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H3PO4 + Ca3(PO4)2 = Ca(H2PO4)2

Input interpretation

H_3PO_4 phosphoric acid + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ Ca(H_2PO_4)_2·H_2O calcium dihydrogen phosphate monohydrate
H_3PO_4 phosphoric acid + Ca_3(PO_4)_2 tricalcium diphosphate ⟶ Ca(H_2PO_4)_2·H_2O calcium dihydrogen phosphate monohydrate

Balanced equation

Balance the chemical equation algebraically: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Ca_3(PO_4)_2 ⟶ c_3 Ca(H_2PO_4)_2·H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Ca: H: | 3 c_1 = 4 c_3 O: | 4 c_1 + 8 c_2 = 8 c_3 P: | c_1 + 2 c_2 = 2 c_3 Ca: | 3 c_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 = 4 c_2 = 1 c_3 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O
Balance the chemical equation algebraically: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Ca_3(PO_4)_2 ⟶ c_3 Ca(H_2PO_4)_2·H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Ca: H: | 3 c_1 = 4 c_3 O: | 4 c_1 + 8 c_2 = 8 c_3 P: | c_1 + 2 c_2 = 2 c_3 Ca: | 3 c_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 = 4 c_2 = 1 c_3 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O

Structures

+ ⟶
+ ⟶

Names

phosphoric acid + tricalcium diphosphate ⟶ calcium dihydrogen phosphate monohydrate
phosphoric acid + tricalcium diphosphate ⟶ calcium dihydrogen phosphate monohydrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O 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: 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O 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 | 4 | -4 Ca_3(PO_4)_2 | 1 | -1 Ca(H_2PO_4)_2·H_2O | 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 | 4 | -4 | ([H3PO4])^(-4) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) Ca(H_2PO_4)_2·H_2O | 3 | 3 | ([Ca(H2PO4)2·H2O])^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])^(-4) ([Ca3(PO4)2])^(-1) ([Ca(H2PO4)2·H2O])^3 = ([Ca(H2PO4)2·H2O])^3/(([H3PO4])^4 [Ca3(PO4)2])
Construct the equilibrium constant, K, expression for: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O 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: 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O 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 | 4 | -4 Ca_3(PO_4)_2 | 1 | -1 Ca(H_2PO_4)_2·H_2O | 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 | 4 | -4 | ([H3PO4])^(-4) Ca_3(PO_4)_2 | 1 | -1 | ([Ca3(PO4)2])^(-1) Ca(H_2PO_4)_2·H_2O | 3 | 3 | ([Ca(H2PO4)2·H2O])^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])^(-4) ([Ca3(PO4)2])^(-1) ([Ca(H2PO4)2·H2O])^3 = ([Ca(H2PO4)2·H2O])^3/(([H3PO4])^4 [Ca3(PO4)2])

Rate of reaction

Construct the rate of reaction expression for: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O 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: 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O 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 | 4 | -4 Ca_3(PO_4)_2 | 1 | -1 Ca(H_2PO_4)_2·H_2O | 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 | 4 | -4 | -1/4 (Δ[H3PO4])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) Ca(H_2PO_4)_2·H_2O | 3 | 3 | 1/3 (Δ[Ca(H2PO4)2·H2O])/(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 = -1/4 (Δ[H3PO4])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = 1/3 (Δ[Ca(H2PO4)2·H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_3PO_4 + Ca_3(PO_4)_2 ⟶ Ca(H_2PO_4)_2·H_2O 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: 4 H_3PO_4 + Ca_3(PO_4)_2 ⟶ 3 Ca(H_2PO_4)_2·H_2O 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 | 4 | -4 Ca_3(PO_4)_2 | 1 | -1 Ca(H_2PO_4)_2·H_2O | 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 | 4 | -4 | -1/4 (Δ[H3PO4])/(Δt) Ca_3(PO_4)_2 | 1 | -1 | -(Δ[Ca3(PO4)2])/(Δt) Ca(H_2PO_4)_2·H_2O | 3 | 3 | 1/3 (Δ[Ca(H2PO4)2·H2O])/(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 = -1/4 (Δ[H3PO4])/(Δt) = -(Δ[Ca3(PO4)2])/(Δt) = 1/3 (Δ[Ca(H2PO4)2·H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate formula | H_3PO_4 | Ca_3(PO_4)_2 | Ca(H_2PO_4)_2·H_2O Hill formula | H_3O_4P | Ca_3O_8P_2 | CaH_4O_8P_2 name | phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate IUPAC name | phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate
| phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate formula | H_3PO_4 | Ca_3(PO_4)_2 | Ca(H_2PO_4)_2·H_2O Hill formula | H_3O_4P | Ca_3O_8P_2 | CaH_4O_8P_2 name | phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate IUPAC name | phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate

Substance properties

| phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate molar mass | 97.994 g/mol | 310.17 g/mol | 234.05 g/mol phase | liquid (at STP) | | melting point | 42.4 °C | | boiling point | 158 °C | | density | 1.685 g/cm^3 | 3.14 g/cm^3 | 2.22 g/cm^3 solubility in water | very soluble | | soluble odor | odorless | |
| phosphoric acid | tricalcium diphosphate | calcium dihydrogen phosphate monohydrate molar mass | 97.994 g/mol | 310.17 g/mol | 234.05 g/mol phase | liquid (at STP) | | melting point | 42.4 °C | | boiling point | 158 °C | | density | 1.685 g/cm^3 | 3.14 g/cm^3 | 2.22 g/cm^3 solubility in water | very soluble | | soluble odor | odorless | |

Units

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