Sure, let's go through the detailed solution to determine the heat given off in the reaction using the data provided:
1. Given Values:
- Volume of [tex]\( H_2SO_4 \)[/tex]: [tex]\( 40.0 \, \text{mL} \)[/tex]
- Concentration of [tex]\( H_2SO_4 \)[/tex]: [tex]\( 1.00 \, \text{M} \)[/tex]
- Volume of [tex]\( NaOH \)[/tex]: [tex]\( 80.0 \, \text{mL} \)[/tex]
- Concentration of [tex]\( NaOH \)[/tex]: [tex]\( 1.00 \, \text{M} \)[/tex]
- Initial Temperature: [tex]\( 20.00 \, ^\circ\text{C} \)[/tex]
- Final Temperature: [tex]\( 29.20 \, ^\circ\text{C} \)[/tex]
- Mass of the solution: [tex]\( 120.00 \, \text{g} \)[/tex]
- Specific Heat Capacity ([tex]\( C_p \)[/tex]): [tex]\( 4.184 \, \text{J/g} \cdot ^\circ\text{C} \)[/tex]
2. Calculate the Change in Temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{Final Temperature} - \text{Initial Temperature}
\][/tex]
[tex]\[
\Delta T = 29.20 \, ^\circ\text{C} - 20.00 \, ^\circ\text{C}
\][/tex]
[tex]\[
\Delta T = 9.20 \, ^\circ\text{C}
\][/tex]
3. Calculate the Heat Given Off in the Reaction (q):
We use the formula [tex]\( q = m \cdot C_p \cdot \Delta T \)[/tex]
[tex]\[
q = 120.00 \, \text{g} \cdot 4.184 \, \text{J/g} \cdot ^\circ\text{C} \cdot 9.20 \, ^\circ\text{C}
\][/tex]
4. Calculate q in Joules:
[tex]\[
q = 120.00 \, \text{g} \cdot 4.184 \, \text{J/g} \cdot ^\circ\text{C} \cdot 9.20 \, ^\circ\text{C}
\][/tex]
[tex]\[
q = 4619.136 \, \text{J}
\][/tex]
5. Convert the Heat from Joules to Kilojoules (kJ):
[tex]\[
\text{Heat given off (in kJ)} = \frac{4619.136 \, \text{J}}{1000}
\][/tex]
[tex]\[
\text{Heat given off} = 4.619136 \, \text{kJ}
\][/tex]
6. Final Answer:
The heat given off in the reaction is approximately [tex]\( 4.62 \, \text{kJ} \)[/tex].
Hence, the correct choice from the given options would be:
[tex]\[ 4.62 \, \text{kJ} \][/tex]
