Question

Performance Design a simple calorimeter investigation to determine the molar enthalpy of fusion of water. Use the following materials: a large plastic-foam cup with cover, a thermometer, a balance, water at room temperature, and an ice cube. Allow your teacher to review your design. Then carry out the investigation, and write a laboratory report including your calculations and a comparison of your quantitative results with known values. Try to account for any disagreements between the experimental and actual values.

Short answer

Set up a foam cup calorimeter, measure initial temperature, add ice, and record the final temperature. Calculate heat absorbed and determine molar enthalpy of fusion. Finally, compare with known value.

Step-by-step solution

- Set Up the Calorimeter

Place the plastic-foam cup on a flat surface and fill it halfway with water at room temperature. Cover the cup with its cover and insert the thermometer through the cover opening.

- Measure the Initial Temperature

Record the initial temperature of the water using the thermometer. Let it stabilize for a few minutes to ensure an accurate reading.

- Measure the Mass of Ice

Weigh the ice cube using the balance. Record its mass accurately as you will need it for calculations later.

- Add Ice to Water

Gently place the ice cube into the water in the foam cup. Ensure that no water spills out while doing this.

- Record Temperature Change

Monitor and record the temperature of the water as the ice melts completely. Make sure to continuously stir the water gently for uniform temperature distribution.

- Calculate Heat Absorbed by Ice

Use the formula: \[ q = m_w c_w (T_{f} - T_{i}) \] where: \( q \) is the heat absorbed by the ice, \( m_w \) is the mass of the water, \( c_w \) is the specific heat capacity of water (4.18 J/g°C), \( T_{f} \) is the final temperature, and \( T_{i} \) is the initial temperature.

- Calculate Molar Enthalpy of Fusion

Using the heat calculated from Step 6, determine the molar enthalpy of fusion \( \triangle H_f \) by dividing the heat absorbed by the number of moles of ice melted. Use: \[ \triangle H_f = \frac{q}{n} \] where \( n \) is the number of moles of ice (mass of ice divided by molar mass of water, 18.015 g/mol).

- Compare with Known Values

Compare the calculated molar enthalpy of fusion with the known value of 6.01 kJ/mol. Discuss any differences and potential sources of error in the experiment.

Key concepts

calorimeter experiment

A calorimeter experiment is a method used to measure the amount of heat transfer in or out of a substance during a physical or chemical change. In this exercise, we're focusing on determining the molar enthalpy of fusion of water using a simple setup.
Start by setting up the calorimeter with a large plastic-foam cup, filling it halfway with room temperature water, and covering it. Inserting a thermometer allows you to monitor temperature changes accurately.
We then measure the initial temperature of the water and the mass of an ice cube. By adding the ice cube to the water and noting the temperature as it melts, we gather the required data for further calculations. Stirring ensures an even temperature distribution.
This experiment's design minimizes heat loss to the environment and uses common lab equipment, making it simple yet effective for high school and introductory college students.

enthalpy calculations

Enthalpy calculations are crucial for understanding heat changes during phase transitions. Once we have the necessary measurements from the calorimeter experiment, we proceed with these calculations.
First, we calculate the heat absorbed by the ice as it melts using the formula:

where:

• \( q \) = heat absorbed by the ice
• \( m_w \) = mass of water
• \( c_w \) = specific heat capacity of water (4.18 J/g°C)
• \( T_{f} \) = final temperature
• \( T_{i} \) = initial temperature

After finding the heat absorbed, we calculate the molar enthalpy of fusion (\( \triangle H_f \)). This value represents the energy required to convert one mole of solid water (ice) to liquid water without temperature change. Using the formula: br>
where \( n \) = number of moles of ice (mass of ice divided by molar mass of water, 18.015 g/mol).
These calculations help us identify and understand the specific energy changes involved in melting ice, forming a foundation for further studies in thermodynamics and physical chemistry.

thermodynamics

Thermodynamics deals with the study of heat energy and its transformation to and from other forms of energy. In the context of this experiment, we're applying the principles of thermodynamics to measure the heat involved in melting ice.
Key concepts here include the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. When ice melts in the water, energy (in the form of heat) is transferred from the water to the ice, causing the ice to melt.
This process involves an enthalpy change, specifically the enthalpy of fusion. Understanding how to measure and calculate these changes using a calorimeter prepares students for more advanced topics in thermodynamics.
Overall, calorimeter experiments not only help students grasp abstract thermodynamic principles but also hone their practical lab skills and improve their ability to critically analyze and compare experimental data with theoretical values.