Determination of Approximate Atomic Weight

The objective of this lab is to determine the approximate atomic weight of several elements using calorimetry and the law of Dulong and Petit. Students will use tools and equipment for scientific analysis, demonstrate safe practices in the chemical laboratory, demonstrate the proper use of exponential notation and significant figures, demonstrate an understanding of the composition of matter and energy, demonstrate an understanding of historical discoveries in chemistry, record their investigation results, use scientific reasoning to evaluate physical and natural phenomena, and identify unifying themes in the scientific field of study.

The discussion provides an overview of the Dulong-Petit law, which relates the specific heat of certain metallic elements to their atomic weight. According to the law, the product of the specific heat and the atomic weight of an element is a constant value of 6.4. Specific heat is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. The specific heat measurements can be used to determine the atomic weight of an element.

In this experiment, a calorimeter cup, previously calibrated for heat capacity, is used. Water is added to the calorimeter, and its temperature is measured. A metallic element is weighed and placed in a test tube. The test tube is connected to a beaker of boiling water using a setup shown in Figure 18. The boiling water is maintained above the test tube for a certain duration. The metal is then rapidly poured into the water in the calorimeter, and the mixture is stirred. The maximum temperature reached by the mixture is recorded.

The calculations involve applying the principle of heat gained equals heat lost. The heat gained by the water in the calorimeter cup is equal to the heat lost by the added metal. The equation used for the calculation is: (grams H2O) × (specific heat of H2O) × (tf - ti) + (calorimeter heat capacity) × (tf - ti) = (grams metal) × (100°C - tf) × (specific heat of metal). The final temperature (tf) and initial temperature (ti) of the water, as well as the temperature of the metal (100°C), are used in the equation.

The specific heat of the metal is the only unknown in the equation. By determining its value and using the Dulong-Petit equation (specific heat) × (atomic weight) = 6.4, the approximate atomic weight of the metal can be calculated.

The lab emphasizes the use of calorimetry and the Dulong-Petit law to estimate the atomic weight of different metallic elements. Students are encouraged to repeat the experiment for reproducibility and to perform it on as many available metals as possible. The percent error can be calculated by comparing the experimental values to the known or accepted atomic weights of the metals.

Through this lab, students gain hands-on experience with calorimetry, learn about the historical contributions of Dulong and Petit, and apply the principles of heat transfer and conservation of energy. The focus is on using measurements of heat exchange to determine specific heat and atomic weight, as well as analyzing the results and calculating percent error.

Objective

·         Use the tools and equipment necessary for basic scientific analysis and research

·         Demonstrate safe practices in the Chemical Laboratory

·         Demonstrate the proper use of Exponential Notation and Significant Figures

·         Demonstrate an understanding of the composition of matter and energy

·         Demonstrate an understanding of historical discoveries in Chemistry

·         Record the results of investigation through writing

·         Use scientific reasoning to evaluate physical and natural phenomena

·         Identify the unifying themes of the scientific field of study

Materials

·         Styrofoam calorimeter cup

·         400 mL Beaker

·         Thermometer

·         Various Pure Metallic Elements

Discussion

The aim of this experiment is to estimate the approximate atomic weight of various elements using calorimetry and the Dulong-Petit law. In 1819, P. Dulong and A. Petit established a correlation between the specific heat of certain metallic elements and their atomic weight, given by the equation:

(specific heat) x (atomic weight) = 6.4.

Specific heat refers to the amount of heat (in calories) required to raise the temperature of one gram of a substance by one °Centigrade. A calorie is defined as the amount of heat necessary to increase the temperature of one gram of water by one °Centigrade.

According to the Dulong-Petit law, specific heat measurements can be used to determine the atomic weight of a substance. To determine the specific heat of a substance, it is necessary to measure the heat required to change its temperature by 1°C. This can be achieved by measuring the heat transfer from a hot metal to a calorimeter. By analyzing the change in temperature of the calorimeter fluid, we can determine the specific heat of the metal and, subsequently, the atomic weight using the Dulong-Petit law.

This experiment employs the law of Conservation of Energy, which states that the hot metal will transfer heat energy to the calorimeter and its contents. All heat (or energy) transfers will be considered in the context of energy conservation.

Procedure

The experiment will utilize the same type of calorimeter employed in the "Heat of Fusion" experiment. The heat capacity previously determined for the calorimeter will be appropriate for the current experiment. Begin by adding 50.0 g of water to the calorimeter and measuring its temperature using a thermometer.

Next, accurately weigh an appropriate quantity (approximately 1/4 - 1/2 of a test tube) of a metallic element and place it inside the test tube. Fill a 400 ml beaker with tap water, filling it up to around two-thirds of its capacity, and connect the test tube setup as illustrated in Figure 18. Proceed to heat the water in the beaker until it reaches boiling point. Maintain the water level in the beaker several centimeters above the contents of the test tube, keeping it at a boiling state for 10-15 minutes.

Finally, swiftly pour the metal into the water within the calorimeter and vigorously stir the mixture.

Take note of the highest temperature reached by the combination of metal and water. This temperature is utilized to determine the heat lost by the metal and the heat gained by the water. Utilize this information to estimate the atomic weight of the element. Repeat the procedure to obtain consistent outcomes. Conduct the experiment as frequently as possible with the metals at hand.

Calculate the percentage of error based on precise weights and record the outcomes on the report sheet.

Calculations

Again, use the concept of HEAT GAINED = HEAT LOST

In this case the heat gained by water in the calorimeter cup will be lost by the added metal.

(grams H2O) (sp.ht.H2O) (tf-ti) + (calorimeter heat capacity) (tf-ti) = (Grams metal) (100°C-tf) (sp.ht. metal)

Where:

ti = final temperature

ti = initial temperature of H2O

100°C = temperature of metal added to calorimeter

The only unknown in the above expression is the specific heat of the metal.  From this value and the equation of Dulong-Petit, the approximate atomic weight of the metal can be determined.

(sp.ht.) (atomic wt.) = 6.4

Report Sheet for DETERMINATION of APPROXIMATE ATOMIC WEIGHT

Name_______________________________________                          Date___________________________

Lab / Section_________________________________

Review Questions

1.       What is the purpose of the experiment in determining the approximate atomic weight of elements?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.       How does the Dulong-Petit law relate to the specific heat and atomic weight of metallic elements?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.       Explain the concept of specific heat and its significance in calorimetry.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

4.       Describe the setup and procedure used in the lab to determine the approximate atomic weight of elements.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5.       What is the relationship between the heat gained by water in the calorimeter and the heat lost by the added metal?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6.       How can the maximum temperature reached by the mixture of metal and water be used in the calculations?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

7.       How does the heat capacity of the calorimeter affect the measurements and calculations?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

8.       Discuss the importance of reproducibility in the experimental results and why repeating the experiment is recommended.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

9.       Explain the concept of percent error and how it can be calculated in this lab.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

10.    What is the significance of using a Styrofoam calorimeter cup in the experiment?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

11.    Describe the principle of energy conservation and how it applies to heat transfer in this lab.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

12.    Compare and contrast specific heat and atomic weight as properties of metallic elements.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

13.    Discuss the historical significance of the Dulong-Petit law and its contributions to the field of chemistry.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

14.    How does the law of conservation of energy play a role in calorimetry experiments?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

15.    Explain the process of determining the specific heat of a metal using the calorimetry setup.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

16.    How can the specific heat of a metal be used to calculate its approximate atomic weight?

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

17.    Discuss the factors that can contribute to sources of error in this experiment and how they can be minimized.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

18.    Analyze the relationship between the mass of water, its specific heat, and the temperature change in the calorimeter.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19.    Evaluate the limitations and assumptions made in using calorimetry to determine atomic weight.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

20.    Apply the concepts learned in this lab to predict the approximate atomic weight of an unknown metal based on its specific heat measurement.

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________