Identifying Three Unknown Metals by Comparing Their Experimentally Determined Specific Heat Capacities to the Known Specific Heat Values for Select Substances
In her advanced chemistry class, Jordyn Pierre-Raphael ('20), explored the concept of specific heat capacity.
As a class, we were given the assignment to identify three different unknown metals by using the heat transfer data that we had collected in the lab to determine their specific heat capacities. The goal of our investigation was to compare our experimentally determined specific heat capacities of each metal to the accepted specific heat values for select substances, which Dr. Lurain provided us with so that we could identify the metals accordingly. Prior to this experiment, we knew that the law of conservation of energy states that energy can neither be created nor destroyed, but can be transferred from one form to another. We also knew that the faster moving particles of the metal would collide with the slower moving particles of the water, which would cause a transfer in kinetic energy of the particles and thermal energy. Therefore, we presumed that when the heated metal was placed into the room-temperature cup of water, the kinetic energy transferred from the pieces of metal pieces would equal the thermal energy gained by the water particles due to equilibration. In other words, the exothermic process of the metal would be balanced to the endothermic process of the water. As a group, we hypothesized that by using the data collected, specifically the temperature change in ℃ and mass of both the water and the metal in grams, and the specific heat capacity of water, we would be able to calculate the relatively accurate specific heat capacity of each metal successfully by using the specific heat formula to create a system of equations. If the energy lost by the metal(-q = specific heat capacity(C) mass(m)change in temp.(t)) was set equal to the energy gained by the water(q=Cmt), we believed that we could solve for the specific heat capacity of the metal since all of the other variables could be substituted.
Once we finished taking our data for our investigation, we proceeded to substitute the data values we had collected into the system of equations, so that we could find the specific heat values of the three different metals. For metal A, we calculated that the specific heat capacity was 0.73 Jg ℃(See page 18 of lab pages), and we compared it to the accepted specific heat values of certain substances that Dr. Lurain had provided us with:
From using Dr. Lurain’s table, we noticed that our value for metal A was closest to aluminum, specifically only 0.169 Jg ℃ less. Therefore, we reasonably deduced that metal A was aluminum because it was the closest value, and besides this, the qualitative data that we collected resembled aluminum as it was silver, shiny, and had a smooth surface. This supported our hypothesis and claim as we were able to determine the specific heat capacity of a metal by using the specific heat formula, as well as the given specific heat values for select substances to identify the metal. Although the identification of metal A seemed to be accurate, we wanted to take into account the average specific heat value of the class data set, which wasn’t very precise due to the large range in values. The class average specific heat value for metal A was 1.31 Jg ℃, and this value was closest to aluminum, just as ours was. Even though our experimentally determined specific heat capacity of metal A was much different than the class average, both values identified metal A to be aluminum.
For metal B and C, we followed the same process as when we calculated the specific heat capacity of metal A. We found that the specific heat capacity of metal B was 0.13 Jg ℃(See page 18 lab pages), which in regards to Dr. Lurain’s reference table was extremely close to the specific heat value for lead as it was only 0.001 Jg ℃greater than lead’s reported specific heat value. Accordingly, we reasonably concluded that metal B was lead because of its specific heat value, as well as its qualitative characteristics that resembled lead balls, specifically its black color, shine, and ball-like shape. However, our class average specific value of metal B was 0.34 Jg ℃, which was closest to specific heat value of zinc. Despite that, our group still decided to identify metal B as lead because of the large disparity in the specific heat values for metal B,(this is addressed in the error analysis) its qualitative characteristics, and the relative certainty in our values.
For metal C, our group calculated the specific heat capacity to be 0.32 Jg ℃(See page 18 lab pages), which we identified to be zinc because it was only 0.065 Jg ℃ less than zinc’s specific heat value. The class average specific heat value for metal C was 1.32 Jg ℃, which was also closest to aluminum, but our group knew that it could not be aluminum because metal A had been identified as aluminum and all of the metals were supposed to be different. Although Metal A and C also may have had similar qualitative characteristics, like their color and shape, we assumed that metal C could not be aluminum and that it was rather zinc, which was the closest value after aluminum. In general, our group found that the class average specific heat values for each metal seemed to be inaccurate due to its large range in values, but especially for metal B and C. This is why we chose to disagree with the identification of both metal B and metal C as our values were more accurate. Although there was a big discrepancy between our values and the class average, we still believed that our experimentally determined specific heat values supported our hypothesis as we were able to calculate the specific heat capacity of a metal by using the specific heat formula and identify the metal as well.
Error Analysis:
When my group was analyzing our data and trying to identify the metals, we were very tempted to simply disregard the class data set because there was an average percent uncertainty of 500%(See calculation on page 20). This was an extremely large number that may have had to do with the inconsistency in procedures that each group followed when doing this experiment, which is why I was apprehensive towards using the class data set to identify the metals. I thought that the procedure we followed had minimal sources of error, such that we could base our identification on solely our specific heat values for each metal. In the end, our group decided to acknowledge the class data set, but our specific heat values took precedence when it came to identifying each metal. This is why we decided to identify metal B and metal C based off the qualitative data collected and our specific heat value since it had a smaller percentage of error than the average of the class data set.
Once we identified all of three metals, which were all in accordance to the class data set except for metal B and Metal C, we wanted to determine the accuracy of the class average specific heat values and our values for each metal. To determine the accuracy of our results, we found the percent error of the class value and our value by using this formula: % error=| measured value - accepted value| accepted value100%. After calculations, we observed that for each metal the percentage of error for the specific heat values that my group had reported was significantly less than the percentage of error of the class average specific heat values. Assuming that Metal A was aluminum, Metal B was lead, and metal C was zinc, we calculated that our percentage error for Metal A was 19%, the percentage error for Metal B was 0%, and the percentage of error for Metal C was 18%(See calculation on page 19 and 20). In comparison, the percentage of error for the class average for metal A was 44%, the percentage of error for Metal B was 200%, and the percentage of error was 240%(See calculation on page 19 and 20).
Besides this, I also wanted to identify the precision of our class data set for each metal, so I used this formula: % uncertainty=|value farthest away from the average-average value|average value100%. I calculated that the percentage of uncertainty for Metal A was 200%, the percentage of uncertainty for Metal B was 400%, and the percentage of uncertainty for Metal C was 920%(See calculation on page 20). Just as I had said earlier, it was evident just from a glance at our class data set was not precise as there was such a large variation in values for each metal, which constituted for such large uncertainties for each of the metals. Such large uncertainties for each metal caused me to decide that I would be better off identifying the metals according to my groups specific heat value since the percentage of uncertainty for each metal was so large. However, if the all of Accelerated Chemistry had followed the same procedure then I would have used the class data average because hypothetically there would have been less uncertainty.
In general, our experiment seemed to have a limited percentage of error, but there were still some significant sources of error. The most significant source of error in our experiment was the energy that we lost to the surrounding air particles during the transfers. As we would transfer the heated metal samples into the styrofoam cup, there was definitely a loss of some heat due to the contact with the air. This loss of heat definitely impacted our final temperature of the water and the metal because the temperature, the average kinetic energy of the particles, must have dropped as it came into contact with the air particles. If our system had been closed, this could have been prevented. This is why in the future, we would use the double cup method, which was successful for another group. By placing another cup on top of the first, the water and the metal would have only been exposed to the air particles that escaped through the small crack, where the thermometer was.
The second source of error that we encountered during our procedure was that the samples of the metals got stuck at the bottom of the test tube when we were trying to pour them into the styrofoam cup, which caused a similar dilemma as the first source of error because some of the heat was lost from the metal. This should have lead to a decrease in its temperature. Due to the size of the metal samples in relation to the graduated cylinder, when we attempted to pour the pieces of metal into the styrofoam cup, they stuck to the bottom of the test tube. In order to get them into the cup, we had to knock and shake the test tube, and during this time the pieces of the metal were exposed to the surrounding air, which must have caused the temperature of the metal to decrease before we could put it into the styrofoam cup. In order to prevent this during future experiments, we would use metal samples with smaller volume and surface areas so that they can fall out of the graduated cylinder easier.
Our third source of error in the design of our experiment was how we indirectly measured the temperature of the metal. There was no fixed method for us to measure the initial and final temperature of it, so we had to devise a way to measure it indirectly. Therefore, we found the temperature of the metal through its equilibration with the water, which may not have been extremely accurate since we assumed that the water and metal had equilibrated once it reached a certain temperature. This is why for future experiments, I would investigate if there is a more accurate way to measure the temperature of a metal directly and use them accordingly. Lastly, our experiment and identification of the metals may have benefited if we were able to do more than one trial per metal because this would potentially lessen or inaccuracy. Therefore, in future experiments, I would conduct three trials per metal instead. Although we had some significant sources of error in the design of our experiment, I still believe that our group can reasonably conclude that the identifications of all three of the metals are correct since we conducted the collection of heat transfer data efficiently. Also, these sources of error shouldn’t have altered our values that much, so I still stand by our groups values and feel like they support our claim.
Works Cited:
Aluminum. (2017, December 4). Retrieved December 4, 2017, from https://en.wikipedia.org/wiki/Aluminium
Epstein, J. (2017, December 4). [A better procedure for keeping the system closed: double cup method.] {Personal interview}.
Pure Lead Images - Reverse Search. (n.d.). Retrieved December 5, 2017, from https://www.picquery.com/c/pure-lead_oPTeUp2l9NUKZ*0HQBGbqQPEQXzKmpyTuU20w0gXbzE/
[Specific Heat of Unknown Metals Class Data Set]. (2017, December 5). Unpublished raw data.
Once we finished taking our data for our investigation, we proceeded to substitute the data values we had collected into the system of equations, so that we could find the specific heat values of the three different metals. For metal A, we calculated that the specific heat capacity was 0.73 Jg ℃(See page 18 of lab pages), and we compared it to the accepted specific heat values of certain substances that Dr. Lurain had provided us with:
From using Dr. Lurain’s table, we noticed that our value for metal A was closest to aluminum, specifically only 0.169 Jg ℃ less. Therefore, we reasonably deduced that metal A was aluminum because it was the closest value, and besides this, the qualitative data that we collected resembled aluminum as it was silver, shiny, and had a smooth surface. This supported our hypothesis and claim as we were able to determine the specific heat capacity of a metal by using the specific heat formula, as well as the given specific heat values for select substances to identify the metal. Although the identification of metal A seemed to be accurate, we wanted to take into account the average specific heat value of the class data set, which wasn’t very precise due to the large range in values. The class average specific heat value for metal A was 1.31 Jg ℃, and this value was closest to aluminum, just as ours was. Even though our experimentally determined specific heat capacity of metal A was much different than the class average, both values identified metal A to be aluminum.
For metal B and C, we followed the same process as when we calculated the specific heat capacity of metal A. We found that the specific heat capacity of metal B was 0.13 Jg ℃(See page 18 lab pages), which in regards to Dr. Lurain’s reference table was extremely close to the specific heat value for lead as it was only 0.001 Jg ℃greater than lead’s reported specific heat value. Accordingly, we reasonably concluded that metal B was lead because of its specific heat value, as well as its qualitative characteristics that resembled lead balls, specifically its black color, shine, and ball-like shape. However, our class average specific value of metal B was 0.34 Jg ℃, which was closest to specific heat value of zinc. Despite that, our group still decided to identify metal B as lead because of the large disparity in the specific heat values for metal B,(this is addressed in the error analysis) its qualitative characteristics, and the relative certainty in our values.
For metal C, our group calculated the specific heat capacity to be 0.32 Jg ℃(See page 18 lab pages), which we identified to be zinc because it was only 0.065 Jg ℃ less than zinc’s specific heat value. The class average specific heat value for metal C was 1.32 Jg ℃, which was also closest to aluminum, but our group knew that it could not be aluminum because metal A had been identified as aluminum and all of the metals were supposed to be different. Although Metal A and C also may have had similar qualitative characteristics, like their color and shape, we assumed that metal C could not be aluminum and that it was rather zinc, which was the closest value after aluminum. In general, our group found that the class average specific heat values for each metal seemed to be inaccurate due to its large range in values, but especially for metal B and C. This is why we chose to disagree with the identification of both metal B and metal C as our values were more accurate. Although there was a big discrepancy between our values and the class average, we still believed that our experimentally determined specific heat values supported our hypothesis as we were able to calculate the specific heat capacity of a metal by using the specific heat formula and identify the metal as well.
Error Analysis:
When my group was analyzing our data and trying to identify the metals, we were very tempted to simply disregard the class data set because there was an average percent uncertainty of 500%(See calculation on page 20). This was an extremely large number that may have had to do with the inconsistency in procedures that each group followed when doing this experiment, which is why I was apprehensive towards using the class data set to identify the metals. I thought that the procedure we followed had minimal sources of error, such that we could base our identification on solely our specific heat values for each metal. In the end, our group decided to acknowledge the class data set, but our specific heat values took precedence when it came to identifying each metal. This is why we decided to identify metal B and metal C based off the qualitative data collected and our specific heat value since it had a smaller percentage of error than the average of the class data set.
Once we identified all of three metals, which were all in accordance to the class data set except for metal B and Metal C, we wanted to determine the accuracy of the class average specific heat values and our values for each metal. To determine the accuracy of our results, we found the percent error of the class value and our value by using this formula: % error=| measured value - accepted value| accepted value100%. After calculations, we observed that for each metal the percentage of error for the specific heat values that my group had reported was significantly less than the percentage of error of the class average specific heat values. Assuming that Metal A was aluminum, Metal B was lead, and metal C was zinc, we calculated that our percentage error for Metal A was 19%, the percentage error for Metal B was 0%, and the percentage of error for Metal C was 18%(See calculation on page 19 and 20). In comparison, the percentage of error for the class average for metal A was 44%, the percentage of error for Metal B was 200%, and the percentage of error was 240%(See calculation on page 19 and 20).
Besides this, I also wanted to identify the precision of our class data set for each metal, so I used this formula: % uncertainty=|value farthest away from the average-average value|average value100%. I calculated that the percentage of uncertainty for Metal A was 200%, the percentage of uncertainty for Metal B was 400%, and the percentage of uncertainty for Metal C was 920%(See calculation on page 20). Just as I had said earlier, it was evident just from a glance at our class data set was not precise as there was such a large variation in values for each metal, which constituted for such large uncertainties for each of the metals. Such large uncertainties for each metal caused me to decide that I would be better off identifying the metals according to my groups specific heat value since the percentage of uncertainty for each metal was so large. However, if the all of Accelerated Chemistry had followed the same procedure then I would have used the class data average because hypothetically there would have been less uncertainty.
In general, our experiment seemed to have a limited percentage of error, but there were still some significant sources of error. The most significant source of error in our experiment was the energy that we lost to the surrounding air particles during the transfers. As we would transfer the heated metal samples into the styrofoam cup, there was definitely a loss of some heat due to the contact with the air. This loss of heat definitely impacted our final temperature of the water and the metal because the temperature, the average kinetic energy of the particles, must have dropped as it came into contact with the air particles. If our system had been closed, this could have been prevented. This is why in the future, we would use the double cup method, which was successful for another group. By placing another cup on top of the first, the water and the metal would have only been exposed to the air particles that escaped through the small crack, where the thermometer was.
The second source of error that we encountered during our procedure was that the samples of the metals got stuck at the bottom of the test tube when we were trying to pour them into the styrofoam cup, which caused a similar dilemma as the first source of error because some of the heat was lost from the metal. This should have lead to a decrease in its temperature. Due to the size of the metal samples in relation to the graduated cylinder, when we attempted to pour the pieces of metal into the styrofoam cup, they stuck to the bottom of the test tube. In order to get them into the cup, we had to knock and shake the test tube, and during this time the pieces of the metal were exposed to the surrounding air, which must have caused the temperature of the metal to decrease before we could put it into the styrofoam cup. In order to prevent this during future experiments, we would use metal samples with smaller volume and surface areas so that they can fall out of the graduated cylinder easier.
Our third source of error in the design of our experiment was how we indirectly measured the temperature of the metal. There was no fixed method for us to measure the initial and final temperature of it, so we had to devise a way to measure it indirectly. Therefore, we found the temperature of the metal through its equilibration with the water, which may not have been extremely accurate since we assumed that the water and metal had equilibrated once it reached a certain temperature. This is why for future experiments, I would investigate if there is a more accurate way to measure the temperature of a metal directly and use them accordingly. Lastly, our experiment and identification of the metals may have benefited if we were able to do more than one trial per metal because this would potentially lessen or inaccuracy. Therefore, in future experiments, I would conduct three trials per metal instead. Although we had some significant sources of error in the design of our experiment, I still believe that our group can reasonably conclude that the identifications of all three of the metals are correct since we conducted the collection of heat transfer data efficiently. Also, these sources of error shouldn’t have altered our values that much, so I still stand by our groups values and feel like they support our claim.
Works Cited:
Aluminum. (2017, December 4). Retrieved December 4, 2017, from https://en.wikipedia.org/wiki/Aluminium
Epstein, J. (2017, December 4). [A better procedure for keeping the system closed: double cup method.] {Personal interview}.
Pure Lead Images - Reverse Search. (n.d.). Retrieved December 5, 2017, from https://www.picquery.com/c/pure-lead_oPTeUp2l9NUKZ*0HQBGbqQPEQXzKmpyTuU20w0gXbzE/
[Specific Heat of Unknown Metals Class Data Set]. (2017, December 5). Unpublished raw data.
