To determine the final temperature of the calorimeter after the combustion of dimethylphthalate, we need to follow these steps:

1. Calculate the number of moles of dimethylphthalate ($C_{10}H_{10}O_4$) combusted.

Given:

• Mass of dimethylphthalate, $m = 0.940 \, \text{g}$
• Molar mass of dimethylphthalate, $M = 194.19 \, \text{g/mol}$ (calculated using the molecular formula)

$\text{Moles of dimethylphthalate} = \frac{m}{M} = \frac{0.940 \, \text{g}}{194.19 \, \text{g/mol}} \approx 0.00484 \, \text{mol}$

2. Calculate the heat released by the combustion of dimethylphthalate.

Given:

• Heat of combustion, $\Delta H_{\text{comb}} = -4685 \, \text{kJ/mol}$

$\text{Heat released} = \text{moles} \times \Delta H_{\text{comb}} = 0.00484 \, \text{mol} \times (-4685 \, \text{kJ/mol}) \approx -22.68 \, \text{kJ}$

3. Calculate the temperature change of the calorimeter.

Given:

• Heat capacity of the calorimeter, $C_{\text{calorimeter}} = 7.65 \, \text{kJ/°C}$

The heat released by the reaction is absorbed by the calorimeter, causing an increase in its temperature.

$q = C_{\text{calorimeter}} \times \Delta T$

$\Delta T = \frac{q}{C_{\text{calorimeter}}} = \frac{-22.68 \, \text{kJ}}{7.65 \, \text{kJ/°C}} \approx -2.96 \, \text{°C}$

4. Determine the final temperature of the calorimeter.

Given:

• Initial temperature of the calorimeter, $T_{\text{initial}} = 20.5 \, \text{°C}$

Since $q$ is negative, it indicates heat is released by the system, causing an increase in temperature.

$T_{\text{final}} = T_{\text{initial}} + \Delta T = 20.5 \, \text{°C} + 2.96 \, \text{°C} \approx 23.46 \, \text{°C}$

So, the final temperature of the calorimeter is approximately 23.46°C.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. What would be the final temperature if twice the amount of dimethylphthalate was combusted?
2. How would the final temperature change if the calorimeter had a heat capacity of 10 kJ/°C?
3. What is the significance of the sign of $\Delta H_{\text{comb}}$ in this context?
4. How do you calculate the molar mass of a compound like dimethylphthalate?
5. What is the role of a calorimeter in measuring heat changes during chemical reactions?

Tip: When performing calorimetry calculations, always ensure that the heat capacity and temperature change are consistent in terms of units, to avoid errors in determining the final temperature.