Question

example 3.6: constant - pressure calorimetry ammonium nitrate (nh₄no₃, m = 80.05 g/mol) is used in cold packs to “ice” injuries. when 20.0 g of this compound dissolves in 125 g of water in a coffee - cup calorimeter, the temperature falls from 23.5 °c to 13.4 °c. determine the q for the dissolving of the compound. is the process exothermic or endothermic?

Explanation:

Step1: Calculate the mass of the solution

The mass of the solution $m$ is the sum of the mass of the compound and the mass of water.
$m = 20.0\ g+ 125\ g=145\ g$

Step2: Calculate the change in temperature $\Delta T$

$\Delta T=T_{final}-T_{initial}=13.4^{\circ}C - 23.5^{\circ}C=- 10.1^{\circ}C$

Step3: Use the specific - heat formula for the solution

Assume the specific heat capacity of the solution $c$ is approximately the same as that of water, $c = 4.18\ J/(g\cdot^{\circ}C)$. The heat absorbed or released by the solution $q$ is given by the formula $q = mc\Delta T$.
$q=(145\ g)\times(4.18\ J/(g\cdot^{\circ}C))\times(- 10.1^{\circ}C)$
$q=145\times4.18\times(-10.1)\ J$
$q=-6119.51\ J\approx - 6.12\times10^{3}\ J$

Step4: Determine the nature of the process

Since $q$ for the solution is negative, the heat is absorbed by the reaction (the dissolving of the compound). So the process is endothermic.

Answer:

$q = 6.12\times10^{3}\ J$ (the magnitude of the heat absorbed by the dissolving process), and the process is endothermic.