H3PO4 + CsOH = H2O + Cs3PO4

H_3PO_4 phosphoric acid + CsOH cesium hydroxide ⟶ H_2O water + Cs3PO4

Balance the chemical equation algebraically: H_3PO_4 + CsOH ⟶ H_2O + Cs3PO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 CsOH ⟶ c_3 H_2O + c_4 Cs3PO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Cs: H: | 3 c_1 + c_2 = 2 c_3 O: | 4 c_1 + c_2 = c_3 + 4 c_4 P: | c_1 = c_4 Cs: | 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 CsOH ⟶ 3 H_2O + Cs3PO4

+ ⟶ + Cs3PO4

phosphoric acid + cesium hydroxide ⟶ water + Cs3PO4

Construct the equilibrium constant, K, expression for: H_3PO_4 + CsOH ⟶ H_2O + Cs3PO4 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 CsOH ⟶ 3 H_2O + Cs3PO4 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 CsOH | 3 | -3 H_2O | 3 | 3 Cs3PO4 | 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) CsOH | 3 | -3 | ([CsHO])^(-3) H_2O | 3 | 3 | ([H2O])^3 Cs3PO4 | 1 | 1 | [Cs3PO4] 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) ([CsHO])^(-3) ([H2O])^3 [Cs3PO4] = (([H2O])^3 [Cs3PO4])/([H3PO4] ([CsHO])^3)

Construct the rate of reaction expression for: H_3PO_4 + CsOH ⟶ H_2O + Cs3PO4 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 CsOH ⟶ 3 H_2O + Cs3PO4 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 CsOH | 3 | -3 H_2O | 3 | 3 Cs3PO4 | 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) CsOH | 3 | -3 | -1/3 (Δ[CsHO])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Cs3PO4 | 1 | 1 | (Δ[Cs3PO4])/(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[CsHO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Cs3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphoric acid | cesium hydroxide | water | Cs3PO4 formula | H_3PO_4 | CsOH | H_2O | Cs3PO4 Hill formula | H_3O_4P | CsHO | H_2O | Cs3O4P name | phosphoric acid | cesium hydroxide | water | IUPAC name | phosphoric acid | cesium;hydroxide | water |

| phosphoric acid | cesium hydroxide | water | Cs3PO4 molar mass | 97.994 g/mol | 149.912 g/mol | 18.015 g/mol | 493.686 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 42.4 °C | 338.85 °C | 0 °C | boiling point | 158 °C | | 99.9839 °C | density | 1.685 g/cm^3 | 1.72 g/cm^3 | 1 g/cm^3 | solubility in water | very soluble | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |