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CuCl2 + K3PO4 = KCl + Cu3(PO4)2

Input interpretation

CuCl_2 copper(II) chloride + K3PO4 ⟶ KCl potassium chloride + Cu_3(PO_4)_2 copper(II) phosphate
CuCl_2 copper(II) chloride + K3PO4 ⟶ KCl potassium chloride + Cu_3(PO_4)_2 copper(II) phosphate

Balanced equation

Balance the chemical equation algebraically: CuCl_2 + K3PO4 ⟶ KCl + Cu_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuCl_2 + c_2 K3PO4 ⟶ c_3 KCl + c_4 Cu_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Cu, K, P and O: Cl: | 2 c_1 = c_3 Cu: | c_1 = 3 c_4 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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_3(PO_4)_2
Balance the chemical equation algebraically: CuCl_2 + K3PO4 ⟶ KCl + Cu_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuCl_2 + c_2 K3PO4 ⟶ c_3 KCl + c_4 Cu_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Cu, K, P and O: Cl: | 2 c_1 = c_3 Cu: | c_1 = 3 c_4 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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_3(PO_4)_2

Structures

+ K3PO4 ⟶ +
+ K3PO4 ⟶ +

Names

copper(II) chloride + K3PO4 ⟶ potassium chloride + copper(II) phosphate
copper(II) chloride + K3PO4 ⟶ potassium chloride + copper(II) phosphate

Equilibrium constant

Construct the equilibrium constant, K, expression for: CuCl_2 + K3PO4 ⟶ KCl + Cu_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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_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 CuCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Cu_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 CuCl_2 | 3 | -3 | ([CuCl2])^(-3) K3PO4 | 2 | -2 | ([K3PO4])^(-2) KCl | 6 | 6 | ([KCl])^6 Cu_3(PO_4)_2 | 1 | 1 | [Cu3(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 = ([CuCl2])^(-3) ([K3PO4])^(-2) ([KCl])^6 [Cu3(PO4)2] = (([KCl])^6 [Cu3(PO4)2])/(([CuCl2])^3 ([K3PO4])^2)
Construct the equilibrium constant, K, expression for: CuCl_2 + K3PO4 ⟶ KCl + Cu_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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_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 CuCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Cu_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 CuCl_2 | 3 | -3 | ([CuCl2])^(-3) K3PO4 | 2 | -2 | ([K3PO4])^(-2) KCl | 6 | 6 | ([KCl])^6 Cu_3(PO_4)_2 | 1 | 1 | [Cu3(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 = ([CuCl2])^(-3) ([K3PO4])^(-2) ([KCl])^6 [Cu3(PO4)2] = (([KCl])^6 [Cu3(PO4)2])/(([CuCl2])^3 ([K3PO4])^2)

Rate of reaction

Construct the rate of reaction expression for: CuCl_2 + K3PO4 ⟶ KCl + Cu_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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_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 CuCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Cu_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 CuCl_2 | 3 | -3 | -1/3 (Δ[CuCl2])/(Δt) K3PO4 | 2 | -2 | -1/2 (Δ[K3PO4])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) Cu_3(PO_4)_2 | 1 | 1 | (Δ[Cu3(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[CuCl2])/(Δt) = -1/2 (Δ[K3PO4])/(Δt) = 1/6 (Δ[KCl])/(Δt) = (Δ[Cu3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: CuCl_2 + K3PO4 ⟶ KCl + Cu_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 CuCl_2 + 2 K3PO4 ⟶ 6 KCl + Cu_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 CuCl_2 | 3 | -3 K3PO4 | 2 | -2 KCl | 6 | 6 Cu_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 CuCl_2 | 3 | -3 | -1/3 (Δ[CuCl2])/(Δt) K3PO4 | 2 | -2 | -1/2 (Δ[K3PO4])/(Δt) KCl | 6 | 6 | 1/6 (Δ[KCl])/(Δt) Cu_3(PO_4)_2 | 1 | 1 | (Δ[Cu3(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[CuCl2])/(Δt) = -1/2 (Δ[K3PO4])/(Δt) = 1/6 (Δ[KCl])/(Δt) = (Δ[Cu3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| copper(II) chloride | K3PO4 | potassium chloride | copper(II) phosphate formula | CuCl_2 | K3PO4 | KCl | Cu_3(PO_4)_2 Hill formula | Cl_2Cu | K3O4P | ClK | Cu_3O_8P_2 name | copper(II) chloride | | potassium chloride | copper(II) phosphate IUPAC name | dichlorocopper | | potassium chloride | tricopper diphosphate
| copper(II) chloride | K3PO4 | potassium chloride | copper(II) phosphate formula | CuCl_2 | K3PO4 | KCl | Cu_3(PO_4)_2 Hill formula | Cl_2Cu | K3O4P | ClK | Cu_3O_8P_2 name | copper(II) chloride | | potassium chloride | copper(II) phosphate IUPAC name | dichlorocopper | | potassium chloride | tricopper diphosphate

Substance properties

| copper(II) chloride | K3PO4 | potassium chloride | copper(II) phosphate molar mass | 134.4 g/mol | 212.26 g/mol | 74.55 g/mol | 380.58 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 620 °C | | 770 °C | boiling point | | | 1420 °C | density | 3.386 g/cm^3 | | 1.98 g/cm^3 | solubility in water | | | soluble | insoluble odor | | | odorless |
| copper(II) chloride | K3PO4 | potassium chloride | copper(II) phosphate molar mass | 134.4 g/mol | 212.26 g/mol | 74.55 g/mol | 380.58 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 620 °C | | 770 °C | boiling point | | | 1420 °C | density | 3.386 g/cm^3 | | 1.98 g/cm^3 | solubility in water | | | soluble | insoluble odor | | | odorless |

Units

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