To determine the heat of the reaction ([tex]\( q_{\text{rxn}} \)[/tex]), we will follow a series of steps to calculate it based on the given data. Here’s a detailed, step-by-step solution:
1. Initial Data:
- Mass of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]: [tex]\( 19.64 \)[/tex] grams
- Mass of water: [tex]\( 100.0 \)[/tex] grams
- Specific heat capacity of the solution ([tex]\( C_{\text{soln}} \)[/tex]): [tex]\( 3.50 \)[/tex] J/g°C
- Initial temperature: [tex]\( 23.12 \)[/tex] °C
- Final temperature: [tex]\( 57.30 \)[/tex] °C
2. Calculate Total Mass of the Solution:
The total mass of the solution is the sum of the mass of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] and the mass of water:
[tex]\[
\text{Total mass of solution} = \text{mass}_{\text{H}_2\text{SO}_4} + \text{mass}_{\text{water}}
\][/tex]
[tex]\[
\text{Total mass of solution} = 19.64 \, \text{grams} + 100.0 \, \text{grams} = 119.64 \, \text{grams}
\][/tex]
3. Calculate the Change in Temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[
\Delta T = \text{final temperature} - \text{initial temperature}
\][/tex]
[tex]\[
\Delta T = 57.30 \, °C - 23.12 \, °C = 34.18 \, °C
\][/tex]
4. Calculate the Heat of the Reaction ([tex]\( q_{\text{rxn}} \)[/tex]) Using [tex]\( q = mc\Delta T \)[/tex]:
[tex]\[
q_{\text{rxn}} = \text{total mass of solution} \times \text{specific heat capacity of solution} \times \Delta T
\][/tex]
[tex]\[
q_{\text{rxn}} = 119.64 \, \text{grams} \times 3.50 \, \text{J/g°C} \times 34.18 \, °C
\][/tex]
[tex]\[
q_{\text{rxn}} = 119.64 \times 3.50 \times 34.18 = 14312.53 \, \text{J}
\][/tex]
The heat of the reaction [tex]\( q_{\text{rxn}} \)[/tex] is positive because the temperature of the solution increased, indicating that the reaction is exothermic and heat was released into the surroundings.
Thus, the heat of the reaction is:
[tex]\[ +14312.53 \, \text{J} \][/tex]
