H2SO4 + PH3 + LiMnO4 = H2O + MnSO4 + H3PO4 + Li2SO4

H_2SO_4 sulfuric acid + PH_3 phosphine + LiMnO4 ⟶ H_2O water + MnSO_4 manganese(II) sulfate + H_3PO_4 phosphoric acid + Li_2SO_4 lithium sulfate

Balance the chemical equation algebraically: H_2SO_4 + PH_3 + LiMnO4 ⟶ H_2O + MnSO_4 + H_3PO_4 + Li_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 PH_3 + c_3 LiMnO4 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 H_3PO_4 + c_7 Li_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, P, Li and Mn: H: | 2 c_1 + 3 c_2 = 2 c_4 + 3 c_6 O: | 4 c_1 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_5 + c_7 P: | c_2 = c_6 Li: | c_3 = 2 c_7 Mn: | c_3 = 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 5/4 c_3 = 2 c_4 = 3 c_5 = 2 c_6 = 5/4 c_7 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 12 c_2 = 5 c_3 = 8 c_4 = 12 c_5 = 8 c_6 = 5 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2SO_4 + 5 PH_3 + 8 LiMnO4 ⟶ 12 H_2O + 8 MnSO_4 + 5 H_3PO_4 + 4 Li_2SO_4

+ + LiMnO4 ⟶ + + +

sulfuric acid + phosphine + LiMnO4 ⟶ water + manganese(II) sulfate + phosphoric acid + lithium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + PH_3 + LiMnO4 ⟶ H_2O + MnSO_4 + H_3PO_4 + Li_2SO_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: 12 H_2SO_4 + 5 PH_3 + 8 LiMnO4 ⟶ 12 H_2O + 8 MnSO_4 + 5 H_3PO_4 + 4 Li_2SO_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 H_2SO_4 | 12 | -12 PH_3 | 5 | -5 LiMnO4 | 8 | -8 H_2O | 12 | 12 MnSO_4 | 8 | 8 H_3PO_4 | 5 | 5 Li_2SO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 12 | -12 | ([H2SO4])^(-12) PH_3 | 5 | -5 | ([PH3])^(-5) LiMnO4 | 8 | -8 | ([LiMnO4])^(-8) H_2O | 12 | 12 | ([H2O])^12 MnSO_4 | 8 | 8 | ([MnSO4])^8 H_3PO_4 | 5 | 5 | ([H3PO4])^5 Li_2SO_4 | 4 | 4 | ([Li2SO4])^4 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 = ([H2SO4])^(-12) ([PH3])^(-5) ([LiMnO4])^(-8) ([H2O])^12 ([MnSO4])^8 ([H3PO4])^5 ([Li2SO4])^4 = (([H2O])^12 ([MnSO4])^8 ([H3PO4])^5 ([Li2SO4])^4)/(([H2SO4])^12 ([PH3])^5 ([LiMnO4])^8)

Construct the rate of reaction expression for: H_2SO_4 + PH_3 + LiMnO4 ⟶ H_2O + MnSO_4 + H_3PO_4 + Li_2SO_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: 12 H_2SO_4 + 5 PH_3 + 8 LiMnO4 ⟶ 12 H_2O + 8 MnSO_4 + 5 H_3PO_4 + 4 Li_2SO_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 H_2SO_4 | 12 | -12 PH_3 | 5 | -5 LiMnO4 | 8 | -8 H_2O | 12 | 12 MnSO_4 | 8 | 8 H_3PO_4 | 5 | 5 Li_2SO_4 | 4 | 4 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_2SO_4 | 12 | -12 | -1/12 (Δ[H2SO4])/(Δt) PH_3 | 5 | -5 | -1/5 (Δ[PH3])/(Δt) LiMnO4 | 8 | -8 | -1/8 (Δ[LiMnO4])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) MnSO_4 | 8 | 8 | 1/8 (Δ[MnSO4])/(Δt) H_3PO_4 | 5 | 5 | 1/5 (Δ[H3PO4])/(Δt) Li_2SO_4 | 4 | 4 | 1/4 (Δ[Li2SO4])/(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 = -1/12 (Δ[H2SO4])/(Δt) = -1/5 (Δ[PH3])/(Δt) = -1/8 (Δ[LiMnO4])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/8 (Δ[MnSO4])/(Δt) = 1/5 (Δ[H3PO4])/(Δt) = 1/4 (Δ[Li2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | phosphine | LiMnO4 | water | manganese(II) sulfate | phosphoric acid | lithium sulfate formula | H_2SO_4 | PH_3 | LiMnO4 | H_2O | MnSO_4 | H_3PO_4 | Li_2SO_4 Hill formula | H_2O_4S | H_3P | LiMnO4 | H_2O | MnSO_4 | H_3O_4P | Li_2O_4S name | sulfuric acid | phosphine | | water | manganese(II) sulfate | phosphoric acid | lithium sulfate IUPAC name | sulfuric acid | phosphine | | water | manganese(+2) cation sulfate | phosphoric acid | dilithium sulfate

| sulfuric acid | phosphine | LiMnO4 | water | manganese(II) sulfate | phosphoric acid | lithium sulfate molar mass | 98.07 g/mol | 33.998 g/mol | 125.9 g/mol | 18.015 g/mol | 150.99 g/mol | 97.994 g/mol | 109.9 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | -132.8 °C | | 0 °C | 710 °C | 42.4 °C | 845 °C boiling point | 279.6 °C | -87.5 °C | | 99.9839 °C | | 158 °C | 1377 °C density | 1.8305 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 3.25 g/cm^3 | 1.685 g/cm^3 | 2.22 g/cm^3 solubility in water | very soluble | slightly soluble | | | soluble | very soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 1.1×10^-5 Pa s (at 0 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | odorless | | odorless |