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H3PO4 + CaCO3 = Ca3(PO4)2 + H2CO3

Input interpretation

H_3PO_4 phosphoric acid + CaCO_3 calcium carbonate ⟶ Ca_3(PO_4)_2 tricalcium diphosphate + H_2CO_3 carbonic acid
H_3PO_4 phosphoric acid + CaCO_3 calcium carbonate ⟶ Ca_3(PO_4)_2 tricalcium diphosphate + H_2CO_3 carbonic acid

Balanced equation

Balance the chemical equation algebraically: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 CaCO_3 ⟶ c_3 Ca_3(PO_4)_2 + c_4 H_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P, C and Ca: H: | 3 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = 8 c_3 + 3 c_4 P: | c_1 = 2 c_3 C: | c_2 = c_4 Ca: | c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_3
Balance the chemical equation algebraically: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 CaCO_3 ⟶ c_3 Ca_3(PO_4)_2 + c_4 H_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P, C and Ca: H: | 3 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = 8 c_3 + 3 c_4 P: | c_1 = 2 c_3 C: | c_2 = c_4 Ca: | c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_3

Structures

+ ⟶ +
+ ⟶ +

Names

phosphoric acid + calcium carbonate ⟶ tricalcium diphosphate + carbonic acid
phosphoric acid + calcium carbonate ⟶ tricalcium diphosphate + carbonic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_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: 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_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 H_3PO_4 | 2 | -2 CaCO_3 | 3 | -3 Ca_3(PO_4)_2 | 1 | 1 H_2CO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) CaCO_3 | 3 | -3 | ([CaCO3])^(-3) Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] H_2CO_3 | 3 | 3 | ([H2CO3])^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 = ([H3PO4])^(-2) ([CaCO3])^(-3) [Ca3(PO4)2] ([H2CO3])^3 = ([Ca3(PO4)2] ([H2CO3])^3)/(([H3PO4])^2 ([CaCO3])^3)
Construct the equilibrium constant, K, expression for: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_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: 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_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 H_3PO_4 | 2 | -2 CaCO_3 | 3 | -3 Ca_3(PO_4)_2 | 1 | 1 H_2CO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) CaCO_3 | 3 | -3 | ([CaCO3])^(-3) Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] H_2CO_3 | 3 | 3 | ([H2CO3])^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 = ([H3PO4])^(-2) ([CaCO3])^(-3) [Ca3(PO4)2] ([H2CO3])^3 = ([Ca3(PO4)2] ([H2CO3])^3)/(([H3PO4])^2 ([CaCO3])^3)

Rate of reaction

Construct the rate of reaction expression for: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_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: 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_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 H_3PO_4 | 2 | -2 CaCO_3 | 3 | -3 Ca_3(PO_4)_2 | 1 | 1 H_2CO_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 H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) CaCO_3 | 3 | -3 | -1/3 (Δ[CaCO3])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(Δt) H_2CO_3 | 3 | 3 | 1/3 (Δ[H2CO3])/(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 = -1/2 (Δ[H3PO4])/(Δt) = -1/3 (Δ[CaCO3])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) = 1/3 (Δ[H2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_3PO_4 + CaCO_3 ⟶ Ca_3(PO_4)_2 + H_2CO_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: 2 H_3PO_4 + 3 CaCO_3 ⟶ Ca_3(PO_4)_2 + 3 H_2CO_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 H_3PO_4 | 2 | -2 CaCO_3 | 3 | -3 Ca_3(PO_4)_2 | 1 | 1 H_2CO_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 H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) CaCO_3 | 3 | -3 | -1/3 (Δ[CaCO3])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(Δt) H_2CO_3 | 3 | 3 | 1/3 (Δ[H2CO3])/(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 = -1/2 (Δ[H3PO4])/(Δt) = -1/3 (Δ[CaCO3])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) = 1/3 (Δ[H2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid formula | H_3PO_4 | CaCO_3 | Ca_3(PO_4)_2 | H_2CO_3 Hill formula | H_3O_4P | CCaO_3 | Ca_3O_8P_2 | CH_2O_3 name | phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid
| phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid formula | H_3PO_4 | CaCO_3 | Ca_3(PO_4)_2 | H_2CO_3 Hill formula | H_3O_4P | CCaO_3 | Ca_3O_8P_2 | CH_2O_3 name | phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid

Substance properties

| phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid molar mass | 97.994 g/mol | 100.09 g/mol | 310.17 g/mol | 62.024 g/mol phase | liquid (at STP) | solid (at STP) | | melting point | 42.4 °C | 1340 °C | | boiling point | 158 °C | | | density | 1.685 g/cm^3 | 2.71 g/cm^3 | 3.14 g/cm^3 | solubility in water | very soluble | insoluble | | odor | odorless | | |
| phosphoric acid | calcium carbonate | tricalcium diphosphate | carbonic acid molar mass | 97.994 g/mol | 100.09 g/mol | 310.17 g/mol | 62.024 g/mol phase | liquid (at STP) | solid (at STP) | | melting point | 42.4 °C | 1340 °C | | boiling point | 158 °C | | | density | 1.685 g/cm^3 | 2.71 g/cm^3 | 3.14 g/cm^3 | solubility in water | very soluble | insoluble | | odor | odorless | | |

Units

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