Question

use NH2CONH2(s), is manufactured on a large scale and used as a fertilizer. To investigate its properties a student places 120.0 mL Of water at 25.0°C into a coffee cup Caloura metre and immerses a thermometer in the water. After about a minute, the student add 5.0 g Of solid urea to the water and measures the temperature of the solution as the urea dissolves. Temperature drops to 22.9°C.

a) calculate the molar enthalpy of solution for urea an H2CONH2(s)

b) Write the thermochemical equation for this reaction

Answer 1

a) The molar enthalpy of solution for urea will be $\Delta H^°_{solv}$ and can be calculated from the heat on the calorimeter because the heat absorbed or given by the water will be the same energy required for the solvation of the solute (urea):

$Q_{solv}=-Q_{H_2O} \\n_{urea}\Delta H^°_{solv}=m_{urea}\Delta H^°_{solv}/M_{urea}=-m_{H_2O}C_{H_2O}\Delta T \\ \text{ } \\ \implies \Delta H^°_{solv}=-\cfrac{m_{H_2O}C_{H_2O}(T_f-T_i) M_{urea}}{m_{urea}}$

We proceed to substitute to find the molar enthalpy of solution considering that 120 mL of water are 120 g of water and M_urea is the molar mass of urea (60 g/mol) and that for water C=4.184 J/g °C:

$\Delta H^°_{solv}=-\cfrac{(120\text{ g water})(4.184 \frac{J}{\text{g water}°C})((22.9-25)°C)(60\frac{\text{ g urea}}{\text{mol urea}})}{5 \text{ g urea}}$

$\Delta H^°_{solv}=12652.416\frac{J}{\text{mol urea}}=12.652\frac{kJ}{\text{mol urea}}$

In conclusion, the molar enthalpy of the solution of urea will be +12.652 kJ/mol (thus this is an endothermic reaction).

b) The thermochemical equation for this reaction will be (where Q is the heat added to the system because it is an endothermic process):

$NH_2CONH_{2(s)} +2H_2O_{(l)} +Q\to NH^+_3CONH^+_{3(aq)}+2OH^-_{(aq)}; \Delta H^°_{solv}\gt0$

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.