C12H22O11 = H2O + C

C_12H_22O_11 sucrose ⟶ H_2O water + C activated charcoal

Balance the chemical equation algebraically: C_12H_22O_11 ⟶ H_2O + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C_12H_22O_11 ⟶ c_2 H_2O + c_3 C Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | 12 c_1 = c_3 H: | 22 c_1 = 2 c_2 O: | 11 c_1 = c_2 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 = 11 c_3 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C_12H_22O_11 ⟶ 11 H_2O + 12 C

⟶ +

sucrose ⟶ water + activated charcoal

Construct the equilibrium constant, K, expression for: C_12H_22O_11 ⟶ H_2O + C 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: C_12H_22O_11 ⟶ 11 H_2O + 12 C 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 C_12H_22O_11 | 1 | -1 H_2O | 11 | 11 C | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C_12H_22O_11 | 1 | -1 | ([C12H22O11])^(-1) H_2O | 11 | 11 | ([H2O])^11 C | 12 | 12 | ([C])^12 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 = ([C12H22O11])^(-1) ([H2O])^11 ([C])^12 = (([H2O])^11 ([C])^12)/([C12H22O11])

Construct the rate of reaction expression for: C_12H_22O_11 ⟶ H_2O + C 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: C_12H_22O_11 ⟶ 11 H_2O + 12 C 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 C_12H_22O_11 | 1 | -1 H_2O | 11 | 11 C | 12 | 12 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 C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) C | 12 | 12 | 1/12 (Δ[C])/(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[C12H22O11])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/12 (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sucrose | water | activated charcoal formula | C_12H_22O_11 | H_2O | C name | sucrose | water | activated charcoal IUPAC name | (2R, 3S, 4S, 5S, 6R)-2-[(2S, 3S, 4S, 5R)-3, 4-dihydroxy-2, 5-bis(hydroxymethyl)oxolan-2-yl]oxy-6-(hydroxymethyl)oxane-3, 4, 5-triol | water | carbon

| sucrose | water | activated charcoal molar mass | 342.3 g/mol | 18.015 g/mol | 12.011 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) melting point | 170 °C | 0 °C | 3550 °C boiling point | | 99.9839 °C | 4027 °C density | 1.59 g/cm^3 | 1 g/cm^3 | 2.26 g/cm^3 solubility in water | | | insoluble surface tension | 0.0622 N/m | 0.0728 N/m | dynamic viscosity | | 8.9×10^-4 Pa s (at 25 °C) | odor | | odorless |