Question

Toluene, \(\mathrm{C}_{7} \mathrm{H}_{8}\), is used in the manufacture of explosives such as TNT (trinitrotoluene). A \(1.500 \mathrm{~g}\) sample of liquid toluene was placed in a bomb calorimeter along with excess oxygen. When the combustion of the toluene was initiated, the temperature of the calorimeter rose from \(25.000^{\circ} \mathrm{C}\) to \(26.413^{\circ} \mathrm{C}\). The products of the combustion were \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l),\) and the heat capacity of the calorimeter was \(45.06 \mathrm{~kJ}^{\circ} \mathrm{C}^{-1}\) (a) Write the balanced chemical equation for the reaction in the calorimeter. (b) How many joules were liberated by the reaction? (c) How many joules would be liberated under similar conditions if 1.000 mol of toluene was burned?

Short answer

The balanced chemical equation is \(2 C_7H_8(l) + 17 O_2(g) \rightarrow 14 CO_2(g) + 8 H_2O(l)\). The energy liberated by the reaction is 63,679.8 J. For 1.000 mol of toluene burned, the energy liberated would be approximately 4,236,593.4 J.

Step-by-step solution

- Write the Balanced Chemical Equation

Toluene, \(C_7H_8\), burns in oxygen to form carbon dioxide and water. The balanced chemical equation for the combustion of toluene is: \[ 2 C_7H_8(l) + 17 O_2(g) \rightarrow 14 CO_2(g) + 8 H_2O(l) \]

- Calculate the Energy Released

To calculate the energy released by the reaction, use the temperature change, and the heat capacity of the calorimeter. The change in energy (\( q \) in joules) can be calculated using the formula: \[ q = C \Delta T \] where, \( C \) is the heat capacity of the calorimeter (45.06 kJ/°C) and \( \Delta T \) is the change in temperature (26.413°C - 25.000°C). Convert \( C \) to joules by multiplying with 1000. \[ q = 45.06 \mathrm{kJ/^\circ C} \times 1000 \frac{\mathrm{J}}{\mathrm{kJ}} \times (26.413 - 25.000) \mathrm{^\circ C} \] \[ q = 45.06 \times 1000 \times 1.413 \] \[ q = 45.06 \times 1000 \times 1.413 \mathrm{J} \]

- Calculate the Energy for 1 Mole of Toluene

The molar mass of toluene (\( C_7H_8 \) is 92.14 g/mol. To calculate the energy released for 1 mole of toluene burned, we determine the energy per gram from Step 2 and then multiply by the molar mass. \[ \frac{q}{mass\ of\ toluene\ in\ sample} = \frac{q}{1.500\ g} \] \[ Energy\ per\ gram\ of\ toluene = \frac{45.06 \times 1000 \times 1.413}{1.500} \mathrm{J/g} \] \[ Energy\ for\ 1\ mole\ of\ toluene = Energy\ per\ gram \times Molar\ Mass\ of\ Toluene \] \[ Energy\ for\ 1\ mole\ of\ toluene = \frac{45.06 \times 1000 \times 1.413}{1.500} \times 92.14 \mathrm{J} \]

Key concepts

Chemical Equation Balancing

Balancing a chemical equation is a fundamental skill in chemistry. It's crucial because it ensures that the law of conservation of mass is followed, meaning the same number of atoms of each element must be present on both sides of the equation. Let's take a closer look at the combustion of toluene, which is represented by the chemical formula \( C_7H_8 \).

When toluene burns in adequate supply of oxygen, \( O_2 \), it produces carbon dioxide, \( CO_2 \), and water, \( H_2O \). To accurately represent this reaction, we must balance the chemical equation so that each element appears the same number of times on both reactant and product sides. This balance is crucial not only for theoretical purposes but also for practical applications, such as calculating the amount of by-products in a chemical manufacturing process.

For example, the balanced equation provided in the step-by-step solution indicates that two moles of liquid toluene react with seventeen moles of gaseous oxygen to produce fourteen moles of carbon dioxide gas and eight moles of liquid water. Balancing this equation involves a clear understanding of stoichiometry and the ability to apply it to ensure that the equation obeys the law of conservation of mass.

Calorimetry

Calorimetry is the measurement of heat transfer from one body to another. Specifically, in a chemical context, it's used to measure the heat released or absorbed during a chemical reaction. A calorimeter is the instrument used for this process, and in the case of the toluene combustion exercise, we're dealing with a bomb calorimeter.

A bomb calorimeter is a sealed container that allows for constant-volume reactions to occur without matter loss or gain with the surroundings. The temperature change that results from the reaction is used to calculate the amount of heat (either absorbed or released). In the provided solution, the calorimeter's heat capacity, \( 45.06 kJ/^\circ C \), plays a critical role. It represents how much energy is required to raise the temperature of the entire calorimeter by one degree Celsius.

From the temperature increase observed in the reaction, the amount of heat evolved can be determined. This calculation relies on the simple relationship \( q = C \Delta T \), where \( q \) is the heat in joules, \( C \) is the heat capacity, and \( \Delta T \) is the change in temperature. By understanding calorimetry, students can foresee energy changes during various chemical processes, which is pivotal for fields like chemistry, physics, material science, and even engineering.

Enthalpy Calculation

Enthalpy, symbolized by \( H \), is a measure of the total heat content of a system and is essential in understanding energy changes during chemical reactions. Enthalpy calculations often employ calorimetry data to relate the heat transfer that occurs to the amount of substance involved in the reaction.

In this particular exercise, enthalpy is not directly measured but rather inferred from the heat released during the combustion of a known mass of toluene. To calculate the enthalpy per mole, one must consider the molar mass of toluene \( (C_7H_8) \) and the heat evolved from a known mass. The molar enthalpy change can be seen as the energy required to break bonds in the reactants minus the energy released when new bonds are formed in the products.

The step-by-step solution provides clarification by determining the energy released per gram of toluene and then extrapolating this value to a per-mole basis. Doing this calculation allows the prediction of how much heat would be released in any given amount of toluene combustion, which is particularly useful for industrial applications where toluene is used as a fuel or precursor. Through understanding enthalpy calculations, students gain deeper insight into the energy profiles of chemical reactions and the practical implications these have on real-world applications.