S + C + KNO3 = CO2 + K2SO4 + N2

S mixed sulfur + C activated charcoal + KNO_3 potassium nitrate ⟶ CO_2 carbon dioxide + K_2SO_4 potassium sulfate + N_2 nitrogen

Balance the chemical equation algebraically: S + C + KNO_3 ⟶ CO_2 + K_2SO_4 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 C + c_3 KNO_3 ⟶ c_4 CO_2 + c_5 K_2SO_4 + c_6 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for S, C, K, N and O: S: | c_1 = c_5 C: | c_2 = c_4 K: | c_3 = 2 c_5 N: | c_3 = 2 c_6 O: | 3 c_3 = 2 c_4 + 4 c_5 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 = 1 c_3 = 2 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + C + 2 KNO_3 ⟶ CO_2 + K_2SO_4 + N_2

+ + ⟶ + +

mixed sulfur + activated charcoal + potassium nitrate ⟶ carbon dioxide + potassium sulfate + nitrogen

Construct the equilibrium constant, K, expression for: S + C + KNO_3 ⟶ CO_2 + K_2SO_4 + N_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: S + C + 2 KNO_3 ⟶ CO_2 + K_2SO_4 + N_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 | 1 | -1 C | 1 | -1 KNO_3 | 2 | -2 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 N_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 | 1 | -1 | ([S])^(-1) C | 1 | -1 | ([C])^(-1) KNO_3 | 2 | -2 | ([KNO3])^(-2) CO_2 | 1 | 1 | [CO2] K_2SO_4 | 1 | 1 | [K2SO4] N_2 | 1 | 1 | [N2] 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) ([C])^(-1) ([KNO3])^(-2) [CO2] [K2SO4] [N2] = ([CO2] [K2SO4] [N2])/([S] [C] ([KNO3])^2)

Construct the rate of reaction expression for: S + C + KNO_3 ⟶ CO_2 + K_2SO_4 + N_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: S + C + 2 KNO_3 ⟶ CO_2 + K_2SO_4 + N_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 | 1 | -1 C | 1 | -1 KNO_3 | 2 | -2 CO_2 | 1 | 1 K_2SO_4 | 1 | 1 N_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 | 1 | -1 | -(Δ[S])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) KNO_3 | 2 | -2 | -1/2 (Δ[KNO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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) = -(Δ[C])/(Δt) = -1/2 (Δ[KNO3])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | activated charcoal | potassium nitrate | carbon dioxide | potassium sulfate | nitrogen formula | S | C | KNO_3 | CO_2 | K_2SO_4 | N_2 Hill formula | S | C | KNO_3 | CO_2 | K_2O_4S | N_2 name | mixed sulfur | activated charcoal | potassium nitrate | carbon dioxide | potassium sulfate | nitrogen IUPAC name | sulfur | carbon | potassium nitrate | carbon dioxide | dipotassium sulfate | molecular nitrogen