H2O + CO(NH2)2 = CO2 + NH3

H_2O water + NH_2CONH_2 urea ⟶ CO_2 carbon dioxide + NH_3 ammonia

Balance the chemical equation algebraically: H_2O + NH_2CONH_2 ⟶ CO_2 + NH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_2CONH_2 ⟶ c_3 CO_2 + c_4 NH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and N: H: | 2 c_1 + 4 c_2 = 3 c_4 O: | c_1 + c_2 = 2 c_3 C: | c_2 = c_3 N: | 2 c_2 = 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + NH_2CONH_2 ⟶ CO_2 + 2 NH_3

+ ⟶ +

water + urea ⟶ carbon dioxide + ammonia

| water | urea | carbon dioxide | ammonia molecular enthalpy | -285.8 kJ/mol | -333.1 kJ/mol | -393.5 kJ/mol | -45.9 kJ/mol total enthalpy | -285.8 kJ/mol | -333.1 kJ/mol | -393.5 kJ/mol | -91.8 kJ/mol | H_initial = -618.9 kJ/mol | | H_final = -485.3 kJ/mol | ΔH_rxn^0 | -485.3 kJ/mol - -618.9 kJ/mol = 133.6 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: H_2O + NH_2CONH_2 ⟶ CO_2 + NH_3 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: H_2O + NH_2CONH_2 ⟶ CO_2 + 2 NH_3 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_2O | 1 | -1 NH_2CONH_2 | 1 | -1 CO_2 | 1 | 1 NH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) NH_2CONH_2 | 1 | -1 | ([NH2CONH2])^(-1) CO_2 | 1 | 1 | [CO2] NH_3 | 2 | 2 | ([NH3])^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 = ([H2O])^(-1) ([NH2CONH2])^(-1) [CO2] ([NH3])^2 = ([CO2] ([NH3])^2)/([H2O] [NH2CONH2])

Construct the rate of reaction expression for: H_2O + NH_2CONH_2 ⟶ CO_2 + NH_3 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: H_2O + NH_2CONH_2 ⟶ CO_2 + 2 NH_3 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_2O | 1 | -1 NH_2CONH_2 | 1 | -1 CO_2 | 1 | 1 NH_3 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) NH_2CONH_2 | 1 | -1 | -(Δ[NH2CONH2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(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[H2O])/(Δt) = -(Δ[NH2CONH2])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[NH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | urea | carbon dioxide | ammonia formula | H_2O | NH_2CONH_2 | CO_2 | NH_3 Hill formula | H_2O | CH_4N_2O | CO_2 | H_3N name | water | urea | carbon dioxide | ammonia

| water | urea | carbon dioxide | ammonia molar mass | 18.015 g/mol | 60.056 g/mol | 44.009 g/mol | 17.031 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) melting point | 0 °C | 133.5 °C | -56.56 °C (at triple point) | -77.73 °C boiling point | 99.9839 °C | 197 °C | -78.5 °C (at sublimation point) | -33.33 °C density | 1 g/cm^3 | 1.335 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 6.96×10^-4 g/cm^3 (at 25 °C) solubility in water | | very soluble | | surface tension | 0.0728 N/m | | | 0.0234 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) odor | odorless | | odorless |