NaOH + H2O2 + P = H2O + NaH2PO4

NaOH sodium hydroxide + H_2O_2 hydrogen peroxide + P red phosphorus ⟶ H_2O water + NaH_2PO_4 sodium dihydrogen phosphate

Balance the chemical equation algebraically: NaOH + H_2O_2 + P ⟶ H_2O + NaH_2PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 H_2O_2 + c_3 P ⟶ c_4 H_2O + c_5 NaH_2PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and P: H: | c_1 + 2 c_2 = 2 c_4 + 2 c_5 Na: | c_1 = c_5 O: | c_1 + 2 c_2 = c_4 + 4 c_5 P: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 5/2 c_3 = 1 c_4 = 2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 5 c_3 = 2 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 5 H_2O_2 + 2 P ⟶ 4 H_2O + 2 NaH_2PO_4

+ + ⟶ +

sodium hydroxide + hydrogen peroxide + red phosphorus ⟶ water + sodium dihydrogen phosphate

Construct the equilibrium constant, K, expression for: NaOH + H_2O_2 + P ⟶ H_2O + NaH_2PO_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: 2 NaOH + 5 H_2O_2 + 2 P ⟶ 4 H_2O + 2 NaH_2PO_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 NaOH | 2 | -2 H_2O_2 | 5 | -5 P | 2 | -2 H_2O | 4 | 4 NaH_2PO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) H_2O_2 | 5 | -5 | ([H2O2])^(-5) P | 2 | -2 | ([P])^(-2) H_2O | 4 | 4 | ([H2O])^4 NaH_2PO_4 | 2 | 2 | ([NaH2PO4])^2 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 = ([NaOH])^(-2) ([H2O2])^(-5) ([P])^(-2) ([H2O])^4 ([NaH2PO4])^2 = (([H2O])^4 ([NaH2PO4])^2)/(([NaOH])^2 ([H2O2])^5 ([P])^2)

Construct the rate of reaction expression for: NaOH + H_2O_2 + P ⟶ H_2O + NaH_2PO_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: 2 NaOH + 5 H_2O_2 + 2 P ⟶ 4 H_2O + 2 NaH_2PO_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 NaOH | 2 | -2 H_2O_2 | 5 | -5 P | 2 | -2 H_2O | 4 | 4 NaH_2PO_4 | 2 | 2 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) H_2O_2 | 5 | -5 | -1/5 (Δ[H2O2])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NaH_2PO_4 | 2 | 2 | 1/2 (Δ[NaH2PO4])/(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 = -1/2 (Δ[NaOH])/(Δt) = -1/5 (Δ[H2O2])/(Δt) = -1/2 (Δ[P])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[NaH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | hydrogen peroxide | red phosphorus | water | sodium dihydrogen phosphate formula | NaOH | H_2O_2 | P | H_2O | NaH_2PO_4 Hill formula | HNaO | H_2O_2 | P | H_2O | H_2NaO_4P name | sodium hydroxide | hydrogen peroxide | red phosphorus | water | sodium dihydrogen phosphate IUPAC name | sodium hydroxide | hydrogen peroxide | phosphorus | water | sodium dihydrogen phosphate

| sodium hydroxide | hydrogen peroxide | red phosphorus | water | sodium dihydrogen phosphate molar mass | 39.997 g/mol | 34.014 g/mol | 30.973761998 g/mol | 18.015 g/mol | 119.98 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 323 °C | -0.43 °C | 579.2 °C | 0 °C | boiling point | 1390 °C | 150.2 °C | | 99.9839 °C | density | 2.13 g/cm^3 | 1.44 g/cm^3 | 2.16 g/cm^3 | 1 g/cm^3 | 0.9996 g/cm^3 solubility in water | soluble | miscible | insoluble | | surface tension | 0.07435 N/m | 0.0804 N/m | | 0.0728 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | 0.001249 Pa s (at 20 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | | | | odorless | odorless