Instant cold packs used to ice athletic injuries on the field contain ammonium
nitrate and water separated by a thin plastic divider. When
the divider is broken, the ammonium nitrate dissolves according to the
endothermic reaction: $$\mathrm { NH } _ { 4 } \mathrm { NO } _ { 3 } ( s )
\longrightarrow \mathrm { NH } _ { 4 } ^ { + } ( a q ) + \mathrm { NO } _ { 3
} ^ { - } ( a q )$$ In order to measure the enthalpy change for this reaction,
1.25 g of
\(\mathrm { NH } _ { 4 } \mathrm { NO } _ { 3 }\) is dissolved in enough water
to make 25.0\(\mathrm { mL }\) of solution.
The initial temperature is \(25.8 ^ { \circ } \mathrm { C }\) , and the final
temperature (after the solid dissolves) is \(21.9 ^ { \circ } \mathrm { C }\) .
Calculate the change in enthalpy for the re-
action in kJ. (Use 1.0\(\mathrm { g } / \mathrm { mL }\) as the density of the
solution and
4.18\(\mathrm { J } / \mathrm { g } \cdot ^ { \circ } \mathrm { C }\) as the
specific heat capacity.)