Calculating the Energy Released per Unit Mass

Oct 13, 2025 by miodeya.com 94 views

Introduction

A bomb calorimeter is a device used to measure the heat of combustion of a substance. It is a sealed vessel that contains the sample to be burned, an oxidizing agent, and a thermometer. When the sample is ignited, the heat released is measured, and this value is used to calculate the energy released per unit mass of the sample. In this article, we will discuss the complete combustion of a 0.350 g sample of a compound in a bomb calorimeter and calculate the energy released per unit mass of the sample.

The Experiment

A 0.350 g sample of a compound was placed in a bomb calorimeter, which has a mass of 1.20 kg and a specific heat of 3.55 J (g^-1 °C^-1). The calorimeter was then sealed, and the sample was ignited. The heat released was measured to be 14.0 kJ.

Calculating the Energy Released per Unit Mass

To calculate the energy released per unit mass of the sample, we need to subtract the heat capacity of the calorimeter from the total heat released. The heat capacity of the calorimeter is given by the product of its mass and specific heat:

C = m \times c = 1.20 \, \text{kg} \times 3.55 \, \text{J} \, \left( \text{g}^{-1} \, ^{\circ}\text{C}^{-1} \right) = 4260 \, \text{J} \, ^{\circ}\text{C}^{-1}

The heat released by the sample is 14.0 kJ, which is equal to 14000 J. To calculate the energy released per unit mass of the sample, we need to subtract the heat capacity of the calorimeter from the total heat released:

\Delta H = Q - C \times \Delta T

where $\Delta H$ is the energy released per unit mass of the sample, $Q$ is the total heat released, $C$ is the heat capacity of the calorimeter, and $\Delta T$ is the change in temperature of the calorimeter.

Since the calorimeter is sealed, the change in temperature is equal to the temperature change of the sample. Therefore, we can write:

\Delta T = \frac{Q - C \times \Delta T}{m}

where $m$ is the mass of the sample.

Rearranging the equation, we get:

\Delta T = \frac{Q}{m + C}

Substituting the values, we get:

\Delta T = \frac{14000 \, \text{J}}{0.350 \, \text{g} + 4260 \, \text{J} \, ^{\circ}\text{C}^{-1}} = 30.4 \, ^{\circ}\text{C}

Now, we can calculate the energy released per unit mass of the sample:

\Delta H = Q - C \times \Delta T = 14000 \, \text{J} - 4260 \, \text{J} \, ^{\circ}\text{C}^{-1} \times 30.4 \, ^{\circ}\text{C} = 10.3 \, \text{kJ} \, \text{g}^{-1}

Conclusion

In this article, we discussed the complete combustion of a 0.350 g sample of a compound in a bomb calorimeter and calculated the energy released per unit mass of the sample. The energy released per unit mass of the sample was found to be 10.3 kJ g^-1. This value can be used to calculate the energy released by the sample when it is burned in a bomb calorimeter.

Limitations of the Experiment

The experiment has several limitations. The bomb calorimeter is a sealed vessel, and the sample is burned in a controlled environment. This means that the experiment is not representative of real-world conditions, where the sample may be burned in a different environment. Additionally, the experiment assumes that the sample is completely burned, which may not be the case in real-world conditions.

Future Directions

The experiment can be improved by using a more accurate method to measure the heat released by the sample. Additionally, the experiment can be repeated with different samples to see if the energy released per unit mass of the sample is consistent.

References

Bomb Calorimeter, Wikipedia, https://en.wikipedia.org/wiki/Bomb_calorimeter
Heat of Combustion, Wikipedia, https://en.wikipedia.org/wiki/Heat_of_combustion

Appendix

The following table shows the calculations performed in the experiment:

Quantity	Value	Unit
Mass of sample	0.350	g
Mass of calorimeter	1.20	kg
Specific heat of calorimeter	3.55	J (g^-1 °C^-1)
Heat released by sample	14000	J
Heat capacity of calorimeter	4260	J °C^-1
Change in temperature	30.4	°C
Energy released per unit mass of sample	10.3	kJ g^-1

Frequently Asked Questions

Q: What is a bomb calorimeter?

A: A bomb calorimeter is a device used to measure the heat of combustion of a substance. It is a sealed vessel that contains the sample to be burned, an oxidizing agent, and a thermometer.

Q: How does a bomb calorimeter work?

A: When the sample is ignited, the heat released is measured, and this value is used to calculate the energy released per unit mass of the sample.

Q: What is the significance of the bomb calorimeter?

A: The bomb calorimeter is a crucial tool in chemistry and physics, allowing researchers to measure the energy released by a substance when it is burned. This information is essential in understanding the chemical properties of a substance and its potential applications.

Q: What are the limitations of the bomb calorimeter?

A: The bomb calorimeter is a sealed vessel, and the sample is burned in a controlled environment. This means that the experiment is not representative of real-world conditions, where the sample may be burned in a different environment. Additionally, the experiment assumes that the sample is completely burned, which may not be the case in real-world conditions.

Q: How can the bomb calorimeter be improved?

A: The bomb calorimeter can be improved by using a more accurate method to measure the heat released by the sample. Additionally, the experiment can be repeated with different samples to see if the energy released per unit mass of the sample is consistent.

Q: What are some common applications of the bomb calorimeter?

A: The bomb calorimeter is used in various fields, including:

Chemistry: To measure the heat of combustion of a substance and understand its chemical properties.
Physics: To study the thermodynamic properties of a substance.
Materials Science: To investigate the thermal properties of materials.
Energy: To evaluate the energy density of fuels and other energy sources.

Q: What are some common mistakes to avoid when using a bomb calorimeter?

A: Some common mistakes to avoid when using a bomb calorimeter include:

Incorrect calibration: Failing to properly calibrate the bomb calorimeter can lead to inaccurate results.
Insufficient sample preparation: Failing to properly prepare the sample can lead to incomplete combustion and inaccurate results.
Inadequate safety precautions: Failing to follow proper safety protocols can lead to accidents and injuries.

Q: How can I get started with using a bomb calorimeter?

A: To get started with using a bomb calorimeter, follow these steps:

Familiarize yourself with the instrument: Read the user manual and understand the operation of the bomb calorimeter.
Prepare the sample: Follow proper procedures to prepare the sample for combustion.
Calibrate the instrument: Ensure that the bomb calorimeter is properly calibrated before use.
Conduct the experiment: Follow the experimental procedure to measure the heat of combustion of the sample.
Analyze the results: Interpret the results and draw conclusions based on the data.

Conclusion

The bomb calorimeter is a powerful tool in chemistry and physics, allowing researchers to measure the energy released by a substance when it is burned. By understanding the principles and limitations of the bomb calorimeter, researchers can use this instrument to gain valuable insights into the chemical properties of a substance and its potential applications.