Input interpretation
![SO_2 sulfur dioxide + C activated charcoal ⟶ CO_2 carbon dioxide + S mixed sulfur](../image_source/9de9ba20ef2e34054f99f71b9921a43f.png)
SO_2 sulfur dioxide + C activated charcoal ⟶ CO_2 carbon dioxide + S mixed sulfur
Balanced equation
![Balance the chemical equation algebraically: SO_2 + C ⟶ CO_2 + S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 C ⟶ c_3 CO_2 + c_4 S Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and C: O: | 2 c_1 = 2 c_3 S: | c_1 = c_4 C: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_2 + C ⟶ CO_2 + S](../image_source/d6e08f10cae3799c0f302e594784f94b.png)
Balance the chemical equation algebraically: SO_2 + C ⟶ CO_2 + S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 C ⟶ c_3 CO_2 + c_4 S Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and C: O: | 2 c_1 = 2 c_3 S: | c_1 = c_4 C: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_2 + C ⟶ CO_2 + S
Structures
![+ ⟶ +](../image_source/4b4af027f546be035b8eefb8bcf72010.png)
+ ⟶ +
Names
![sulfur dioxide + activated charcoal ⟶ carbon dioxide + mixed sulfur](../image_source/255a5e2729233a50274eb1deab5a5f6c.png)
sulfur dioxide + activated charcoal ⟶ carbon dioxide + mixed sulfur
Equilibrium constant
![Construct the equilibrium constant, K, expression for: SO_2 + C ⟶ CO_2 + S 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: SO_2 + C ⟶ CO_2 + S 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 SO_2 | 1 | -1 C | 1 | -1 CO_2 | 1 | 1 S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 1 | -1 | ([SO2])^(-1) C | 1 | -1 | ([C])^(-1) CO_2 | 1 | 1 | [CO2] S | 1 | 1 | [S] 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 = ([SO2])^(-1) ([C])^(-1) [CO2] [S] = ([CO2] [S])/([SO2] [C])](../image_source/4b556e6f8a263707a78eb71b0f7913c3.png)
Construct the equilibrium constant, K, expression for: SO_2 + C ⟶ CO_2 + S 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: SO_2 + C ⟶ CO_2 + S 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 SO_2 | 1 | -1 C | 1 | -1 CO_2 | 1 | 1 S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 1 | -1 | ([SO2])^(-1) C | 1 | -1 | ([C])^(-1) CO_2 | 1 | 1 | [CO2] S | 1 | 1 | [S] 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 = ([SO2])^(-1) ([C])^(-1) [CO2] [S] = ([CO2] [S])/([SO2] [C])
Rate of reaction
![Construct the rate of reaction expression for: SO_2 + C ⟶ CO_2 + S 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: SO_2 + C ⟶ CO_2 + S 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 SO_2 | 1 | -1 C | 1 | -1 CO_2 | 1 | 1 S | 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 SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) S | 1 | 1 | (Δ[S])/(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[SO2])/(Δt) = -(Δ[C])/(Δt) = (Δ[CO2])/(Δt) = (Δ[S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/2f81d54ea34688255085f6538fb95ec1.png)
Construct the rate of reaction expression for: SO_2 + C ⟶ CO_2 + S 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: SO_2 + C ⟶ CO_2 + S 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 SO_2 | 1 | -1 C | 1 | -1 CO_2 | 1 | 1 S | 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 SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) S | 1 | 1 | (Δ[S])/(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[SO2])/(Δt) = -(Δ[C])/(Δt) = (Δ[CO2])/(Δt) = (Δ[S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfur dioxide | activated charcoal | carbon dioxide | mixed sulfur formula | SO_2 | C | CO_2 | S Hill formula | O_2S | C | CO_2 | S name | sulfur dioxide | activated charcoal | carbon dioxide | mixed sulfur IUPAC name | sulfur dioxide | carbon | carbon dioxide | sulfur](../image_source/91f6a2797fcdb983bfd89599dca12a2e.png)
| sulfur dioxide | activated charcoal | carbon dioxide | mixed sulfur formula | SO_2 | C | CO_2 | S Hill formula | O_2S | C | CO_2 | S name | sulfur dioxide | activated charcoal | carbon dioxide | mixed sulfur IUPAC name | sulfur dioxide | carbon | carbon dioxide | sulfur