Problem 70 - General Chemistry

Question

A sample of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), weighing \(3.51 \mathrm{~g}\) was burned in an excess of oxygen in a bomb calorimeter. The temperature of the calorimeter rose from \(25.00^{\circ} \mathrm{C}\) to \(37.18^{\circ} \mathrm{C}\). If the heat capacity of the calorimeter and contents was \(12.05 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\), what is the value of \(q\) for burning \(1.25 \mathrm{~mol}\) of benzene at constant volume and \(25.00^{\circ} \mathrm{C} ?\) The reaction is $$ \mathrm{C}_{6} \mathrm{H}_{6}(l)+\frac{15}{2} \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) $$

Step-by-Step Solution

Answer

The heat released for burning 1.25 mol of benzene is 4076.38 kJ.

Step 1: Calculate Temperature Change

Determine the temperature change of the calorimeter, \( \Delta T \). The initial temperature is \(25.00^{\circ} \mathrm{C} \) and the final temperature is \(37.18^{\circ} \mathrm{C} \).\[ \Delta T = 37.18^{\circ} \mathrm{C} - 25.00^{\circ} \mathrm{C} = 12.18^{\circ} \mathrm{C} \]

Step 2: Calculate Heat Released by Combustion

Use the formula \( q = C \times \Delta T \) to find the heat released in the calorimeter, where \( C \) is the heat capacity (\(12.05 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} \)).\[ q = 12.05 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} \times 12.18^{\circ} \mathrm{C} = 146.529 \mathrm{~kJ} \]This is the heat released from burning \(3.51 \mathrm{~g}\) of benzene.

Step 3: Calculate Moles of Benzene Burned

Determine the moles of benzene using its molar mass (\( \mathrm{C}_{6} \mathrm{H}_{6} \) has a molar mass of \(78.11 \mathrm{~g/mol} \)).\[ \text{Moles of } \mathrm{C}_{6} \mathrm{H}_{6} = \frac{3.51 \mathrm{~g}}{78.11 \mathrm{~g/mol}} = 0.0449 \mathrm{~mol} \]

Step 4: Calculate Heat per Mole of Benzene

Calculate the heat released per mole of benzene burned.\[ \text{Heat per mole} = \frac{146.529 \mathrm{~kJ}}{0.0449 \mathrm{~mol}} = 3261.1 \mathrm{~kJ/mol} \]This is the heat released for burning 1 mole of benzene.

Step 5: Calculate Heat for 1.25 Mol of Benzene

Calculate the heat released for burning 1.25 mol of benzene using the heat per mole.\[ q_{1.25 \text{ mol}} = 1.25 \mathrm{~mol} \times 3261.1 \mathrm{~kJ/mol} = 4076.38 \mathrm{~kJ} \]

Key Concepts

Bomb Calorimeter

The bomb calorimeter is an essential device in calorimetry. It allows us to measure the heat released during a chemical reaction. In this case, benzene combusts in excess oxygen. The entire reaction occurs in a sealed container known as a 'bomb.' This container is submerged in a water-filled calorimeter to heat exchange exothermically or endothermically.
The bomb calorimeter, therefore, is ideal for studying reactions with gases or those requiring constant volume.
Key points to remember:

• The bomb calorimeter measures the heat (also noted as q) of combustion reactions.
• It maintains a constant volume, differing it from other calorimeters like coffee-cup types.
• Usually used for reactions involving high temperatures and pressures.

This exercise's setup used a bomb calorimeter to burn benzene, revealing the heat change from the combustion reaction. By calculating the heat absorbed by the calorimeter, we obtained insights into the energy changes involved.

Heat Capacity

Heat capacity is a crucial concept in thermodynamics. It denotes the amount of heat required to change the temperature of a system by one degree Celsius. Calculating heat capacities involves using the equation: \[q = C \times \Delta T\] Where:

• \(q\) represents the heat absorbed or released.
• \(C\) is the calorimeter's heat capacity.
• \(\Delta T\) is the change in temperature.

In our scenario, the calorimeter's heat capacity was known to be \(12.05 \text{ kJ/}^\circ \text{C}\). This value ensures accuracy in determining the reaction's heat flow. Recognize that higher heat capacity indicates a more considerable amount of heat is needed to change the calorimeter's temperature, reflecting an instrument's ability to absorb heat. Understanding heat capacity is critical for translating temperature changes into quantitative heat changes. It is pivotal when determining energy changes, like in our combustion experiment.

Enthalpy Change

Enthalpy change is a core concept when studying chemical reactions. It refers to the total heat content change in a system at constant pressure. However, in bomb calorimetry, reactions occur at a constant volume, which connects to the conservation of energy principle. This allows us to use the heat absorbed to find enthalpy changes specific to the reaction's conditions. For the exercise at hand, we initially calculated the reaction's temperature change and then used it to find the heat change for the known mass of benzene. Following the setup, we computed the heat change per mole of benzene, leading to the final calculation of heat change for a given number of moles (1.25 mol in this case).

• This helped us understand the exothermic nature of the combustion reaction.
• Quantitatively translating temperature change into energy terms gave us insight into handling reactions quantitatively.

The enthalpy change provides much-needed energy transfer information, essential for chemical process understanding.