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[tex]$7.5 \text{ g } KNO_3$[/tex] dissociated in [tex]$49.0 \text{ g}$[/tex] of water in a coffee cup calorimeter. The thermometer reading changed from [tex]$20.4^{\circ} C$[/tex] to [tex]$9.7^{\circ} C$[/tex]. What is the heat of the reaction?

[tex]\[
\begin{array}{c}
KNO_3 \rightarrow K^+ + NO_3^- \\
C_{\text{soln}} = 4.18 \text{ J/g} \cdot {^{\circ} C} \quad C_{\text{cal}} = 6.5 \text{ J/} {^{\circ} C}
\end{array}
\][/tex]


Sagot :

To determine the heat of the reaction when [tex]\( 7.5 \, \text{g} \)[/tex] of [tex]\( \text{KNO}_3 \)[/tex] dissociates in [tex]\( 49.0 \, \text{g} \)[/tex] of water in a coffee cup calorimeter, where the temperature changes from [tex]\( 20.4\,^\circ \text{C} \)[/tex] to [tex]\( 9.7\,^\circ \text{C} \)[/tex], follow the steps below:

### Step-by-Step Solution

1. Identify the temperature change: Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):

[tex]\[ \Delta T = \text{final temperature} - \text{initial temperature} \][/tex]

[tex]\[ \Delta T = 9.7\, ^\circ \text{C} - 20.4\, ^\circ \text{C} = -10.7\, ^\circ \text{C} \][/tex]

2. Calculate the heat absorbed by the solution: Use the given specific heat capacity of the solution ([tex]\( C_{\text{soln}} = 4.18 \, \text{J/g} ^\circ \text{C} \)[/tex]) and the mass of the water ([tex]\( 49.0 \, \text{g} \)[/tex]):

[tex]\[ q_{\text{solution}} = \text{mass of water} \times C_{\text{soln}} \times \Delta T \][/tex]

Substitute the values:

[tex]\[ q_{\text{solution}} = 49.0 \, \text{g} \times 4.18 \, \text{J/g} \, ^\circ \text{C} \times (-10.7 \, ^\circ \text{C}) \][/tex]

[tex]\[ q_{\text{solution}} = -2191.574 \, \text{J} \][/tex]

3. Calculate the heat absorbed by the calorimeter: Use the calorimeter heat capacity ([tex]\( C_{\text{cal}} = 6.5 \, \text{J/} ^\circ \text{C} \)[/tex]):

[tex]\[ q_{\text{calorimeter}} = C_{\text{cal}} \times \Delta T \][/tex]

Substitute the values:

[tex]\[ q_{\text{calorimeter}} = 6.5 \, \text{J/} ^\circ \text{C} \times (-10.7 \, ^\circ \text{C}) \][/tex]

[tex]\[ q_{\text{calorimeter}} = -69.55 \, \text{J} \][/tex]

4. Calculate the total heat of the reaction: Sum the heat absorbed by the solution and the calorimeter:

[tex]\[ q_{\text{reaction}} = q_{\text{solution}} + q_{\text{calorimeter}} \][/tex]

[tex]\[ q_{\text{reaction}} = -2191.574 \, \text{J} + (-69.55 \, \text{J}) \][/tex]

[tex]\[ q_{\text{reaction}} = -2261.124 \, \text{J} \][/tex]

### Result

The heat of the reaction is [tex]\(-2261.124 \, \text{J}\)[/tex], indicating an endothermic process since the heat is absorbed (indicated by the negative sign).
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