Question

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. Since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains 1.00 \(\mathrm{kg}\) water and has a total heat capacity of \(10.84 \mathrm{kJ} / \mathrm{C},\) what is the heat capacity of the calorimeter components?

Short answer

Heat capacity (water) = \(4.18 \frac{kJ}{C}\) #tag_title# Step 2: Calculate the heat capacity of calorimeter components #tag_content# To find the heat capacity of the calorimeter components, subtract the heat capacity of water from the total heat capacity given: Heat capacity (calorimeter components) = Total heat capacity - Heat capacity (water) Heat capacity (calorimeter components) = \(10.84 \frac{kJ}{C} - 4.18 \frac{kJ}{C}\) Heat capacity (calorimeter components) = \(6.66 \frac{kJ}{C}\)

Step-by-step solution

Calculate the heat capacity of water

To calculate the heat capacity of water, we will use the mass of water and the specific heat capacity of water. The specific heat capacity of water is constant and equal to \(4.18 \frac{kJ}{kg \cdot C}\). The formula to find the heat capacity of water is: Heat capacity (water) = Mass (water) × Specific heat capacity (water) Heat capacity (water) = \(1.00 kg \times 4.18 \frac{kJ}{kg \cdot C}\)

Key concepts

Heat capacity

Heat capacity refers to the amount of heat needed to change the temperature of an object by a certain amount. It is an important concept in calorimetry, especially when working with systems like calorimeters.
The formula for heat capacity is:

• Heat capacity (C) = mass (m) × specific heat capacity (c)

Here, mass refers to the amount of substance being heated, and specific heat capacity is a property of the material itself. This makes heat capacity dependent on both the mass and the material type.
In a calorimeter, the heat capacity helps determine the total energy change involved when substances react or change state. For example, in a bomb calorimeter, the total heat capacity would include the contributions from the water and the calorimeter's structural components, as outlined in the exercise solution above.

Specific heat capacity

Specific heat capacity is a measure of how much heat energy a given mass of a substance needs to experience a specific temperature change. It reflects how much energy is needed to raise the temperature of 1 kilogram of a material by 1 degree Celsius.
Specific heat capacity is denoted by the symbol 'c' and can differ considerably among materials. For instance, water has a high specific heat capacity of about 4.18 \(\frac{kJ}{kg\cdot C}\), allowing it to absorb a lot of heat before its temperature rises significantly.
The formula involving specific heat capacity in relation to heat energy is:

• Heat energy (q) = mass (m) × specific heat capacity (c) × temperature change (ΔT)

This formula helps in calculations when dealing with energy changes, such as those observed inside a calorimeter. Understanding specific heat capacity is crucial in accurately measuring and predicting how substances will behave thermally.

Bomb calorimeter

A bomb calorimeter is a device used to measure the heat of combustion of a particular reaction. It is a robust, heat-resistant device that provides a more controlled environment for these types of measurements.
In this device, a sample is placed in a strong steel container called a "bomb," then the bomb is filled with oxygen and submerged in water inside the calorimeter. When the sample burns, the heat produced will increase the water's temperature, and since the calorimeter's total heat capacity is known, the heat of the reaction can be determined.
Key features of a bomb calorimeter include:

• The inner steel container (bomb) where the reaction occurs
• Surrounding water to absorb the heat produced
• Precise temperature measurement capabilities

The bomb calorimeter provides a closed system which is ideal for measuring reactions that can release or absorb large amounts of heat. By understanding the components involved and how they interact thermally, it becomes easier to calculate the desired thermal quantities.