Input interpretation
C activated charcoal + SiO_2 silicon dioxide + CaSO_4 calcium sulfate ⟶ S mixed sulfur + CO carbon monoxide + CaSiO_3 calcium silicate
Balanced equation
Balance the chemical equation algebraically: C + SiO_2 + CaSO_4 ⟶ S + CO + CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 SiO_2 + c_3 CaSO_4 ⟶ c_4 S + c_5 CO + c_6 CaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O, Si, Ca and S: C: | c_1 = c_5 O: | 2 c_2 + 4 c_3 = c_5 + 3 c_6 Si: | c_2 = c_6 Ca: | c_3 = c_6 S: | c_3 = c_4 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 = 3 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + SiO_2 + CaSO_4 ⟶ S + 3 CO + CaSiO_3
Structures
+ + ⟶ + +
Names
activated charcoal + silicon dioxide + calcium sulfate ⟶ mixed sulfur + carbon monoxide + calcium silicate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: C + SiO_2 + CaSO_4 ⟶ S + CO + CaSiO_3 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: 3 C + SiO_2 + CaSO_4 ⟶ S + 3 CO + CaSiO_3 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 C | 3 | -3 SiO_2 | 1 | -1 CaSO_4 | 1 | -1 S | 1 | 1 CO | 3 | 3 CaSiO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) SiO_2 | 1 | -1 | ([SiO2])^(-1) CaSO_4 | 1 | -1 | ([CaSO4])^(-1) S | 1 | 1 | [S] CO | 3 | 3 | ([CO])^3 CaSiO_3 | 1 | 1 | [CaSiO3] 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 = ([C])^(-3) ([SiO2])^(-1) ([CaSO4])^(-1) [S] ([CO])^3 [CaSiO3] = ([S] ([CO])^3 [CaSiO3])/(([C])^3 [SiO2] [CaSO4])](../image_source/7e9adbbd39bdf1b194bdeeda64f46046.png)
Construct the equilibrium constant, K, expression for: C + SiO_2 + CaSO_4 ⟶ S + CO + CaSiO_3 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: 3 C + SiO_2 + CaSO_4 ⟶ S + 3 CO + CaSiO_3 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 C | 3 | -3 SiO_2 | 1 | -1 CaSO_4 | 1 | -1 S | 1 | 1 CO | 3 | 3 CaSiO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) SiO_2 | 1 | -1 | ([SiO2])^(-1) CaSO_4 | 1 | -1 | ([CaSO4])^(-1) S | 1 | 1 | [S] CO | 3 | 3 | ([CO])^3 CaSiO_3 | 1 | 1 | [CaSiO3] 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 = ([C])^(-3) ([SiO2])^(-1) ([CaSO4])^(-1) [S] ([CO])^3 [CaSiO3] = ([S] ([CO])^3 [CaSiO3])/(([C])^3 [SiO2] [CaSO4])
Rate of reaction
![Construct the rate of reaction expression for: C + SiO_2 + CaSO_4 ⟶ S + CO + CaSiO_3 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: 3 C + SiO_2 + CaSO_4 ⟶ S + 3 CO + CaSiO_3 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 C | 3 | -3 SiO_2 | 1 | -1 CaSO_4 | 1 | -1 S | 1 | 1 CO | 3 | 3 CaSiO_3 | 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 C | 3 | -3 | -1/3 (Δ[C])/(Δt) SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) CaSiO_3 | 1 | 1 | (Δ[CaSiO3])/(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 = -1/3 (Δ[C])/(Δt) = -(Δ[SiO2])/(Δt) = -(Δ[CaSO4])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[CO])/(Δt) = (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/71e88ac6a1cbd80ec60d2984eab93e8c.png)
Construct the rate of reaction expression for: C + SiO_2 + CaSO_4 ⟶ S + CO + CaSiO_3 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: 3 C + SiO_2 + CaSO_4 ⟶ S + 3 CO + CaSiO_3 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 C | 3 | -3 SiO_2 | 1 | -1 CaSO_4 | 1 | -1 S | 1 | 1 CO | 3 | 3 CaSiO_3 | 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 C | 3 | -3 | -1/3 (Δ[C])/(Δt) SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) CaSiO_3 | 1 | 1 | (Δ[CaSiO3])/(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 = -1/3 (Δ[C])/(Δt) = -(Δ[SiO2])/(Δt) = -(Δ[CaSO4])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[CO])/(Δt) = (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| activated charcoal | silicon dioxide | calcium sulfate | mixed sulfur | carbon monoxide | calcium silicate formula | C | SiO_2 | CaSO_4 | S | CO | CaSiO_3 Hill formula | C | O_2Si | CaO_4S | S | CO | CaO_3Si name | activated charcoal | silicon dioxide | calcium sulfate | mixed sulfur | carbon monoxide | calcium silicate IUPAC name | carbon | dioxosilane | calcium sulfate | sulfur | carbon monoxide | calcium dioxido-oxosilane