Question

A sample gives off 5228 cal when burned in a bomb calorimeter. The temperature of the calorimeter assembly increases by \(4.39^{\circ} \mathrm{C} .\) Calculate the heat capacity of the calorimeter, in kilojoules per degree Celsius.

Short answer

The value obtained after performing the calculations in step 2 will be the heat capacity of the calorimeter, in kJ/°C.

Step-by-step solution

Convert Calories to Kilojoules

Knowing that 1 calorie is approximately equivalent to 0.004184 kilojoules, let's firstly convert the heat emitted by the sample from calories to kilojoules. Multiply the given value of 5228 cal by 0.004184 kJ/cal.

Calculate the heat capacity

Next, having the heat absorbed by the calorimeter in kilojoules and the calorimeter's temperature increase, let's use the formula of heat capacity \(C = \frac{q}{\Delta T}\), where \(q\) represents the heat absorbed by the calorimeter (in kJ) and \(\Delta T\) is the change in temperature (°C). Hence, the heat capacity is obtained by dividing the heat in kJ by the change in temperature in °C.

Key concepts

Understanding Heat Capacity

Heat capacity is a fundamental concept when studying thermal processes, such as those occurring in a bomb calorimeter. It measures the amount of heat required to change the temperature of a substance by a given amount, typically one degree Celsius. Heat capacity is expressed in units of energy per degree, like kilojoules per degree Celsius (kJ/°C).

In the context of the bomb calorimeter, heat capacity helps us understand and measure how much heat the calorimeter absorbs during a reaction. When a sample burns inside the calorimeter, it releases heat, leading to a temperature increase. By measuring this temperature change, we can calculate the calorimeter's heat capacity, giving us valuable insights into the energy content of the sample.

To calculate heat capacity, you use the formula:

• \( C = \frac{q}{\Delta T} \)

where:\( q \) represents the amount of heat absorbed (in kilojoules) and \( \Delta T \) is the change in temperature (in °C). Understanding this relationship is key to interpreting calorimetry data and determining the energy values of various materials.

The Role of Calorimeter

A calorimeter is an essential device used in experiments that measure heat changes during chemical reactions. Specifically, a bomb calorimeter is designed to manage controlled, high-pressure environments where substances combust, providing highly accurate measurements of heat exchange.

The importance of a bomb calorimeter lies in its ability to insulate the reaction, minimizing heat loss to the environment. This ensures that the heat measured by the device closely approximates the actual heat generated by the reaction. The calorimeter consists of a container that holds the sample, water surrounding the container, and a means to measure the temperature change. The entire setup helps field exact energy measurements from reactions occurring within.

Understanding how a calorimeter functions is crucial for experiments where precise heat measurements are necessary, such as determining the energy content of fuels or food samples. The calorimeter's design helps retain stability and consistency in experiments, allowing scientists to gather repeatable and reliable data.

Concept of Heat Conversion

Heat conversion is an important concept in the study of calorimetry, as it involves transforming the energy released or absorbed by a sample into a measurable quantity. In this context, converting units of measurement, such as calories to kilojoules, is a fundamental step.

A calorie is a traditional unit of heat energy, while the joule is the standard unit in the International System of Units. When performing experiments, it's often necessary to convert between these units to maintain consistency and comparability of data. In the exercise provided, the conversion factor is that 1 calorie equals approximately 0.004184 kilojoules.

Understanding and performing these conversions empowers us to make accurate calculations about the energy content of materials. This process ensures that the experimental observations can be correctly interpreted within the broader scope of scientific research and applications.