To determine the enthalpy change \(\Delta H_{rxn}\) for the reaction, we'll go through the following steps:
1. Calculate the mass of the solution:
Given the volume of the solution is \(100.0 \, \text{mL}\) and the density is \(1.00 \, \text{g/mL}\):
[tex]\[
\text{mass of the solution} = \text{volume} \times \text{density} = 100.0 \, \text{mL} \times 1.00 \, \text{g/mL} = 100.0 \, \text{g}
\][/tex]
2. Calculate the change in temperature:
The initial temperature is \(24.0^{\circ}\text{C}\) and the final temperature is \(29.1^{\circ}\text{C}\). Therefore, the change in temperature (\(\Delta T\)) is:
[tex]\[
\Delta T = \text{final temperature} - \text{initial temperature} = 29.1^{\circ}\text{C} - 24.0^{\circ}\text{C} = 5.1^{\circ}\text{C}
\][/tex]
3. Calculate the heat absorbed by the solution (q):
We use the formula:
[tex]\[
q = \text{mass} \times \text{specific heat capacity} \times \Delta T
\][/tex]
Given the specific heat capacity is \(4.18 \, \text{J/g} \cdot {}^{\circ}\text{C}\):
[tex]\[
q = 100.0 \, \text{g} \times 4.18 \, \text{J/g} \cdot {}^{\circ}\text{C} \times 5.1^{\circ}\text{C} = 2131.8 \, \text{J}
\][/tex]
4. Convert the heat absorbed to kilojoules:
Since \(1 \, \text{kJ} = 1000 \, \text{J}\):
[tex]\[
q_{\text{kJ}} = \frac{2131.8 \, \text{J}}{1000} = 2.1318 \, \text{kJ}
\][/tex]
5. Determine the enthalpy change \(\Delta H_{rxn}\) for the reaction:
Given that the reaction is exothermic (the solution's temperature increased), the heat q reflects the enthalpy change but will be negative. The most appropriate option from the provided choices matching this value is:
[tex]\[
\Delta H_{rxn} = -2.13 \, \text{kJ}
\][/tex]
Hence, the enthalpy change for the reaction, [tex]\(\Delta H_{rxn}\)[/tex], is [tex]\(\boxed{-2.13 \, \text{kJ}}\)[/tex].
