Question

Phthalates used as plasticizers in rubber and plastic products are believed to act as hormone mimics in humans. The value of ΔH comb for dimethylphthalate (C10H10O4) is −4685 kJ/mol. Assume 1.07 g of dimethylphthalate is combusted in a calorimeter whose heat capacity (C calorimeter is 6.15 kJ/ ∘C at 21.0∘C. What is the final temperature of the calorimeter? ∘C

Answer 1

To measure the heat capacity of a calorimeter, a standard compound with a known enthalpy of combustion is burned in a bomb calorimeter. The increase in temperature of the calorimeter is measured, and this information is used to calculate the heat capacity. The final temperature of the calorimeter can be determined using the equation Calorimeter = Bomb calorimeter × ΔT.

Step-by-step explanation:

To measure the heat capacity of the calorimeter, a standard compound with a known enthalpy of combustion is burned in a bomb calorimeter. The increase in temperature of the calorimeter is measured, and this information is used to calculate the heat capacity of the calorimeter. In this case, benzoic acid is used as the standard compound.

Using benzoic acid as the standard compound, we can determine the heat capacity of the calorimeter. The combustion of benzoic acid in a bomb calorimeter releases 26.38 kJ of heat per gram. By measuring the increase in temperature of the calorimeter, we can calculate the heat capacity using the equation: Calorimeter = Bomb calorimeter × ΔT.

In the given problem, the heat capacity of the calorimeter (C calorimeter) is 6.15 kJ/°C, and the change in temperature (ΔT) is the value we need to find. We are given the enthalpy of combustion (ΔH comb) for dimethylphthalate (-4685 kJ/mol). By using the equation Calorimeter = Bomb calorimeter × ΔT and substituting the values, we can solve for the final temperature of the calorimeter.

Answer 2

To find the final temperature of a calorimeter after the combustion of dimethylphthalate, we use the provided ΔH comb value and the mass of dimethylphthalate to calculate the heat released, then use the calorimeter's heat capacity to determine the temperature change, leading to a final temperature of 25.19°C.

Step-by-step explanation:

To calculate the final temperature of a calorimeter when dimethylphthalate is combusted, we use the information given about the combustion: ΔH comb for dimethylphthalate (C₁₀H₁₀O₄) is −4685 kJ/mol, and the mass of dimethylphthalate is 1.07 g.

The heat capacity of the calorimeter (C calorimeter) is given as 6.15 kJ/°C. The initial temperature is 21.0°C. To find the final temperature (Tfinal), we use the formula:

q = C calorimeter × ΔT

Where q is the heat released, C calorimeter is the heat capacity of the calorimeter, and ΔT is the change in temperature.

First, calculate the heat released by the combustion of 1.07 g of dimethylphthalate:

• The molar mass of dimethylphthalate (C₁₀H₁₀O₄) is 194.19 g/mol.
• Find moles of dimethylphthalate: (1.07 g) / (194.19 g/mol) = 0.00551 mol.
• Calculate the heat released (q): ΔH comb × moles = -4685 kJ/mol × 0.00551 mol = -25.8 kJ.

Using the heat released (q) and the heat capacity (C calorimeter), find ΔT:

ΔT = q / C calorimeter = -25.8 kJ / 6.15 kJ/°C = -4.19°C

Since the combustion process releases heat, the temperature of the calorimeter increases, so the negative sign indicates a release of heat. Therefore, the final temperature is:

Tfinal = Initial Temperature + ΔT = 21.0°C - (-4.19°C) = 25.19°C