Problem 60 - Chemistry The Central Science

Question

Under constant-volume conditions, the heat of combustion of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) ) is 26.38 \(\mathrm{kJ} / \mathrm{g} .\) A 2.760 -g sample of \right. benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.60 to \(29.93^{\circ} \mathrm{C}\) (a) What is the total heat capacity of the calorimeter? \(\mathrm{b}\) ) \(\mathrm{A} 1.440\) -g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 22.14 to \(27.09^{\circ} \mathrm{C} .\) What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Step-by-Step Solution

Answer

The total heat capacity of the calorimeter is 8.74 kJ/°C. The heat of combustion per gram of the new substance is 30.04 kJ/g. If a portion of water in the calorimeter is lost, the heat capacity of the calorimeter would decrease, possibly affecting the measured change in temperature and the accuracy of calculations.

Step 1: Calculate the heat of combustion for the benzoic acid sample

The heat of combustion of benzoic acid is given as 26.38 kJ/g. To find the heat of combustion for the 2.760 g sample, we can use the following formula: Heat = mass × heat of combustion per gram \(q_{benzoic\_acid} = m \times H\) where q is the heat, m is the mass, and H is the heat of combustion per gram. \(q_{benzoic\_acid} = 2.760 \times 26.38 = 72.8072 kJ\)

Step 2: Calculate the total heat capacity of the calorimeter

We can use the change in temperature for the calorimeter to calculate its total heat capacity. The change in temperature is the final temperature minus the initial temperature: ΔT = T_final - T_initial ΔT = \(29.93^{\circ} \mathrm{C} - 21.60^{\circ} \mathrm{C} = 8.33^{\circ} \mathrm{C}\) Using the heat of the benzoic acid sample and the change in temperature, we can find the total heat capacity C of the calorimeter: C = q/ΔT C = 72.8072 kJ / 8.33 °C C = 8.74 kJ/°C

Step 3: Calculate the heat transfer of the new substance

Next, we can find the heat transfer for the new substance using the change in temperature of the calorimeter: ΔT = T_final - T_initial ΔT = \(27.09^{\circ} \mathrm{C} - 22.14^{\circ} \mathrm{C} = 4.95^{\circ} \mathrm{C}\) Now, using the total heat capacity of the calorimeter found in step 2 and the change in temperature, we can find the heat transfer of the new substance: q = C × ΔT q = 8.74 kJ/°C × 4.95 °C q = 43.261 kJ

Step 4: Calculate the heat of combustion per gram of the new substance

Now that we have the heat transfer of the new substance, we can find the heat of combustion per gram. We are given that the mass of the new substance is 1.440 g: Heat of combustion per gram (H) = q / m H = 43.261 kJ / 1.440 g H = 30.04 kJ/g

Step 5: Discuss the effect of water loss on the calorimeter's heat capacity

In case a portion of water in the calorimeter is lost, the heat capacity of the calorimeter would decrease. This is because water has a specific heat capacity and, as such, contributes to the overall heat capacity of the calorimeter. If less water is present, the calorimeter will absorb less heat, resulting in a lower heat capacity. However, this would not directly affect the heat of combustion of either substance, though it may affect the measured change in temperature and result in less accurate calculations.

Key Concepts

Heat of Combustion

Heat of combustion is a crucial concept in calorimetry. It refers to the amount of energy released when a compound undergoes complete combustion in the presence of oxygen.
This process is important in determining how much energy can be obtained from a fuel or a chemical substance. In the context of this exercise, the heat of combustion is our main measure to calculate how the energy of a substance like benzoic acid is converted to heat.

When you know the heat of combustion, you can determine the heat involved using the formula:

• Heat (q) = mass (m) × heat of combustion per gram (H)

In our exercise, we used the heat of combustion value of 26.38 kJ/g for benzoic acid, showing how the mass of the substance directly affects the total heat released.

Heat Capacity

Heat capacity is a term you'll often encounter in studies involving temperature changes. Essentially, it describes the amount of heat needed to change an object's temperature by a certain amount.
Think of it as an indicator of how well a substance can absorb and store heat. The higher the heat capacity, the more energy it can hold without drastically changing its temperature.

In this solution:

• We calculated the total heat capacity of a bomb calorimeter.
• This was key to determining how much heat the calorimeter absorbed when a sample was burned.

The formula used was:

• Total Heat Capacity (C) = Heat (q) / Temperature Change (ΔT)

It was given that the benzoic acid combustion raised the calorimeter temperature from 21.60°C to 29.93°C, allowing us to calculate the calorimeter's heat capacity as 8.74 kJ/°C.

Bomb Calorimeter

The bomb calorimeter is a device used to measure the heat of combustion of a substance. It's a special type of calorimeter that operates under constant volume conditions.
This instrument is designed to withstand the high pressure generated when a sample is burned, providing an isolated environment to accurately measure the energy transfer.

Here's why a bomb calorimeter is effective:

• It keeps gases produced during the combustion inside, ensuring complete combustion.
• The high-strength container prevents heat loss to the surroundings, keeping the environment controlled.

The bomb calorimeter is essential for precisely determining the heat capacity of the calorimeter system when a known energy-producing reaction occurs.

Temperature Change

Temperature change is one of the easiest ways to observe energy transfer in calorimetry. When a sample is burned, it releases energy in the form of heat, causing the temperature of the surrounding system (like a calorimeter) to increase.
This change in temperature indicates how much energy was transferred during the reaction.

In our exercise, evaluating temperature change was critical:

• For the benzoic acid, the temperature rose from 21.60°C to 29.93°C.
• For the new substance, a rise from 22.14°C to 27.09°C was noticed.

Each temperature change helps calculate the specific heat transfer of the reaction, revealing how much energy was released by combustion.