H2SO4 + KMnO4 + C6H12O6 = H2O + CO2 + K2SO4 + MnSO4

H_2SO_4 (sulfuric acid) + KMnO_4 (potassium permanganate) + C_6H_12O_6 (D-(+)-glucose) ⟶ H_2O (water) + CO_2 (carbon dioxide) + K_2SO_4 (potassium sulfate) + MnSO_4 (manganese(II) sulfate)

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_6H_12O_6 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_6H_12O_6 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and C: H: | 2 c_1 + 12 c_3 = 2 c_4 O: | 4 c_1 + 4 c_2 + 6 c_3 = c_4 + 2 c_5 + 4 c_6 + 4 c_7 S: | c_1 = c_6 + c_7 K: | c_2 = 2 c_6 Mn: | c_2 = c_7 C: | 6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 36/5 c_2 = 24/5 c_3 = 1 c_4 = 66/5 c_5 = 6 c_6 = 12/5 c_7 = 24/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 36 c_2 = 24 c_3 = 5 c_4 = 66 c_5 = 30 c_6 = 12 c_7 = 24 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 36 H_2SO_4 + 24 KMnO_4 + 5 C_6H_12O_6 ⟶ 66 H_2O + 30 CO_2 + 12 K_2SO_4 + 24 MnSO_4

+ + ⟶ + + +

sulfuric acid + potassium permanganate + D-(+)-glucose ⟶ water + carbon dioxide + potassium sulfate + manganese(II) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C_6H_12O_6 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_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: 36 H_2SO_4 + 24 KMnO_4 + 5 C_6H_12O_6 ⟶ 66 H_2O + 30 CO_2 + 12 K_2SO_4 + 24 MnSO_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 | 36 | -36 KMnO_4 | 24 | -24 C_6H_12O_6 | 5 | -5 H_2O | 66 | 66 CO_2 | 30 | 30 K_2SO_4 | 12 | 12 MnSO_4 | 24 | 24 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 36 | -36 | ([H2SO4])^(-36) KMnO_4 | 24 | -24 | ([KMnO4])^(-24) C_6H_12O_6 | 5 | -5 | ([C6H12O6])^(-5) H_2O | 66 | 66 | ([H2O])^66 CO_2 | 30 | 30 | ([CO2])^30 K_2SO_4 | 12 | 12 | ([K2SO4])^12 MnSO_4 | 24 | 24 | ([MnSO4])^24 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])^(-36) ([KMnO4])^(-24) ([C6H12O6])^(-5) ([H2O])^66 ([CO2])^30 ([K2SO4])^12 ([MnSO4])^24 = (([H2O])^66 ([CO2])^30 ([K2SO4])^12 ([MnSO4])^24)/(([H2SO4])^36 ([KMnO4])^24 ([C6H12O6])^5)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C_6H_12O_6 ⟶ H_2O + CO_2 + K_2SO_4 + MnSO_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: 36 H_2SO_4 + 24 KMnO_4 + 5 C_6H_12O_6 ⟶ 66 H_2O + 30 CO_2 + 12 K_2SO_4 + 24 MnSO_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 | 36 | -36 KMnO_4 | 24 | -24 C_6H_12O_6 | 5 | -5 H_2O | 66 | 66 CO_2 | 30 | 30 K_2SO_4 | 12 | 12 MnSO_4 | 24 | 24 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 | 36 | -36 | -1/36 (Δ[H2SO4])/(Δt) KMnO_4 | 24 | -24 | -1/24 (Δ[KMnO4])/(Δt) C_6H_12O_6 | 5 | -5 | -1/5 (Δ[C6H12O6])/(Δt) H_2O | 66 | 66 | 1/66 (Δ[H2O])/(Δt) CO_2 | 30 | 30 | 1/30 (Δ[CO2])/(Δt) K_2SO_4 | 12 | 12 | 1/12 (Δ[K2SO4])/(Δt) MnSO_4 | 24 | 24 | 1/24 (Δ[MnSO4])/(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 = -1/36 (Δ[H2SO4])/(Δt) = -1/24 (Δ[KMnO4])/(Δt) = -1/5 (Δ[C6H12O6])/(Δt) = 1/66 (Δ[H2O])/(Δt) = 1/30 (Δ[CO2])/(Δt) = 1/12 (Δ[K2SO4])/(Δt) = 1/24 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | D-(+)-glucose | water | carbon dioxide | potassium sulfate | manganese(II) sulfate formula | H_2SO_4 | KMnO_4 | C_6H_12O_6 | H_2O | CO_2 | K_2SO_4 | MnSO_4 Hill formula | H_2O_4S | KMnO_4 | C_6H_12O_6 | H_2O | CO_2 | K_2O_4S | MnSO_4 name | sulfuric acid | potassium permanganate | D-(+)-glucose | water | carbon dioxide | potassium sulfate | manganese(II) sulfate IUPAC name | sulfuric acid | potassium permanganate | 6-(hydroxymethyl)oxane-2, 3, 4, 5-tetrol | water | carbon dioxide | dipotassium sulfate | manganese(+2) cation sulfate

| sulfuric acid | potassium permanganate | D-(+)-glucose | water | carbon dioxide | potassium sulfate | manganese(II) sulfate molar mass | 98.07 g/mol | 158.03 g/mol | 180.16 g/mol | 18.015 g/mol | 44.009 g/mol | 174.25 g/mol | 150.99 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | | solid (at STP) melting point | 10.371 °C | 240 °C | 146 °C | 0 °C | -56.56 °C (at triple point) | | 710 °C boiling point | 279.6 °C | | | 99.9839 °C | -78.5 °C (at sublimation point) | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 1.54 g/cm^3 | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | | 3.25 g/cm^3 solubility in water | very soluble | | soluble | | | soluble | soluble surface tension | 0.0735 N/m | | 0.07173 N/m | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 0.56 Pa s (at 145 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | | odorless | odorless | |