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CaCl2 + K3PO4 = KCl + Ca3(PO4)2

Input interpretation

CaCl_2 calcium chloride + K3PO4 ⟶ KCl potassium chloride + Ca_3(PO_4)_2 tricalcium diphosphate
CaCl_2 calcium chloride + K3PO4 ⟶ KCl potassium chloride + Ca_3(PO_4)_2 tricalcium diphosphate

Balanced equation

Balance the chemical equation algebraically: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 K3PO4 ⟶ c_3 KCl + c_4 Ca_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, K, P and O: Ca: | c_1 = 3 c_4 Cl: | 2 c_1 = c_3 K: | 3 c_2 = c_3 P: | c_2 = 2 c_4 O: | 4 c_2 = 8 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2
Balance the chemical equation algebraically: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 K3PO4 ⟶ c_3 KCl + c_4 Ca_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, K, P and O: Ca: | c_1 = 3 c_4 Cl: | 2 c_1 = c_3 K: | 3 c_2 = c_3 P: | c_2 = 2 c_4 O: | 4 c_2 = 8 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2

Structures

+ K3PO4 ⟶ +
+ K3PO4 ⟶ +

Names

calcium chloride + K3PO4 ⟶ potassium chloride + tricalcium diphosphate
calcium chloride + K3PO4 ⟶ potassium chloride + tricalcium diphosphate

Equilibrium constant

Construct the equilibrium constant, K, expression for: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 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 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2 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 CaCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCl_2 | 3 | -3 | ([CaCl2])^(-3) K3PO4 | 2 | -2 | ([K3PO4])^(-2) KCl | 6 | 6 | ([KCl])^6 Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] 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 = ([CaCl2])^(-3) ([K3PO4])^(-2) ([KCl])^6 [Ca3(PO4)2] = (([KCl])^6 [Ca3(PO4)2])/(([CaCl2])^3 ([K3PO4])^2)
Construct the equilibrium constant, K, expression for: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 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 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2 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 CaCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaCl_2 | 3 | -3 | ([CaCl2])^(-3) K3PO4 | 2 | -2 | ([K3PO4])^(-2) KCl | 6 | 6 | ([KCl])^6 Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] 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 = ([CaCl2])^(-3) ([K3PO4])^(-2) ([KCl])^6 [Ca3(PO4)2] = (([KCl])^6 [Ca3(PO4)2])/(([CaCl2])^3 ([K3PO4])^2)

Rate of reaction

Construct the rate of reaction expression for: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 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 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2 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 CaCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 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 CaCl_2 | 3 | -3 | -1/3 (Δ[CaCl2])/(Δt) K3PO4 | 2 | -2 | -1/2 (Δ[K3PO4])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(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[CaCl2])/(Δt) = -1/2 (Δ[K3PO4])/(Δt) = 1/6 (Δ[KCl])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: CaCl_2 + K3PO4 ⟶ KCl + Ca_3(PO_4)_2 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 CaCl_2 + 2 K3PO4 ⟶ 6 KCl + Ca_3(PO_4)_2 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 CaCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 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 CaCl_2 | 3 | -3 | -1/3 (Δ[CaCl2])/(Δt) K3PO4 | 2 | -2 | -1/2 (Δ[K3PO4])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(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[CaCl2])/(Δt) = -1/2 (Δ[K3PO4])/(Δt) = 1/6 (Δ[KCl])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| calcium chloride | K3PO4 | potassium chloride | tricalcium diphosphate formula | CaCl_2 | K3PO4 | KCl | Ca_3(PO_4)_2 Hill formula | CaCl_2 | K3O4P | ClK | Ca_3O_8P_2 name | calcium chloride | | potassium chloride | tricalcium diphosphate IUPAC name | calcium dichloride | | potassium chloride | tricalcium diphosphate
| calcium chloride | K3PO4 | potassium chloride | tricalcium diphosphate formula | CaCl_2 | K3PO4 | KCl | Ca_3(PO_4)_2 Hill formula | CaCl_2 | K3O4P | ClK | Ca_3O_8P_2 name | calcium chloride | | potassium chloride | tricalcium diphosphate IUPAC name | calcium dichloride | | potassium chloride | tricalcium diphosphate

Substance properties

| calcium chloride | K3PO4 | potassium chloride | tricalcium diphosphate molar mass | 111 g/mol | 212.26 g/mol | 74.55 g/mol | 310.17 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 772 °C | | 770 °C | boiling point | | | 1420 °C | density | 2.15 g/cm^3 | | 1.98 g/cm^3 | 3.14 g/cm^3 solubility in water | soluble | | soluble | odor | | | odorless |
| calcium chloride | K3PO4 | potassium chloride | tricalcium diphosphate molar mass | 111 g/mol | 212.26 g/mol | 74.55 g/mol | 310.17 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 772 °C | | 770 °C | boiling point | | | 1420 °C | density | 2.15 g/cm^3 | | 1.98 g/cm^3 | 3.14 g/cm^3 solubility in water | soluble | | soluble | odor | | | odorless |

Units

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