Ca(OH)2 + H3PO4 = H2O + Ca(H2PO4)2

Input interpretation

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Ca(OH)_2 (calcium hydroxide) + H_3PO_4 (phosphoric acid) ⟶ H_2O (water) + Ca(H_2PO_4)_2·H_2O (calcium dihydrogen phosphate monohydrate)

Balanced equation

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Balance the chemical equation algebraically: Ca(OH)_2 + H_3PO_4 ⟶ H_2O + Ca(H_2PO_4)_2·H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 H_3PO_4 ⟶ c_3 H_2O + c_4 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 Ca, H, O and P: Ca: | c_1 = c_4 H: | 2 c_1 + 3 c_2 = 2 c_3 + 4 c_4 O: | 2 c_1 + 4 c_2 = c_3 + 8 c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ca(OH)_2 + 2 H_3PO_4 ⟶ 2 H_2O + Ca(H_2PO_4)_2·H_2O

+ ⟶ +

Names

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calcium hydroxide + phosphoric acid ⟶ water + calcium dihydrogen phosphate monohydrate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: Ca(OH)_2 + H_3PO_4 ⟶ H_2O + 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: Ca(OH)_2 + 2 H_3PO_4 ⟶ 2 H_2O + 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 Ca(OH)_2 | 1 | -1 H_3PO_4 | 2 | -2 H_2O | 2 | 2 Ca(H_2PO_4)_2·H_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 1 | -1 | ([Ca(OH)2])^(-1) H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 Ca(H_2PO_4)_2·H_2O | 1 | 1 | [Ca(H2PO4)2·H2O] 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(OH)2])^(-1) ([H3PO4])^(-2) ([H2O])^2 [Ca(H2PO4)2·H2O] = (([H2O])^2 [Ca(H2PO4)2·H2O])/([Ca(OH)2] ([H3PO4])^2)

Rate of reaction

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