madey21
Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

What temperature increase would be expected if the same [tex]$1.200 \, \text{g}$[/tex] sample of benzoic acid were combusted when the calorimeter contained [tex]$1.00 \, \text{kg}$[/tex] of water?

[tex]\[
\begin{aligned}
q_{\text{rxn}} & = -31.66 \, \text{kJ} \\
C_{\text{cal (dry)}} & = 2.39 \, \text{kJ/}^{\circ}\text{C} \\
-q_{\text{rxn}} & = q_{\text{cal}} = \left[ C_{\text{cal, dry}} (\Delta T) + C_{\text{cal, } H_2O} (\Delta T) \right] \\
q_{\text{cal}} & = \left[ C_{\text{cal, dry}} (\Delta T) + (m_{H_2O}) (c_{H_2O}) (\Delta T) \right]
\end{aligned}
\][/tex]

Combine like terms using [tex] \Delta T [/tex]:

[tex]\[
31.66 \, \text{kJ} = \left[ 2.39 \, \text{kJ/}^{\circ}\text{C} + (1.00 \, \text{kg} \times 4.184 \, \text{kJ/kg}^{\circ}\text{C}) \right] (\Delta T)
\][/tex]

[tex]\[
\Delta T = [?] \, ^{\circ}\text{C}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's solve this step-by-step.

Given:
[tex]\[ q_{\text{rxn}} = -31.66 \, \text{kJ} \][/tex]
[tex]\[ C_{\text{cal, dry}} = 2.39 \, \text{kJ}/{^\circ}\text{C} \][/tex]
[tex]\[ m_{\text{H}_2\text{O}} = 1.00 \, \text{kg} \][/tex]
[tex]\[ c_{\text{H}_2\text{O}} = 4.184 \, \text{kJ}/(\text{kg} \cdot {^\circ}\text{C}) \][/tex]

We need to calculate the temperature increase [tex]\( \Delta T \)[/tex] expected when the sample of benzoic acid is combusted in the calorimeter that contains 1.00 kg of water.

First, let's express the combined heat capacity term:

[tex]\[ C_{\text{total}} = C_{\text{cal, dry}} + (m_{\text{H}_2\text{O}} \cdot c_{\text{H}_2\text{O}}) \][/tex]

Substituting the given values:

[tex]\[ C_{\text{total}} = 2.39 \, \text{kJ}/{^\circ}\text{C} + (1.00 \, \text{kg} \cdot 4.184 \, \text{kJ}/(\text{kg} \cdot {^\circ}\text{C})) \][/tex]

[tex]\[ C_{\text{total}} = 2.39 \, \text{kJ}/{^\circ}\text{C} + 4.184 \, \text{kJ}/{^\circ}\text{C} \][/tex]

[tex]\[ C_{\text{total}} = 6.574 \, \text{kJ}/{^\circ}\text{C} \][/tex]

Now, using the energy conservation equation, we know that the heat released by the reaction [tex]\( q_{\text{rxn}} \)[/tex] will be absorbed by the calorimeter and the water, causing a temperature change [tex]\(\Delta T\)[/tex]:

[tex]\[ q_{\text{cal}} = C_{\text{total}} \cdot \Delta T \][/tex]

Since [tex]\( q_{\text{cal}} = -q_{\text{rxn}} \)[/tex]:

[tex]\[ 31.66 \, \text{kJ} = 6.574 \, \text{kJ}/{^\circ}\text{C} \cdot \Delta T \][/tex]

Solving for [tex]\(\Delta T\)[/tex]:

[tex]\[ \Delta T = \frac{31.66 \, \text{kJ}}{6.574 \, \text{kJ}/{^\circ}\text{C}} \][/tex]

[tex]\[ \Delta T \approx 4.816 \, {^\circ}\text{C} \][/tex]

Thus, the expected temperature increase [tex]\(\Delta T\)[/tex] would be approximately 4.816°C.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.