfur | potassium | K2S molar mass | 32.06 g/mol | 39.0983 g/mol | 110.26 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 64 °C | boiling point | 444.7 °C | 760 °C | density | 2.07 g/cm^3 | 0.86 g/cm^3 | solubility in water | | reacts |