H3PO4 + NH4OH = H2O + (NH4)3PO4

Input interpretation

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H_3PO_4 (phosphoric acid) + NH_4OH (ammonium hydroxide) ⟶ H_2O (water) + (NH4)3PO4

Balanced equation

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Balance the chemical equation algebraically: H_3PO_4 + NH_4OH ⟶ H_2O + (NH4)3PO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 NH_4OH ⟶ c_3 H_2O + c_4 (NH4)3PO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and N: H: | 3 c_1 + 5 c_2 = 2 c_3 + 12 c_4 O: | 4 c_1 + c_2 = c_3 + 4 c_4 P: | c_1 = c_4 N: | c_2 = 3 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 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_3PO_4 + 3 NH_4OH ⟶ 3 H_2O + (NH4)3PO4

+ ⟶ + (NH4)3PO4

Names

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phosphoric acid + ammonium hydroxide ⟶ water + (NH4)3PO4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_3PO_4 + NH_4OH ⟶ H_2O + (NH4)3PO4 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: H_3PO_4 + 3 NH_4OH ⟶ 3 H_2O + (NH4)3PO4 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 | 1 | -1 NH_4OH | 3 | -3 H_2O | 3 | 3 (NH4)3PO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) NH_4OH | 3 | -3 | ([NH4OH])^(-3) H_2O | 3 | 3 | ([H2O])^3 (NH4)3PO4 | 1 | 1 | [(NH4)3PO4] 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])^(-1) ([NH4OH])^(-3) ([H2O])^3 [(NH4)3PO4] = (([H2O])^3 [(NH4)3PO4])/([H3PO4] ([NH4OH])^3)

Rate of reaction

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Construct the rate of reaction expression for: H_3PO_4 + NH_4OH ⟶ H_2O + (NH4)3PO4 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: H_3PO_4 + 3 NH_4OH ⟶ 3 H_2O + (NH4)3PO4 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 | 1 | -1 NH_4OH | 3 | -3 H_2O | 3 | 3 (NH4)3PO4 | 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 H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) NH_4OH | 3 | -3 | -1/3 (Δ[NH4OH])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) (NH4)3PO4 | 1 | 1 | (Δ[(NH4)3PO4])/(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[H3PO4])/(Δt) = -1/3 (Δ[NH4OH])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[(NH4)3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)