Ca(NO3)2 + K3PO4 = KNO3 + Ca3(PO4)2

Input interpretation

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Ca(NO_3)_2 calcium nitrate + K3PO4 ⟶ KNO_3 potassium nitrate + Ca_3(PO_4)_2 tricalcium diphosphate

Balanced equation

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Balance the chemical equation algebraically: Ca(NO_3)_2 + K3PO4 ⟶ KNO_3 + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(NO_3)_2 + c_2 K3PO4 ⟶ c_3 KNO_3 + 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, N, O, K and P: Ca: | c_1 = 3 c_4 N: | 2 c_1 = c_3 O: | 6 c_1 + 4 c_2 = 3 c_3 + 8 c_4 K: | 3 c_2 = c_3 P: | c_2 = 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_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 Ca(NO_3)_2 + 2 K3PO4 ⟶ 6 KNO_3 + Ca_3(PO_4)_2

+ K3PO4 ⟶ +

Names

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calcium nitrate + K3PO4 ⟶ potassium nitrate + tricalcium diphosphate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Ca(NO_3)_2 + K3PO4 ⟶ KNO_3 + 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 Ca(NO_3)_2 + 2 K3PO4 ⟶ 6 KNO_3 + 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 Ca(NO_3)_2 | 3 | -3 K3PO4 | 2 | -2 KNO_3 | 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 Ca(NO_3)_2 | 3 | -3 | ([Ca(NO3)2])^(-3) K3PO4 | 2 | -2 | ([K3PO4])^(-2) KNO_3 | 6 | 6 | ([KNO3])^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 = ([Ca(NO3)2])^(-3) ([K3PO4])^(-2) ([KNO3])^6 [Ca3(PO4)2] = (([KNO3])^6 [Ca3(PO4)2])/(([Ca(NO3)2])^3 ([K3PO4])^2)

Rate of reaction

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Construct the rate of reaction expression for: Ca(NO_3)_2 + K3PO4 ⟶ KNO_3 + 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 Ca(NO_3)_2 + 2 K3PO4 ⟶ 6 KNO_3 + 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 Ca(NO_3)_2 | 3 | -3 K3PO4 | 2 | -2 KNO_3 | 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 Ca(NO_3)_2 | 3 | -3 | -1/3 (Δ[Ca(NO3)2])/(Δt) K3PO4 | 2 | -2 | -1/2 (Δ[K3PO4])/(Δt) KNO_3 | 6 | 6 | 1/6 (Δ[KNO3])/(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[Ca(NO3)2])/(Δt) = -1/2 (Δ[K3PO4])/(Δt) = 1/6 (Δ[KNO3])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)