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C + SiO2 + Ca3(PO4)2 = CO2 + P + CaSiO3

Input interpretation

C activated charcoal + SiO_2 silicon dioxide + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ CO_2 carbon dioxide + P red phosphorus + CaSiO_3 calcium silicate
C activated charcoal + SiO_2 silicon dioxide + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ CO_2 carbon dioxide + P red phosphorus + CaSiO_3 calcium silicate

Balanced equation

Balance the chemical equation algebraically: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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_2 + 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 = 2 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 = 5/2 c_2 = 3 c_3 = 1 c_4 = 5/2 c_5 = 2 c_6 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 6 c_3 = 2 c_4 = 5 c_5 = 4 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 CaSiO_3
Balance the chemical equation algebraically: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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_2 + 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 = 2 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 = 5/2 c_2 = 3 c_3 = 1 c_4 = 5/2 c_5 = 2 c_6 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 6 c_3 = 2 c_4 = 5 c_5 = 4 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 CaSiO_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

activated charcoal + silicon dioxide + tricalcium diphosphate ⟶ carbon dioxide + red phosphorus + calcium silicate
activated charcoal + silicon dioxide + tricalcium diphosphate ⟶ carbon dioxide + red phosphorus + calcium silicate

Equilibrium constant

Construct the equilibrium constant, K, expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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 + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 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 | 6 | -6 Ca_3(PO_4)_2 | 2 | -2 CO_2 | 5 | 5 P | 4 | 4 CaSiO_3 | 6 | 6 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 | 6 | -6 | ([SiO2])^(-6) Ca_3(PO_4)_2 | 2 | -2 | ([Ca3(PO4)2])^(-2) CO_2 | 5 | 5 | ([CO2])^5 P | 4 | 4 | ([P])^4 CaSiO_3 | 6 | 6 | ([CaSiO3])^6 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])^(-6) ([Ca3(PO4)2])^(-2) ([CO2])^5 ([P])^4 ([CaSiO3])^6 = (([CO2])^5 ([P])^4 ([CaSiO3])^6)/(([C])^5 ([SiO2])^6 ([Ca3(PO4)2])^2)
Construct the equilibrium constant, K, expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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 + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 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 | 6 | -6 Ca_3(PO_4)_2 | 2 | -2 CO_2 | 5 | 5 P | 4 | 4 CaSiO_3 | 6 | 6 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 | 6 | -6 | ([SiO2])^(-6) Ca_3(PO_4)_2 | 2 | -2 | ([Ca3(PO4)2])^(-2) CO_2 | 5 | 5 | ([CO2])^5 P | 4 | 4 | ([P])^4 CaSiO_3 | 6 | 6 | ([CaSiO3])^6 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])^(-6) ([Ca3(PO4)2])^(-2) ([CO2])^5 ([P])^4 ([CaSiO3])^6 = (([CO2])^5 ([P])^4 ([CaSiO3])^6)/(([C])^5 ([SiO2])^6 ([Ca3(PO4)2])^2)

Rate of reaction

Construct the rate of reaction expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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 + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 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 | 6 | -6 Ca_3(PO_4)_2 | 2 | -2 CO_2 | 5 | 5 P | 4 | 4 CaSiO_3 | 6 | 6 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 | 6 | -6 | -1/6 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 2 | -2 | -1/2 (Δ[Ca3(PO4)2])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) P | 4 | 4 | 1/4 (Δ[P])/(Δt) CaSiO_3 | 6 | 6 | 1/6 (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) = -1/6 (Δ[SiO2])/(Δt) = -1/2 (Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/4 (Δ[P])/(Δt) = 1/6 (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: C + SiO_2 + Ca_3(PO_4)_2 ⟶ CO_2 + 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 + 6 SiO_2 + 2 Ca_3(PO_4)_2 ⟶ 5 CO_2 + 4 P + 6 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 | 6 | -6 Ca_3(PO_4)_2 | 2 | -2 CO_2 | 5 | 5 P | 4 | 4 CaSiO_3 | 6 | 6 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 | 6 | -6 | -1/6 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 2 | -2 | -1/2 (Δ[Ca3(PO4)2])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) P | 4 | 4 | 1/4 (Δ[P])/(Δt) CaSiO_3 | 6 | 6 | 1/6 (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) = -1/6 (Δ[SiO2])/(Δt) = -1/2 (Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/4 (Δ[P])/(Δt) = 1/6 (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 dioxide | red phosphorus | calcium silicate formula | C | SiO_2 | Ca_3(PO_4)_2 | CO_2 | P | CaSiO_3 Hill formula | C | O_2Si | Ca_3O_8P_2 | CO_2 | P | CaO_3Si name | activated charcoal | silicon dioxide | tricalcium diphosphate | carbon dioxide | red phosphorus | calcium silicate IUPAC name | carbon | dioxosilane | tricalcium diphosphate | carbon dioxide | phosphorus | calcium dioxido-oxosilane
| activated charcoal | silicon dioxide | tricalcium diphosphate | carbon dioxide | red phosphorus | calcium silicate formula | C | SiO_2 | Ca_3(PO_4)_2 | CO_2 | P | CaSiO_3 Hill formula | C | O_2Si | Ca_3O_8P_2 | CO_2 | P | CaO_3Si name | activated charcoal | silicon dioxide | tricalcium diphosphate | carbon dioxide | red phosphorus | calcium silicate IUPAC name | carbon | dioxosilane | tricalcium diphosphate | carbon dioxide | phosphorus | calcium dioxido-oxosilane

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