Students were given five masses of an unknown metal. Your job is to determine the identity of the metal by analyzing the data that the students collected. Their experiment is described below.
First, they measured the mass and temperature of a sample of water in a calorimeter. Then, they heated the 100 g metal sample in a beaker filled with boiling water and waited until the metal sample reached 100°C. They transferred the metal sample into the calorimeter and placed the lid on the calorimeter. They stirred until the temperature no longer changed, and the water and metal reached equilibrium.
They repeated the procedure with a 200 g, 300 g, 400 g, and 500 g sample of the metal.
With the information above, as many questions as you can below.
1. What is the specific heat of the masses in this experiment? Infer the substance the masses are made of and explain your inference using the data as support. Based on your calculation of the metal's specific heat, what is the metal? Show your work.
2. List three sources of error the students may have encountered that would account for the differences between your values and the accepted value. Some of your focus should be on considering that heat transfer should only have taken place between the water and the unknown substance in the calorimeter.
3. Explain in your own words how a calorimeter works.
1. To determine the specific heat of the masses in this experiment, we can use the principle of conservation of energy. The heat gained by the water and the calorimeter is equal to the heat lost by the metal. Since the metal was initially at boiling temperature (100°C) and then transferred to the calorimeter until both the water and metal reached equilibrium, we can assume that the metal reached the same final temperature as the water.
Let's say the final temperature of the water and metal mixture in the calorimeter is Tf. The heat gained by the water and calorimeter (q1) can be calculated using the formula:
q1 = mass_water * specific_heat_water * (Tf - initial_temperature_water)
The heat lost by the metal (q2) can be calculated using the formula:
q2 = mass_metal * specific_heat_metal * (initial_temperature_metal - Tf)
Since q1 = q2 (as per the principle of conservation of energy), we can equate the two equations:
mass_water * specific_heat_water * (Tf - initial_temperature_water) = mass_metal * specific_heat_metal * (initial_temperature_metal - Tf)
Given the mass of water (100 grams) and the initial and final temperatures, we can solve for specific_heat_metal:
specific_heat_metal = (mass_water * specific_heat_water * (Tf - initial_temperature_water)) / (mass_metal * (initial_temperature_metal - Tf))
Using the masses of the metal samples and their corresponding temperatures, we can calculate the specific heat for each metal sample. Based on the specific heat values obtained, we can infer the substance that the masses are made of. Different substances have different specific heat values, so by comparing the calculated specific heat values to known specific heat values for common substances, we can determine the metal. For example, if the calculated specific heat value matches the known specific heat value for copper, we can infer that the metal samples are made of copper.
2. There are several potential sources of error the students may have encountered that could account for differences between their values and the accepted value:
a. Heat loss to the surroundings: The students should have ensured that there was minimal heat loss to the surroundings during the transfer of the metal and the stirring process. Any heat lost to the surroundings could lead to inaccuracies in the temperature measurements and affect the calculation of specific heat.
b. Incomplete heat transfer: It is possible that not all of the heat from the boiling water transferred to the metal, or the metal did not reach the same final temperature as the water and calorimeter. This could be due to inefficient heat conduction or insulating effects, leading to an underestimation or overestimation of the specific heat value.
c. Measurement errors: Errors in measuring the mass of the metal samples or the temperature could also contribute to discrepancies. Using precise and accurate measuring instruments and techniques is essential to minimize measurement errors.
3. A calorimeter is a device used to measure the change in thermal energy of a substance. It typically consists of a container, often insulated, where a chemical reaction or physical process takes place, allowing the exchange of heat with the surroundings to be monitored.
In the context of this experiment, the calorimeter is used to measure the amount of heat exchanged between the water and the metal sample. It works based on the principle of energy conservation, where any heat lost or gained by the water and the calorimeter is equal to the heat lost or gained by the metal.
The calorimeter traps the heat released or absorbed by the metal and water, preventing it from escaping to the surroundings as much as possible. By stirring the mixture and waiting until the temperatures stabilize, the calorimeter ensures that the heat transfer process reaches equilibrium.
The calorimeter allows for accurate measurement of temperature changes, which can be used along with mass measurements and known specific heat values to calculate the specific heat of the metal samples.