Problem 67 - Chemistry The Science in Context

Question

Phthalates, used to make plastics flexible, are among the most abundant industrial contaminants in the environment. Several have been shown to act as hormone mimics in humans by activating the receptors for estrogen, a female sex hormone. In characterizing the compounds completely, the value of \(\Delta H_{\text {comb }}\) for dimethyl phthalate \(\left(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{O}_{4}\right)\) was determined to be \(-4685 \mathrm{kJ} / \mathrm{mol}\). Assume that \(1.00 \mathrm{g}\) of dimethyl phthalate is combusted in a calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C}\) at \(20.215^{\circ} \mathrm{C} .\) What is the final temperature of the calorimeter?

Step-by-Step Solution

Answer

Answer: The final temperature of the calorimeter is 17.145°C.

Step 1: Calculate the moles of dimethyl phthalate combusted

To calculate the moles of dimethyl phthalate combusted, we need to use its molar mass: Dimethyl phthalate, C10H10O4, has the molar mass of 194.18 g/mol (10 * 12.01 + 10 * 1.01 + 4 * 16.00). Given that 1.00 g of dimethyl phthalate is combusted: moles of dimethyl phthalate = (1.00 g) / (194.18 g/mol) = 0.00515 mol

Step 2: Calculate the heat released during combustion

To calculate the heat released during the combustion, we can use the enthalpy of combustion and the moles of dimethyl phthalate combusted: ∆H_comb = -4685 kJ/mol Since the enthalpy of combustion is given in kJ/mol, we can multiply it by the moles of dimethyl phthalate combusted to find the heat released: q = (0.00515 mol)(-4685 kJ/mol) = -24.12 kJ Note that the negative sign indicates that the heat is released (exothermic).

Step 3: Calculate the change in temperature

We can now use the heat capacity of the calorimeter (C_calorimeter) to determine the change in temperature (∆T). The heat capacity is given as 7.854 kJ/°C. Recall that q = C∆T, where q is the heat released, C is the heat capacity, and ∆T is the change in temperature. By rearranging the equation, we obtain: ∆T = q / C_calorimeter = -24.12 kJ / 7.854 kJ/°C = -3.07 °C

Step 4: Find the final temperature of the calorimeter

We can now add the change in temperature to the initial temperature of the calorimeter to find the final temperature: T_initial = 20.215°C ∆T = -3.07°C T_final = T_initial + ∆T = 20.215°C + (-3.07°C) = 17.145°C Thus, the final temperature of the calorimeter is 17.145°C.

Key Concepts

Enthalpy of Combustion

When it comes to calorimetry, understanding the enthalpy of combustion, defined with the symbol \(\Delta H_{\text{comb}}\), is crucial.This concept helps us comprehend how much heat energy is released when one mole of a substance combusts completely. In the exercise, we encountered dimethyl phthalate as the chemical of interest.For dimethyl phthalate, the enthalpy of combustion is given as -4685 kJ/mol.The negative sign indicates that the process is exothermic, meaning heat is released during combustion.

To find the total heat released, we multiply the enthalpy of combustion by the moles of substance burned. For example, if we burn 0.00515 moles of dimethyl phthalate, the heat released is calculated as \(-4685 \text{ kJ/mol} \times 0.00515 \text{ mol} = -24.12 \text{ kJ}\). Understanding this allows us to quantify the energy changes occurring in chemical reactions.

It's essential for students to grasp this process, as it's a fundamental principle in energy conversion and applications across chemistry.

Heat Capacity

Heat capacity is another essential concept in calorimetry. It tells us how much heat a substance can absorb before experiencing a change in temperature. In the context of a calorimeter, which is an apparatus used to measure the heat of chemical reactions, heat capacity is an inherent characteristic.

A calorimeter with a high heat capacity can absorb a lot of heat before its temperature increases significantly. In this exercise, we have a calorimeter with a heat capacity of 7.854 kJ/°C.This means that for every 7.854 kJ of heat absorbed, the temperature of the calorimeter rises by 1°C.

Heat capacity is crucial because it determines how much an apparatus can withstand without significant temperature changes. For calorimetry calculations, we use the formula \(q = C\Delta T\), where \(q\) is the heat exchanged, \(C\) is the heat capacity, and \(\Delta T\) is the change in temperature. In this exercise, by knowing the heat exchanged and the calorimeter's heat capacity, we can determine the associated temperature change of the calorimeter.

Temperature Change

Temperature change (\(\Delta T\)) is one of the most straightforward yet vital calculations in calorimetry.It represents how much the temperature of our system has altered due to the heat transferred.To find the change in temperature, we rely on the equation \(q = C\Delta T\), which links heat transferred to temperature change.

For example, in our exercise, the calorimeter releases 24.12 kJ of heat during the combustion process.Using the defined heat capacity (7.854 kJ/°C), we determine the temperature change:\(\Delta T = \frac{-24.12 \text{ kJ}}{7.854 \text{ kJ/°C}} = -3.07 °C\).

This calculation shows the system's response to the released heat. A negative value indicates a decrease in temperature, which is consistent as we discuss an exothermic reaction. Understanding temperature change helps us predict how reactions affect their environments and is key to designing reactions with controlled outcomes.

Whether it's in industry or laboratory practice, mastering temperature changes in calorimetry guides effective thermal management.