PH3 + HMnO4 = H2O + MnO2 + H3PO4

PH_3 phosphine + HMnO4 ⟶ H_2O water + MnO_2 manganese dioxide + H_3PO_4 phosphoric acid

Balance the chemical equation algebraically: PH_3 + HMnO4 ⟶ H_2O + MnO_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 PH_3 + c_2 HMnO4 ⟶ c_3 H_2O + c_4 MnO_2 + c_5 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, P, Mn and O: H: | 3 c_1 + c_2 = 2 c_3 + 3 c_5 P: | c_1 = c_5 Mn: | c_2 = c_4 O: | 4 c_2 = c_3 + 2 c_4 + 4 c_5 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 = 8/3 c_3 = 4/3 c_4 = 8/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 3 c_2 = 8 c_3 = 4 c_4 = 8 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 PH_3 + 8 HMnO4 ⟶ 4 H_2O + 8 MnO_2 + 3 H_3PO_4

+ HMnO4 ⟶ + +

phosphine + HMnO4 ⟶ water + manganese dioxide + phosphoric acid

Construct the equilibrium constant, K, expression for: PH_3 + HMnO4 ⟶ H_2O + MnO_2 + H_3PO_4 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 PH_3 + 8 HMnO4 ⟶ 4 H_2O + 8 MnO_2 + 3 H_3PO_4 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 PH_3 | 3 | -3 HMnO4 | 8 | -8 H_2O | 4 | 4 MnO_2 | 8 | 8 H_3PO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression PH_3 | 3 | -3 | ([PH3])^(-3) HMnO4 | 8 | -8 | ([HMnO4])^(-8) H_2O | 4 | 4 | ([H2O])^4 MnO_2 | 8 | 8 | ([MnO2])^8 H_3PO_4 | 3 | 3 | ([H3PO4])^3 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 = ([PH3])^(-3) ([HMnO4])^(-8) ([H2O])^4 ([MnO2])^8 ([H3PO4])^3 = (([H2O])^4 ([MnO2])^8 ([H3PO4])^3)/(([PH3])^3 ([HMnO4])^8)

Construct the rate of reaction expression for: PH_3 + HMnO4 ⟶ H_2O + MnO_2 + H_3PO_4 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 PH_3 + 8 HMnO4 ⟶ 4 H_2O + 8 MnO_2 + 3 H_3PO_4 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 PH_3 | 3 | -3 HMnO4 | 8 | -8 H_2O | 4 | 4 MnO_2 | 8 | 8 H_3PO_4 | 3 | 3 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 PH_3 | 3 | -3 | -1/3 (Δ[PH3])/(Δt) HMnO4 | 8 | -8 | -1/8 (Δ[HMnO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) MnO_2 | 8 | 8 | 1/8 (Δ[MnO2])/(Δt) H_3PO_4 | 3 | 3 | 1/3 (Δ[H3PO4])/(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[PH3])/(Δt) = -1/8 (Δ[HMnO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/8 (Δ[MnO2])/(Δt) = 1/3 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphine | HMnO4 | water | manganese dioxide | phosphoric acid formula | PH_3 | HMnO4 | H_2O | MnO_2 | H_3PO_4 Hill formula | H_3P | HMnO4 | H_2O | MnO_2 | H_3O_4P name | phosphine | | water | manganese dioxide | phosphoric acid IUPAC name | phosphine | | water | dioxomanganese | phosphoric acid

| phosphine | HMnO4 | water | manganese dioxide | phosphoric acid molar mass | 33.998 g/mol | 119.94 g/mol | 18.015 g/mol | 86.936 g/mol | 97.994 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) | liquid (at STP) melting point | -132.8 °C | | 0 °C | 535 °C | 42.4 °C boiling point | -87.5 °C | | 99.9839 °C | | 158 °C density | 0.00139 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 5.03 g/cm^3 | 1.685 g/cm^3 solubility in water | slightly soluble | | | insoluble | very soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 1.1×10^-5 Pa s (at 0 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | | odorless