H2C2O4 = H2O + CO2 + CO

HO_2CCO_2H oxalic acid ⟶ H_2O water + CO_2 carbon dioxide + CO carbon monoxide

Balance the chemical equation algebraically: HO_2CCO_2H ⟶ H_2O + CO_2 + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HO_2CCO_2H ⟶ c_2 H_2O + c_3 CO_2 + c_4 CO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | 2 c_1 = c_3 + c_4 H: | 2 c_1 = 2 c_2 O: | 4 c_1 = c_2 + 2 c_3 + c_4 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HO_2CCO_2H ⟶ H_2O + CO_2 + CO

⟶ + +

oxalic acid ⟶ water + carbon dioxide + carbon monoxide

| oxalic acid | water | carbon dioxide | carbon monoxide molecular enthalpy | -829.9 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol | -110.5 kJ/mol total enthalpy | -829.9 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol | -110.5 kJ/mol | H_initial = -829.9 kJ/mol | H_final = -789.8 kJ/mol | | ΔH_rxn^0 | -789.8 kJ/mol - -829.9 kJ/mol = 40.07 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: HO_2CCO_2H ⟶ H_2O + CO_2 + CO 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: HO_2CCO_2H ⟶ H_2O + CO_2 + CO 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 HO_2CCO_2H | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HO_2CCO_2H | 1 | -1 | ([HO2CCO2H])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] CO | 1 | 1 | [CO] 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 = ([HO2CCO2H])^(-1) [H2O] [CO2] [CO] = ([H2O] [CO2] [CO])/([HO2CCO2H])

Construct the rate of reaction expression for: HO_2CCO_2H ⟶ H_2O + CO_2 + CO 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: HO_2CCO_2H ⟶ H_2O + CO_2 + CO 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 HO_2CCO_2H | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 CO | 1 | 1 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 HO_2CCO_2H | 1 | -1 | -(Δ[HO2CCO2H])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) CO | 1 | 1 | (Δ[CO])/(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[HO2CCO2H])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxalic acid | water | carbon dioxide | carbon monoxide formula | HO_2CCO_2H | H_2O | CO_2 | CO Hill formula | C_2H_2O_4 | H_2O | CO_2 | CO name | oxalic acid | water | carbon dioxide | carbon monoxide