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Instant cold packs, often 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 following endothermic reaction: NH4NO3(s)-->NH4 ^+(aq) + NO3^-(aq). In order to measure the enthalpy change for this reaction, 1.25 g of NH4NO3 is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 degrees C and the final temperature (after the solid dissolves) is 21.9 degrees C. Calculate the change in enthalpy for the reaction. (Use 1.0g/mL as the density of the solution and 4.18 J/g . degrees C as the specific heat capacity.)

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Answer:

The change in enthalpy is 4.1 × 10² J.

Explanation:

We can calculate the change in enthaply (ΔH°) using the following equation:

ΔH° = c . m . ΔT [1]

where,

c is the specific heat capacity of the solution

m is the mass of the solution

ΔT is the change in temperature (Tfinal - Tinitial)

We can calculate the mass, from the density formula:

[tex]\rho=\frac{m}{V} \\m = \rho . V\\m = 1.0g/mL . 25.0mL=25g[/tex]

If we replace this data in equation [1]:

[tex]\Delta H\textdegree = c.m. \Delta T\\\Delta H\textdegree = 4.18\frac{J}{g.\textdegree} .25g.(25.8 \textdegree C - 21.9 \textdegree C)\\\Delta H\textdegree =4.1 \times 10^{2} J[/tex]

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