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SiO2 + Ca3(PO4)2 = P2O5 + CaSiO3

Input interpretation

SiO_2 silicon dioxide + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ P2O5 + CaSiO_3 calcium silicate
SiO_2 silicon dioxide + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ P2O5 + CaSiO_3 calcium silicate

Balanced equation

Balance the chemical equation algebraically: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SiO_2 + c_2 Ca_3(PO_4)_2 ⟶ c_3 P2O5 + c_4 CaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Si, Ca and P: O: | 2 c_1 + 8 c_2 = 5 c_3 + 3 c_4 Si: | c_1 = c_4 Ca: | 3 c_2 = c_4 P: | 2 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 3 CaSiO_3
Balance the chemical equation algebraically: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SiO_2 + c_2 Ca_3(PO_4)_2 ⟶ c_3 P2O5 + c_4 CaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Si, Ca and P: O: | 2 c_1 + 8 c_2 = 5 c_3 + 3 c_4 Si: | c_1 = c_4 Ca: | 3 c_2 = c_4 P: | 2 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 3 CaSiO_3

Structures

+ ⟶ P2O5 +
+ ⟶ P2O5 +

Names

silicon dioxide + tricalcium diphosphate ⟶ P2O5 + calcium silicate
silicon dioxide + tricalcium diphosphate ⟶ P2O5 + calcium silicate

Equilibrium constant

Construct the equilibrium constant, K, expression for: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 P2O5 | 1 | 1 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 SiO_2 | 3 | -3 | ([SiO2])^(-3) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) P2O5 | 1 | 1 | [P2O5] 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 = ([SiO2])^(-3) ([Ca3(PO4)2])^(-1) [P2O5] ([CaSiO3])^3 = ([P2O5] ([CaSiO3])^3)/(([SiO2])^3 [Ca3(PO4)2])
Construct the equilibrium constant, K, expression for: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 P2O5 | 1 | 1 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 SiO_2 | 3 | -3 | ([SiO2])^(-3) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) P2O5 | 1 | 1 | [P2O5] 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 = ([SiO2])^(-3) ([Ca3(PO4)2])^(-1) [P2O5] ([CaSiO3])^3 = ([P2O5] ([CaSiO3])^3)/(([SiO2])^3 [Ca3(PO4)2])

Rate of reaction

Construct the rate of reaction expression for: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 P2O5 | 1 | 1 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 SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) P2O5 | 1 | 1 | (Δ[P2O5])/(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 = -1/3 (Δ[SiO2])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = (Δ[P2O5])/(Δt) = 1/3 (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 + Ca_3(PO_4)_2 ⟶ P2O5 + 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 SiO_2 | 3 | -3 Ca_3(PO_4)_2 | 1 | -1 P2O5 | 1 | 1 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 SiO_2 | 3 | -3 | -1/3 (Δ[SiO2])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) P2O5 | 1 | 1 | (Δ[P2O5])/(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 = -1/3 (Δ[SiO2])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = (Δ[P2O5])/(Δt) = 1/3 (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| silicon dioxide | tricalcium diphosphate | P2O5 | calcium silicate formula | SiO_2 | Ca_3(PO_4)_2 | P2O5 | CaSiO_3 Hill formula | O_2Si | Ca_3O_8P_2 | O5P2 | CaO_3Si name | silicon dioxide | tricalcium diphosphate | | calcium silicate IUPAC name | dioxosilane | tricalcium diphosphate | | calcium dioxido-oxosilane
| silicon dioxide | tricalcium diphosphate | P2O5 | calcium silicate formula | SiO_2 | Ca_3(PO_4)_2 | P2O5 | CaSiO_3 Hill formula | O_2Si | Ca_3O_8P_2 | O5P2 | CaO_3Si name | silicon dioxide | tricalcium diphosphate | | calcium silicate IUPAC name | dioxosilane | tricalcium diphosphate | | calcium dioxido-oxosilane

Substance properties

| silicon dioxide | tricalcium diphosphate | P2O5 | calcium silicate molar mass | 60.083 g/mol | 310.17 g/mol | 141.94 g/mol | 116.16 g/mol phase | solid (at STP) | | | melting point | 1713 °C | | | boiling point | 2950 °C | | | density | 2.196 g/cm^3 | 3.14 g/cm^3 | | solubility in water | insoluble | | | odor | odorless | | |
| silicon dioxide | tricalcium diphosphate | P2O5 | calcium silicate molar mass | 60.083 g/mol | 310.17 g/mol | 141.94 g/mol | 116.16 g/mol phase | solid (at STP) | | | melting point | 1713 °C | | | boiling point | 2950 °C | | | density | 2.196 g/cm^3 | 3.14 g/cm^3 | | solubility in water | insoluble | | | odor | odorless | | |

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