NaOH + CH3COH + NaMnO4 = H2O + MnO2 + CH3COONa

NaOH sodium hydroxide + CH_3CHO acetaldehyde + NaMnO_4 sodium permanganate ⟶ H_2O water + MnO_2 manganese dioxide + CH_3COONa sodium acetate

Balance the chemical equation algebraically: NaOH + CH_3CHO + NaMnO_4 ⟶ H_2O + MnO_2 + CH_3COONa Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 CH_3CHO + c_3 NaMnO_4 ⟶ c_4 H_2O + c_5 MnO_2 + c_6 CH_3COONa Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, C and Mn: H: | c_1 + 4 c_2 = 2 c_4 + 3 c_6 Na: | c_1 + c_3 = c_6 O: | c_1 + c_2 + 4 c_3 = c_4 + 2 c_5 + 2 c_6 C: | 2 c_2 = 2 c_6 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NaOH + 3 CH_3CHO + 2 NaMnO_4 ⟶ 2 H_2O + 2 MnO_2 + 3 CH_3COONa

+ + ⟶ + +

sodium hydroxide + acetaldehyde + sodium permanganate ⟶ water + manganese dioxide + sodium acetate

Construct the equilibrium constant, K, expression for: NaOH + CH_3CHO + NaMnO_4 ⟶ H_2O + MnO_2 + CH_3COONa 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: NaOH + 3 CH_3CHO + 2 NaMnO_4 ⟶ 2 H_2O + 2 MnO_2 + 3 CH_3COONa 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 | 1 | -1 CH_3CHO | 3 | -3 NaMnO_4 | 2 | -2 H_2O | 2 | 2 MnO_2 | 2 | 2 CH_3COONa | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 1 | -1 | ([NaOH])^(-1) CH_3CHO | 3 | -3 | ([CH3CHO])^(-3) NaMnO_4 | 2 | -2 | ([NaMnO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 MnO_2 | 2 | 2 | ([MnO2])^2 CH_3COONa | 3 | 3 | ([CH3COONa])^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 = ([NaOH])^(-1) ([CH3CHO])^(-3) ([NaMnO4])^(-2) ([H2O])^2 ([MnO2])^2 ([CH3COONa])^3 = (([H2O])^2 ([MnO2])^2 ([CH3COONa])^3)/([NaOH] ([CH3CHO])^3 ([NaMnO4])^2)

Construct the rate of reaction expression for: NaOH + CH_3CHO + NaMnO_4 ⟶ H_2O + MnO_2 + CH_3COONa 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: NaOH + 3 CH_3CHO + 2 NaMnO_4 ⟶ 2 H_2O + 2 MnO_2 + 3 CH_3COONa 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 | 1 | -1 CH_3CHO | 3 | -3 NaMnO_4 | 2 | -2 H_2O | 2 | 2 MnO_2 | 2 | 2 CH_3COONa | 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 NaOH | 1 | -1 | -(Δ[NaOH])/(Δt) CH_3CHO | 3 | -3 | -1/3 (Δ[CH3CHO])/(Δt) NaMnO_4 | 2 | -2 | -1/2 (Δ[NaMnO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnO_2 | 2 | 2 | 1/2 (Δ[MnO2])/(Δt) CH_3COONa | 3 | 3 | 1/3 (Δ[CH3COONa])/(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[NaOH])/(Δt) = -1/3 (Δ[CH3CHO])/(Δt) = -1/2 (Δ[NaMnO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[MnO2])/(Δt) = 1/3 (Δ[CH3COONa])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | acetaldehyde | sodium permanganate | water | manganese dioxide | sodium acetate formula | NaOH | CH_3CHO | NaMnO_4 | H_2O | MnO_2 | CH_3COONa Hill formula | HNaO | C_2H_4O | MnNaO_4 | H_2O | MnO_2 | C_2H_3NaO_2 name | sodium hydroxide | acetaldehyde | sodium permanganate | water | manganese dioxide | sodium acetate IUPAC name | sodium hydroxide | acetaldehyde | sodium permanganate | water | dioxomanganese | sodium acetate

| sodium hydroxide | acetaldehyde | sodium permanganate | water | manganese dioxide | sodium acetate molar mass | 39.997 g/mol | 44.053 g/mol | 141.92 g/mol | 18.015 g/mol | 86.936 g/mol | 82.034 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | -123 °C | | 0 °C | 535 °C | 300 °C boiling point | 1390 °C | 20.1 °C | 100 °C | 99.9839 °C | | 881.4 °C density | 2.13 g/cm^3 | 0.784 g/cm^3 (at 20 °C) | 1.391 g/cm^3 | 1 g/cm^3 | 5.03 g/cm^3 | 1.528 g/cm^3 solubility in water | soluble | miscible | | | insoluble | soluble surface tension | 0.07435 N/m | 0.0212 N/m | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 2.456×10^-4 Pa s (at 15 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | | odorless | | odorless