H2 + Ag3PO4 = H3PO4 + Ag

H_2 hydrogen + Ag_3PO_4 silver phosphate ⟶ H_3PO_4 phosphoric acid + Ag silver

Balance the chemical equation algebraically: H_2 + Ag_3PO_4 ⟶ H_3PO_4 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 Ag_3PO_4 ⟶ c_3 H_3PO_4 + c_4 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for H, Ag, O and P: H: | 2 c_1 = 3 c_3 Ag: | 3 c_2 = c_4 O: | 4 c_2 = 4 c_3 P: | c_2 = c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + 2 Ag_3PO_4 ⟶ 2 H_3PO_4 + 6 Ag

+ ⟶ +

hydrogen + silver phosphate ⟶ phosphoric acid + silver

Construct the equilibrium constant, K, expression for: H_2 + Ag_3PO_4 ⟶ H_3PO_4 + Ag 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 H_2 + 2 Ag_3PO_4 ⟶ 2 H_3PO_4 + 6 Ag 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_2 | 3 | -3 Ag_3PO_4 | 2 | -2 H_3PO_4 | 2 | 2 Ag | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 3 | -3 | ([H2])^(-3) Ag_3PO_4 | 2 | -2 | ([Ag3PO4])^(-2) H_3PO_4 | 2 | 2 | ([H3PO4])^2 Ag | 6 | 6 | ([Ag])^6 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 = ([H2])^(-3) ([Ag3PO4])^(-2) ([H3PO4])^2 ([Ag])^6 = (([H3PO4])^2 ([Ag])^6)/(([H2])^3 ([Ag3PO4])^2)

Construct the rate of reaction expression for: H_2 + Ag_3PO_4 ⟶ H_3PO_4 + Ag 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 H_2 + 2 Ag_3PO_4 ⟶ 2 H_3PO_4 + 6 Ag 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_2 | 3 | -3 Ag_3PO_4 | 2 | -2 H_3PO_4 | 2 | 2 Ag | 6 | 6 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_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) Ag_3PO_4 | 2 | -2 | -1/2 (Δ[Ag3PO4])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(Δt) Ag | 6 | 6 | 1/6 (Δ[Ag])/(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[H2])/(Δt) = -1/2 (Δ[Ag3PO4])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) = 1/6 (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | silver phosphate | phosphoric acid | silver formula | H_2 | Ag_3PO_4 | H_3PO_4 | Ag Hill formula | H_2 | Ag_3O_4P | H_3O_4P | Ag name | hydrogen | silver phosphate | phosphoric acid | silver IUPAC name | molecular hydrogen | trisilver phosphate | phosphoric acid | silver

| hydrogen | silver phosphate | phosphoric acid | silver molar mass | 2.016 g/mol | 418.574 g/mol | 97.994 g/mol | 107.8682 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -259.2 °C | 485 °C | 42.4 °C | 960 °C boiling point | -252.8 °C | | 158 °C | 2212 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 4.449 g/cm^3 | 1.685 g/cm^3 | 10.49 g/cm^3 solubility in water | | insoluble | very soluble | insoluble dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | | odor | odorless | | odorless |