Question

In earlier times, ethyl ether was commonly used as an anesthetic. It is, however, highly flammable. When five milliliters of ethyl ether, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)(d=0.714 \mathrm{~g} / \mathrm{mL}),\) are burned in a bomb calorimeter, the temperature rises from \(23.5^{\circ} \mathrm{C}\) to \(39.7^{\circ} \mathrm{C}\). The calorimeter contains \(1.200 \mathrm{~kg}\) of water and has a heat capacity of \(5.32 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). (a) What is \(q_{\mathrm{H}_{2} \mathrm{O}}\) ? (b) What is \(q_{\mathrm{cal}}\) ? (c) What is \(q\) for the combustion of \(5.00 \mathrm{~mL}\) of ethyl ether? (d) What is \(q\) for the combustion of one mole of ethyl ether?

Short answer

The mass of 5 mL of ethyl ether is 3.57 g. 2. What is the temperature change during the combustion of ethyl ether? The temperature change during the combustion of ethyl ether is 16.2°C. 3. How much heat is absorbed by the water? The heat absorbed by the water is 81.29 kJ. 4. How much heat is absorbed by the calorimeter? The heat absorbed by the calorimeter is 86.18 kJ. 5. What is the heat released by the combustion of 5 mL of ethyl ether? The heat released by the combustion of 5 mL of ethyl ether is 167.47 kJ. 6. What is the heat released by the combustion of one mole of ethyl ether? The heat released by the combustion of one mole of ethyl ether is approximately 3479.43 kJ/mol.

Step-by-step solution

Calculate the mass of ethyl ether

To find the mass of ethyl ether, we will use the formula mass = volume × density. mass = 5 mL × 0.714 g/mL = 3.57 g

Calculate the temperature change

The temperature change can be found by subtracting the initial temperature from the final temperature. ΔT = \(39.7^{\circ} \mathrm{C} - 23.5^{\circ} \mathrm{C} = 16.2 ^{\circ} \mathrm{C}\)

Calculate \(q_{\mathrm{H}_{2} \mathrm{O}}\)

To find the heat absorbed by water, we will use the formula \(q = m \times c \times \Delta T\), where \(m\) is the mass of water, \(c\) is the specific heat capacity of water, and \(\Delta T\) is the temperature change. \(q_{\mathrm{H}_{2} \mathrm{O}} = 1.200 \mathrm{~kg} \times 4.184 \mathrm{~kJ} / \mathrm{kg} \cdot { }^{\circ} \mathrm{C} \times 16.2^{\circ}\mathrm{C} = 81.29 \mathrm{~kJ}\)

Calculate \(q_{\mathrm{cal}}\)

To find the heat absorbed by the calorimeter, we will again use the formula \(q = m \times c \times \Delta T\), where \(c\) is now the heat capacity of the calorimeter and \(\Delta T\) is still the temperature change. \(q_{\mathrm{cal}} = 5.32 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} \times 16.2^{\circ} \mathrm{C} = 86.18 \mathrm{~kJ}\)

Calculate \(q_{\mathrm{combustion}}\) for 5 mL of ethyl ether

The heat released by the combustion of ethyl ether equals the total heat absorbed by both water and the calorimeter. Therefore: \(q_{\mathrm{combustion}} = q_{\mathrm{H}_{2} \mathrm{O}} + q_{\mathrm{cal}} = 81.29 \mathrm{~kJ} + 86.18 \mathrm{~kJ} = 167.47 \mathrm{~kJ}\)

Calculate moles of ethyl ether

The molar mass of ethyl ether is \(C_4H_{10}O\): \(4\times12.01 + 10\times1.01 + 16.00 = 74.12 \mathrm{~g/mol}\). To find the moles, we will use the mass we calculated in Step 1. moles = mass / molar mass = 3.57 g / 74.12 g/mol = 0.0481 mol

Calculate \(q_{\mathrm{combustion}}\) for one mole of ethyl ether

To find the heat released by the combustion of one mole of ethyl ether, we will use the ratio we found in Step 6. \(q_{\mathrm{combustion,1mol}} = \frac{167.47 \mathrm{~kJ}}{0.0481 \mathrm{~mol}} = 3479.43 \mathrm{~kJ/mol}\) The heat released by combustion of 5 mL of ethyl ether is 167.47 kJ, and the heat released by combustion of one mole of ethyl ether is approximately 3479.43 kJ/mol.

Key concepts

Heat Capacity

Understanding heat capacity is fundamental to analyzing energy changes in chemical reactions. Heat capacity represents the amount of heat energy required to raise the temperature of a substance by one degree Celsius. It is an extensive property, meaning it depends on the amount of substance being considered. A calorimeter’s heat capacity, as mentioned in the textbook exercise, accounts for all components of the calorimeter, including the water and the calorimeter itself.

Expressed mathematically, heat capacity (\(C\)) is calculated by the equation \(C = q / \Delta T\), where \(q\) is the heat added to the system, and \(\Delta T\) is the change in temperature. In the context of the exercise, the calorimeter's heat capacity is used to find the heat absorbed by the system during the combustion of ethyl ether.

Enthalpy of Combustion

Enthalpy of combustion refers to the heat released when one mole of a substance burns in the presence of oxygen. It is a key piece of information for understanding energy changes in chemical reactions, particularly combustion reactions. In calorimetry, it is measured by capturing the heat released by a known quantity of a substance and extrapolating that data to a per-mole basis.

The exercise provided walks through this process by determining the heat release from the combustion of a known volume of ethyl ether. By calculating the heat absorbed by water and the calorimeter, we can infer the total heat released by the reaction. The enthalpy of combustion is finally expressed on a molar basis by dividing the total heat by the number of moles of ethyl ether combusted, revealing the heat released per mole.

Molar Mass

The molar mass of a compound is the weight of one mole of that compound, represented in grams per mole (\(g/mol\)). It is calculated by summing up the atomic masses of the elements present in a molecule according to its chemical formula. This characteristic is critical in converting between the mass of a substance and the number of moles, which is often necessary in quantitative chemical analysis and stoichiometry.

In the textbook example, calculating the molar mass of ethyl ether is crucial for further computations, such as determining the number of moles burnt in the reaction. Once the number of moles is known, it facilitates the calculation of the heat released per mole—the enthalpy of combustion.

Specific Heat

Specific heat is the amount of heat per unit mass required to raise the temperature of the substance by one degree Celsius. Unlike the general heat capacity, specific heat is an intensive property and does not vary with the amount of the substance. In the textbook exercise, the specific heat is used to calculate the heat absorbed by the water in the bomb calorimeter.

The equation for specific heat is \(c = q / (m \times \Delta T)\), where \(c\) is the specific heat, \(q\) is the heat absorbed or released, \(m\) is the mass of the sample, and \(\Delta T\) is the temperature change. Specific heat is a critical concept in calorimetry, as substances have different capacities for storing thermal energy. The specific heat of water, often used in calorimetry, is particularly high, which is why water is a common component in calorimeters.