Input interpretation
C (activated charcoal) + SiO_2 (silicon dioxide) + Ca_3(PO_4)_2 (tricalcium diphosphate) ⟶ CO (carbon monoxide) + P (red phosphorus) + CaSiO_3 (calcium silicate)
Balanced equation
Balance the chemical equation algebraically: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO + P + CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 SiO_2 + c_3 Ca_3(PO_4)_2 ⟶ c_4 CO + c_5 P + 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 P: C: | c_1 = c_4 O: | 2 c_2 + 8 c_3 = c_4 + 3 c_6 Si: | c_2 = c_6 Ca: | 3 c_3 = c_6 P: | 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3 c_3 = 1 c_4 = 5 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + 3 SiO_2 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaSiO_3
Names
activated charcoal + silicon dioxide + tricalcium diphosphate ⟶ carbon monoxide + red phosphorus + calcium silicate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO + P + 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: 5 C + 3 SiO_2 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 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 | 5 | -5 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaSiO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 5 | -5 | ([C])^(-5) SiO_2 | 3 | -3 | ([SiO2])^(-3) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) CO | 5 | 5 | ([CO])^5 P | 2 | 2 | ([P])^2 CaSiO_3 | 3 | 3 | ([CaSiO3])^3 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])^(-5) ([SiO2])^(-3) ([Ca3(PO4)2])^(-1) ([CO])^5 ([P])^2 ([CaSiO3])^3 = (([CO])^5 ([P])^2 ([CaSiO3])^3)/(([C])^5 ([SiO2])^3 [Ca3(PO4)2])](../image_source/2b4a22b4e25ae8d9f3321d2b4523c970.png)
Construct the equilibrium constant, K, expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO + P + 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: 5 C + 3 SiO_2 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 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 | 5 | -5 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaSiO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 5 | -5 | ([C])^(-5) SiO_2 | 3 | -3 | ([SiO2])^(-3) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) CO | 5 | 5 | ([CO])^5 P | 2 | 2 | ([P])^2 CaSiO_3 | 3 | 3 | ([CaSiO3])^3 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])^(-5) ([SiO2])^(-3) ([Ca3(PO4)2])^(-1) ([CO])^5 ([P])^2 ([CaSiO3])^3 = (([CO])^5 ([P])^2 ([CaSiO3])^3)/(([C])^5 ([SiO2])^3 [Ca3(PO4)2])
Rate of reaction
![Construct the rate of reaction expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO + P + 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: 5 C + 3 SiO_2 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 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 | 5 | -5 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaSiO_3 | 3 | 3 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 | 5 | -5 | -1/5 (Δ[C])/(Δt) SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) CO | 5 | 5 | 1/5 (Δ[CO])/(Δt) P | 2 | 2 | 1/2 (Δ[P])/(Δt) CaSiO_3 | 3 | 3 | 1/3 (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 = -1/5 (Δ[C])/(Δt) = -1/3 (Δ[SiO2])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO])/(Δt) = 1/2 (Δ[P])/(Δt) = 1/3 (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/8ea3d59af20f2255a115f0cbb7114d82.png)
Construct the rate of reaction expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO + P + 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: 5 C + 3 SiO_2 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 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 | 5 | -5 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaSiO_3 | 3 | 3 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 | 5 | -5 | -1/5 (Δ[C])/(Δt) SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) CO | 5 | 5 | 1/5 (Δ[CO])/(Δt) P | 2 | 2 | 1/2 (Δ[P])/(Δt) CaSiO_3 | 3 | 3 | 1/3 (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 = -1/5 (Δ[C])/(Δt) = -1/3 (Δ[SiO2])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO])/(Δt) = 1/2 (Δ[P])/(Δt) = 1/3 (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| activated charcoal | silicon dioxide | tricalcium diphosphate | carbon monoxide | red phosphorus | calcium silicate formula | C | SiO_2 | Ca_3(PO_4)_2 | CO | P | CaSiO_3 Hill formula | C | O_2Si | Ca_3O_8P_2 | CO | P | CaO_3Si name | activated charcoal | silicon dioxide | tricalcium diphosphate | carbon monoxide | red phosphorus | calcium silicate IUPAC name | carbon | dioxosilane | tricalcium diphosphate | carbon monoxide | phosphorus | calcium dioxido-oxosilane