S + C + KNO3 = CO2 + SO2 + KNO2

S mixed sulfur + C activated charcoal + KNO_3 potassium nitrate ⟶ CO_2 carbon dioxide + SO_2 sulfur dioxide + KNO_2 potassium nitrite

Balance the chemical equation algebraically: S + C + KNO_3 ⟶ CO_2 + SO_2 + KNO_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 SO_2 + c_6 KNO_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 = c_6 N: | c_3 = c_6 O: | 3 c_3 = 2 c_4 + 2 c_5 + 2 c_6 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_3 = 2 c_2 + 2 c_4 = c_2 c_5 = 1 c_6 = 2 c_2 + 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + C + 4 KNO_3 ⟶ CO_2 + SO_2 + 4 KNO_2

+ + ⟶ + +

mixed sulfur + activated charcoal + potassium nitrate ⟶ carbon dioxide + sulfur dioxide + potassium nitrite

Construct the equilibrium constant, K, expression for: S + C + KNO_3 ⟶ CO_2 + SO_2 + KNO_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 + 4 KNO_3 ⟶ CO_2 + SO_2 + 4 KNO_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 | 4 | -4 CO_2 | 1 | 1 SO_2 | 1 | 1 KNO_2 | 4 | 4 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 | 4 | -4 | ([KNO3])^(-4) CO_2 | 1 | 1 | [CO2] SO_2 | 1 | 1 | [SO2] KNO_2 | 4 | 4 | ([KNO2])^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 = ([S])^(-1) ([C])^(-1) ([KNO3])^(-4) [CO2] [SO2] ([KNO2])^4 = ([CO2] [SO2] ([KNO2])^4)/([S] [C] ([KNO3])^4)

Construct the rate of reaction expression for: S + C + KNO_3 ⟶ CO_2 + SO_2 + KNO_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 + 4 KNO_3 ⟶ CO_2 + SO_2 + 4 KNO_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 | 4 | -4 CO_2 | 1 | 1 SO_2 | 1 | 1 KNO_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 S | 1 | -1 | -(Δ[S])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) KNO_3 | 4 | -4 | -1/4 (Δ[KNO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) KNO_2 | 4 | 4 | 1/4 (Δ[KNO2])/(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) = -1/4 (Δ[KNO3])/(Δt) = (Δ[CO2])/(Δt) = (Δ[SO2])/(Δt) = 1/4 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | activated charcoal | potassium nitrate | carbon dioxide | sulfur dioxide | potassium nitrite formula | S | C | KNO_3 | CO_2 | SO_2 | KNO_2 Hill formula | S | C | KNO_3 | CO_2 | O_2S | KNO_2 name | mixed sulfur | activated charcoal | potassium nitrate | carbon dioxide | sulfur dioxide | potassium nitrite IUPAC name | sulfur | carbon | potassium nitrate | carbon dioxide | sulfur dioxide | potassium nitrite