To determine the heat of the reaction ([tex]\( q_{\text{rxn}} \)[/tex]), we follow a series of steps to calculate the heat absorbed by the solution upon the dissociation of sulfuric acid ([tex]\( H_2SO_4 \)[/tex]) in water, considering the given information. Here's a detailed step-by-step solution:
### Step 1: Calculate the Total Mass of the Solution
The total mass of the solution is the sum of the mass of [tex]\( H_2SO_4 \)[/tex] and the mass of water.
Given:
- Mass of [tex]\( H_2SO_4 \)[/tex] = [tex]\( 19.64 \)[/tex] grams
- Mass of water = [tex]\( 100.0 \)[/tex] grams
[tex]\[ \text{Total mass} = 19.64 \, \text{grams} + 100.0 \, \text{grams} = 119.64 \, \text{grams} \][/tex]
### Step 2: Calculate the Change in Temperature ([tex]\( \Delta T \)[/tex])
The change in temperature ([tex]\( \Delta T \)[/tex]) is the difference between the final temperature and the initial temperature.
Given:
- Initial temperature = [tex]\( 23.12 \, ^\circ \text{C} \)[/tex]
- Final temperature = [tex]\( 57.30 \, ^\circ \text{C} \)[/tex]
[tex]\[ \Delta T = 57.30 \, ^\circ \text{C} - 23.12 \, ^\circ \text{C} = 34.18 \, ^\circ \text{C} \][/tex]
### Step 3: Calculate the Heat of the Reaction ([tex]\( q_{\text{rxn}} \)[/tex])
To find [tex]\( q_{\text{rxn}} \)[/tex], we use the formula for heat absorbed or released by a solution:
[tex]\[ q_{\text{rxn}} = \text{Total mass} \times c_{\text{soln}} \times \Delta T \][/tex]
Where:
- [tex]\( \text{Total mass} = 119.64 \, \text{grams} \)[/tex]
- [tex]\( c_{\text{soln}} \)[/tex] (specific heat capacity of the solution) = [tex]\( 3.50 \, \text{J/g} \cdot ^\circ \text{C} \)[/tex]
- [tex]\( \Delta T = 34.18 \, ^\circ \text{C} \)[/tex]
Substitute the values into the equation:
[tex]\[ q_{\text{rxn}} = 119.64 \, \text{grams} \times 3.50 \, \text{J/g} \cdot ^\circ \text{C} \times 34.18 \, ^\circ \text{C} \][/tex]
### Step 4: Calculation
Multiplying these values together we get:
[tex]\[ q_{\text{rxn}} \approx 119.64 \times 3.50 \times 34.18 \][/tex]
[tex]\[ q_{\text{rxn}} \approx 14312.53 \, \text{J} \][/tex]
### Final Answer
The heat of the reaction ([tex]\( q_{\text{rxn}} \)[/tex]) is:
[tex]\[ q_{\text{rxn}} \approx 14312.53 \, \text{J} \][/tex]
