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C + Ca3(PO4)2 = CO + P + CaO

Input interpretation

C activated charcoal + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ CO carbon monoxide + P red phosphorus + CaO lime
C activated charcoal + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ CO carbon monoxide + P red phosphorus + CaO lime

Balanced equation

Balance the chemical equation algebraically: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Ca_3(PO_4)_2 ⟶ c_3 CO + c_4 P + c_5 CaO Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and P: C: | c_1 = c_3 Ca: | 3 c_2 = c_5 O: | 8 c_2 = c_3 + c_5 P: | 2 c_2 = 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 = 5 c_2 = 1 c_3 = 5 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO
Balance the chemical equation algebraically: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Ca_3(PO_4)_2 ⟶ c_3 CO + c_4 P + c_5 CaO Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and P: C: | c_1 = c_3 Ca: | 3 c_2 = c_5 O: | 8 c_2 = c_3 + c_5 P: | 2 c_2 = 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 = 5 c_2 = 1 c_3 = 5 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 C + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO

Structures

+ ⟶ + +
+ ⟶ + +

Names

activated charcoal + tricalcium diphosphate ⟶ carbon monoxide + red phosphorus + lime
activated charcoal + tricalcium diphosphate ⟶ carbon monoxide + red phosphorus + lime

Equilibrium constant

Construct the equilibrium constant, K, expression for: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO 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 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO 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 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaO | 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) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) CO | 5 | 5 | ([CO])^5 P | 2 | 2 | ([P])^2 CaO | 3 | 3 | ([CaO])^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) ([Ca3(PO4)2])^(-1) ([CO])^5 ([P])^2 ([CaO])^3 = (([CO])^5 ([P])^2 ([CaO])^3)/(([C])^5 [Ca3(PO4)2])
Construct the equilibrium constant, K, expression for: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO 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 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO 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 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaO | 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) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) CO | 5 | 5 | ([CO])^5 P | 2 | 2 | ([P])^2 CaO | 3 | 3 | ([CaO])^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) ([Ca3(PO4)2])^(-1) ([CO])^5 ([P])^2 ([CaO])^3 = (([CO])^5 ([P])^2 ([CaO])^3)/(([C])^5 [Ca3(PO4)2])

Rate of reaction

Construct the rate of reaction expression for: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO 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 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO 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 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaO | 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) 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) CaO | 3 | 3 | 1/3 (Δ[CaO])/(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) = -(Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO])/(Δt) = 1/2 (Δ[P])/(Δt) = 1/3 (Δ[CaO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: C + Ca_3(PO_4)_2 ⟶ CO + P + CaO 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 + Ca_3(PO_4)_2 ⟶ 5 CO + 2 P + 3 CaO 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 Ca_3(PO_4)_2 | 1 | -1 CO | 5 | 5 P | 2 | 2 CaO | 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) 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) CaO | 3 | 3 | 1/3 (Δ[CaO])/(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) = -(Δ[Ca3(PO4)2])/(Δt) = 1/5 (Δ[CO])/(Δt) = 1/2 (Δ[P])/(Δt) = 1/3 (Δ[CaO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime formula | C | Ca_3(PO_4)_2 | CO | P | CaO Hill formula | C | Ca_3O_8P_2 | CO | P | CaO name | activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime IUPAC name | carbon | tricalcium diphosphate | carbon monoxide | phosphorus |
| activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime formula | C | Ca_3(PO_4)_2 | CO | P | CaO Hill formula | C | Ca_3O_8P_2 | CO | P | CaO name | activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime IUPAC name | carbon | tricalcium diphosphate | carbon monoxide | phosphorus |

Substance properties

| activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime molar mass | 12.011 g/mol | 310.17 g/mol | 28.01 g/mol | 30.973761998 g/mol | 56.077 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) | solid (at STP) melting point | 3550 °C | | -205 °C | 579.2 °C | 2580 °C boiling point | 4027 °C | | -191.5 °C | | 2850 °C density | 2.26 g/cm^3 | 3.14 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 2.16 g/cm^3 | 3.3 g/cm^3 solubility in water | insoluble | | | insoluble | reacts dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | odor | | | odorless | |
| activated charcoal | tricalcium diphosphate | carbon monoxide | red phosphorus | lime molar mass | 12.011 g/mol | 310.17 g/mol | 28.01 g/mol | 30.973761998 g/mol | 56.077 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) | solid (at STP) melting point | 3550 °C | | -205 °C | 579.2 °C | 2580 °C boiling point | 4027 °C | | -191.5 °C | | 2850 °C density | 2.26 g/cm^3 | 3.14 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 2.16 g/cm^3 | 3.3 g/cm^3 solubility in water | insoluble | | | insoluble | reacts dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | odor | | | odorless | |

Units

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