During the titration lab, we had to determine the percentage ionization of acetic acid in vinegar. We did this by titrating the acetic acid present with a strong base, sodium hydroxide.
We first filled a erlenmeyer flask with 7.63 mL of vinegar, 20 mL of water, and 4 drops of phenolphthalein. We stirred it around and then put it under the burette. We then opened the bottom of the burette to let some of the base [NaOH] out to fall into the erlenmeyer flask. We kept the burette open until the mixture in the erlenmeyer flask turned a light pink.
We had two trials and the first trial we let too much of the NaOH fall into the erlenmeyer flask, so the mixture turned a deep pink. The second time, we added just enough so that the mixture turned a light pink.
After we had collected some data about the volume of NaOH used in each trial and the pH level of the vinegar we used, we had to calculate the molarity of the acid for each trial, the average concentration of the vinegar, how much H₃O⁺ was in the vinegar, and the percent ionization of the vinegar.
Here is a picture of my calculations:
The percent ionization of the vinegar is such a small number because vinegar is a weak acid meaning that not all the acid molecules in the reactants dissociate into their ions in the product.
Adina's CTD Chemistry Blog
Thursday, July 13, 2017
Wednesday, July 12, 2017
Solubility: A Guided Inquiry Lab
Introduction:
During our solubility: a guided inquiry lab, we were tasked with creating and implementing a procedure to identify an unknown solid using experimental data and known solubility data. Solubility is the ability for a given substance, the solute, to dissolve in a solvent. The solvent is the liquid you are dissolving the substance into. We were able to use hot plates, balances, test tubes, a thermometer, beakers, erlenmeyer flasks, and stirring rods. The way we knew if we had the right substance was based on if our solution was saturated. A saturated solution is a solution in which no more solute can be dissolved in the solvent. The saturation of the solution has been achieved when any additional substance that is added results in a solid precipitate which collects at the bottom of the beaker. The solid we had to identify was in container "A".
Here is a picture of our known solubility data:
Procedure:
My partner and I started by filling a small beaker with 10 mL of water and heating it up on a hot plate till it was 50℃. While the water was heating up, we measured out 5 grams of our unknown solid. We did 5 grams because when we looked at our solubility graph, we saw that 5 grams was above the NaCl line so if the solid did not dissolve we would know that our unknown solid was NaCl. As soon as the water was 50℃, we poured the 5 grams of our solid into the water and stirred it to see if it dissolved. It fully dissolved so we now knew that our solid was not NaCl.
We then put our beaker back onto the hot plate so we can keep the water at 50℃ while we measured out 2 more grams of our known solid. After the water was heated again, we poured the 2 grams of solid into our beaker and stirred it; Now we had a total 7 grams of our solid in the beaker. The solid fully dissolved again so it did not give us any new information about the identity of our solid, it just proved the fact that our solid was not NaCl.
We put the beaker back on the heat again and measured out 2 more grams of our solid. When the water was heated, we poured the 2 grams of solid that we had just measured out and started stirring it. Now we had a total of 9 grams of our substance. Looking at our solubility graph we saw that if these 2 more grams of solid dissolved, our substance would be NaNO₃, and that if it did not dissolve our substance would be KNO₃. We saw that the solid fully dissolved into the water which told us that the only possibility left for the identity of our unknown solid, was NaNO₃.
Here is a picture of our set up:
Here is a table of my data:
Conclusion:
In the end we found that our unknown solid in container "A" was NaNO3. We know that we are correct because when we dissolved 9 grams of the solid into our 10 mL of water, it fully dissolved and the solubility graph shows that if our substance was any of the other two options, the solution would have been saturated, which it wasn't. We also initially thought that our substance was KNO3 because our solute wasn't dissolving into the water but we realized that our water was only heated to 45℃ so we reheated the water to 50℃ and it dissolved completely which officially ruled out that our substance was KNO3. Also, for any solid substance, when temperature increases, solubility also increases which is how why every time we reheated the water, we kept adding more of our solid.
During our solubility: a guided inquiry lab, we were tasked with creating and implementing a procedure to identify an unknown solid using experimental data and known solubility data. Solubility is the ability for a given substance, the solute, to dissolve in a solvent. The solvent is the liquid you are dissolving the substance into. We were able to use hot plates, balances, test tubes, a thermometer, beakers, erlenmeyer flasks, and stirring rods. The way we knew if we had the right substance was based on if our solution was saturated. A saturated solution is a solution in which no more solute can be dissolved in the solvent. The saturation of the solution has been achieved when any additional substance that is added results in a solid precipitate which collects at the bottom of the beaker. The solid we had to identify was in container "A".
Here is a picture of our known solubility data:
Procedure:
My partner and I started by filling a small beaker with 10 mL of water and heating it up on a hot plate till it was 50℃. While the water was heating up, we measured out 5 grams of our unknown solid. We did 5 grams because when we looked at our solubility graph, we saw that 5 grams was above the NaCl line so if the solid did not dissolve we would know that our unknown solid was NaCl. As soon as the water was 50℃, we poured the 5 grams of our solid into the water and stirred it to see if it dissolved. It fully dissolved so we now knew that our solid was not NaCl.
We then put our beaker back onto the hot plate so we can keep the water at 50℃ while we measured out 2 more grams of our known solid. After the water was heated again, we poured the 2 grams of solid into our beaker and stirred it; Now we had a total 7 grams of our solid in the beaker. The solid fully dissolved again so it did not give us any new information about the identity of our solid, it just proved the fact that our solid was not NaCl.
We put the beaker back on the heat again and measured out 2 more grams of our solid. When the water was heated, we poured the 2 grams of solid that we had just measured out and started stirring it. Now we had a total of 9 grams of our substance. Looking at our solubility graph we saw that if these 2 more grams of solid dissolved, our substance would be NaNO₃, and that if it did not dissolve our substance would be KNO₃. We saw that the solid fully dissolved into the water which told us that the only possibility left for the identity of our unknown solid, was NaNO₃.
Here is a picture of our set up:
Here is a table of my data:
Conclusion:
In the end we found that our unknown solid in container "A" was NaNO3. We know that we are correct because when we dissolved 9 grams of the solid into our 10 mL of water, it fully dissolved and the solubility graph shows that if our substance was any of the other two options, the solution would have been saturated, which it wasn't. We also initially thought that our substance was KNO3 because our solute wasn't dissolving into the water but we realized that our water was only heated to 45℃ so we reheated the water to 50℃ and it dissolved completely which officially ruled out that our substance was KNO3. Also, for any solid substance, when temperature increases, solubility also increases which is how why every time we reheated the water, we kept adding more of our solid.
Tuesday, July 11, 2017
Gas Law Lab
During the Gas Law Lab my partner and I did a reaction between alka seltzer tablets and water. We had to take data about the mass of the alka seltzer powder we used, the circumference of the filled balloon, the volume of water that fits in the balloon, the room temperature, and the barometric pressure. The materials we had were a mortar, a pestle, 2 alka seltzer tablets, a 9-inch round balloon, a test tube, a piece of string, a ruler, a graduated cylinder, a barometer, and a thermometer.
We had to crush the alka seltzer tablets using the mortar and pestle, then weigh the crushed up tablets and pour them into a round balloon. We then filled up a test tube up to the top with water and put the balloon around the top of the test tube. To start the reaction, we flipped the balloon so the powder went into the water and started fizzing up and filling the balloon with gas. Once the reaction had ended, we were left with a full balloon of gas which we then measured the circumference of, with a piece of string and a ruler. We then used the data we had collected and Dalton's Law to find the mass of the CO₂ gas, the pressure of the gas, and the number of moles of CO₂ gas.
Here is a picture of my data:
Here is a picture of my calculations:
Discuss an area in this lab where experimental error may have occurred.
Experimental error may have occurred when we were measuring the amount of water the balloon could hold to fit our circumference because some of our water spilled out of the balloon into the sink when we were pouring it into the graduated cylinder. We also may have measured the circumference of the balloon too early when the reaction may have still been going on.
Choose one error from above and discuss if it would make 'n' the number of moles of CO₂ too big or too small.
If we had measured the circumference too early when the reaction was still going on, it would have made the moles of CO₂ gas too small because the reaction was still releasing gas into the balloon making the balloon bigger and able to hold more moles of CO₂ gas.
Filling the balloon with water may be one place where error could have occurred. Using the value for the circumference of the balloon in cm, calculate the volume of balloon mathematically.
Our circumference was measured to be 32.8 cm and using the circumference formula, we figured out that the radius was 5.22 cm. We then plugged that into the volume formula to calculate what our volume would be if we had done it mathematically. Here is the volume formula with our answer below.
5.22³ x (4/3)π 'Pi' = 596 cm³
Compare your answer to #3 of the volume obtained by filling the balloon with water. Is it close? Which do you feel is more accurate and why?
Our measured volume was 717.5 mL and our mathematically calculated volume was 596 mL (since cm³ = mL). Our values were not close and I felt that our mathematically calculated volume is more correct because we used the circumference we had measured ourselves when calculating it, and not had had to recreate the circumference using water in order to get the volume.
The ideal gas law technically applies to ideal gases. Give two differences between a real gas and an ideal gas. You may use your computer or book to research.
Some differences between real gases and ideal gases are that ideal gases have no attractive or repulsive forces between particles, while real gases have small attractive and repulsive forces between particles. Ideal gases also have particles with no volume while real gases have a small volume.
Would the CO₂ you collected in this lab be considered ideal? Why or why not?
The CO₂ we collected in this lab would not be considered ideal because it has attractive and repulsive forces in between the particles. It also has volume in between the particles of the gas. Since the gas exists in normal conditions it exhibits properties such as the ones above that classify it as a real gas.
Using the information provided on the label, and stoichiometry, calculate the mass of CO₂ that sho7ld be collected per tablet.
What percent is the percent yield for the CO₂ collected in your sample?
CO₂ is water soluble. The solubility around room temperature is around 90 mL/100mL of water. What effect does this have on your calculated "n" value?
When we dissolved the Alka Seltzer tablets into the water, some of the CO₂ gas also may have dissolved into the water. This would have left us with less CO₂ gas and less CO₂ moles in the balloon so we would have a smaller "n" value.
We had to crush the alka seltzer tablets using the mortar and pestle, then weigh the crushed up tablets and pour them into a round balloon. We then filled up a test tube up to the top with water and put the balloon around the top of the test tube. To start the reaction, we flipped the balloon so the powder went into the water and started fizzing up and filling the balloon with gas. Once the reaction had ended, we were left with a full balloon of gas which we then measured the circumference of, with a piece of string and a ruler. We then used the data we had collected and Dalton's Law to find the mass of the CO₂ gas, the pressure of the gas, and the number of moles of CO₂ gas.
Picture of setup before the reaction |
Picture of the set up after the reaction |
Here is a picture of my calculations:
Analysis Questions:
Discuss an area in this lab where experimental error may have occurred.
Experimental error may have occurred when we were measuring the amount of water the balloon could hold to fit our circumference because some of our water spilled out of the balloon into the sink when we were pouring it into the graduated cylinder. We also may have measured the circumference of the balloon too early when the reaction may have still been going on.
Choose one error from above and discuss if it would make 'n' the number of moles of CO₂ too big or too small.
If we had measured the circumference too early when the reaction was still going on, it would have made the moles of CO₂ gas too small because the reaction was still releasing gas into the balloon making the balloon bigger and able to hold more moles of CO₂ gas.
Filling the balloon with water may be one place where error could have occurred. Using the value for the circumference of the balloon in cm, calculate the volume of balloon mathematically.
Our circumference was measured to be 32.8 cm and using the circumference formula, we figured out that the radius was 5.22 cm. We then plugged that into the volume formula to calculate what our volume would be if we had done it mathematically. Here is the volume formula with our answer below.
5.22³ x (4/3)π 'Pi' = 596 cm³
Compare your answer to #3 of the volume obtained by filling the balloon with water. Is it close? Which do you feel is more accurate and why?
Our measured volume was 717.5 mL and our mathematically calculated volume was 596 mL (since cm³ = mL). Our values were not close and I felt that our mathematically calculated volume is more correct because we used the circumference we had measured ourselves when calculating it, and not had had to recreate the circumference using water in order to get the volume.
The ideal gas law technically applies to ideal gases. Give two differences between a real gas and an ideal gas. You may use your computer or book to research.
Some differences between real gases and ideal gases are that ideal gases have no attractive or repulsive forces between particles, while real gases have small attractive and repulsive forces between particles. Ideal gases also have particles with no volume while real gases have a small volume.
Would the CO₂ you collected in this lab be considered ideal? Why or why not?
The CO₂ we collected in this lab would not be considered ideal because it has attractive and repulsive forces in between the particles. It also has volume in between the particles of the gas. Since the gas exists in normal conditions it exhibits properties such as the ones above that classify it as a real gas.
Advanced Questions:
Using the information provided on the label, and stoichiometry, calculate the mass of CO₂ that sho7ld be collected per tablet.
What percent is the percent yield for the CO₂ collected in your sample?
CO₂ is water soluble. The solubility around room temperature is around 90 mL/100mL of water. What effect does this have on your calculated "n" value?
When we dissolved the Alka Seltzer tablets into the water, some of the CO₂ gas also may have dissolved into the water. This would have left us with less CO₂ gas and less CO₂ moles in the balloon so we would have a smaller "n" value.
Monday, July 10, 2017
Specific Heat of a Metal Lab
During the specific heat of a metal lab, we were given a cylinder of metal and told that we had to identify that metal based on its' specific heat. We were able to use a balance, thermometer, two styrofoam cups, a glass beaker, a hot plate, and tongs.
Here is a picture of our setup:
My partner and I first took the mass of the metal cylinder, the mass of a styrofoam cup, the mass of the cup + water, and initial temperature of water in the cup. We then put the water and cylinder of metal in a glass beaker, then put the beaker on a hot plate in order to boil the water. After the water had boiled we took the initial temperature of the boiling water + metal, then quickly took the metal cylinder out of the water and put it into cool water. We kept taking the temperature of the metal in the cool water until it stopped changing. We now had all the data we needed to identify what the cylinder of metal was.
We used the data to figure out the amount of heat gained by the water which ended up being 1800 Joules.
We then used the amount of heat gained by the water, the mass of the water, and the change in temperature to figure out the amount of heat lost by the water which ended up being 0.32 Joules/Grams Celcius. Since our answer was in Grams and we needed it to be in Kilograms, we multiplied our answer by 1000 and got 320 Joules/Kg℃
We compared our answer to the specific heats' of multiple metals and saw that our metals' specific heat was similar to Zincs' specific heat. Zinc's specific heat was 390 Joules/Kg℃ so we were pretty close with our calculations but not exact. Some reasons for my partner and I being a little off in our calculations could be that since we were taking the temperature of the water in a closed styrofoam cup where we couldn't see the exact reading until we took the thermometer out, our readings were not as accurate as they could've been. We also may not have boiled the water enough so our initial temperature was lower and therefore our change in temperature would be off leading to our final specific heat.
Here is a picture of our setup:
My partner and I first took the mass of the metal cylinder, the mass of a styrofoam cup, the mass of the cup + water, and initial temperature of water in the cup. We then put the water and cylinder of metal in a glass beaker, then put the beaker on a hot plate in order to boil the water. After the water had boiled we took the initial temperature of the boiling water + metal, then quickly took the metal cylinder out of the water and put it into cool water. We kept taking the temperature of the metal in the cool water until it stopped changing. We now had all the data we needed to identify what the cylinder of metal was.
We used the data to figure out the amount of heat gained by the water which ended up being 1800 Joules.
We then used the amount of heat gained by the water, the mass of the water, and the change in temperature to figure out the amount of heat lost by the water which ended up being 0.32 Joules/Grams Celcius. Since our answer was in Grams and we needed it to be in Kilograms, we multiplied our answer by 1000 and got 320 Joules/Kg℃
We compared our answer to the specific heats' of multiple metals and saw that our metals' specific heat was similar to Zincs' specific heat. Zinc's specific heat was 390 Joules/Kg℃ so we were pretty close with our calculations but not exact. Some reasons for my partner and I being a little off in our calculations could be that since we were taking the temperature of the water in a closed styrofoam cup where we couldn't see the exact reading until we took the thermometer out, our readings were not as accurate as they could've been. We also may not have boiled the water enough so our initial temperature was lower and therefore our change in temperature would be off leading to our final specific heat.
Sunday, July 9, 2017
Evaporation and Intermolecular Attractions Lab
During the evaporation and intermolecular attraction lab, we dipped a thermometer into different solutions and recorded their temperature before they started to evaporate, and 240 seconds after they had started evaporating. To do this we used a LabQuest device which kept a running table/graph of temperature data from the thermometer.
Here is a picture of the pre-lab:
Here is a picture of my data table:
Questions:
Explain the differences in the difference in temperature of these substances as they evaporated. Explain your results in terms of intermolecular forces.
The differences in the difference in temperature of these substances did not very too much from each other. Methanol and ethanol had large changes while n-Butanol, glycerin, and water had smaller changes in temperature. This means that methanol and ethanol had weaker intermolecular forces as they were easier to overcome and had large vapor pressures, while n-Butanol, glycerin, and water had stronger intermolecular forces and smaller vapor pressures.
Explain the difference in evaporation of any two compounds that have similar molar masses. Explain your results in terms of intermolecular forces.
Methanol and ethanol had similar molar masses and also had similar changes in temperature. Even though they were similar, methanol had a larger change in temperature because it had a smaller molar mass than ethanol. The London dispersion bonds are stronger in molecules with more molar mass because it is more polarized, which explains why methanol had a larger change in temperature [it had a smaller molar mass than ethanol].
Explain how the number of -OH groups in the substances tested affects the ability of the tested compounds to evaporate. Explain your results in terms of intermolecular forces.
Methanol, ethanol, water and n-butanol had one -OH group each, so their molar mass affected the temperature change more then glycerin. Glycerin had three -OH groups making it have the smallest temperature change. This happens because the hydrogen bonds are stronger when there are more -OH groups in a substance. The stronger the hydrogen bonds, the harder the forces are to break which is why glycerin had a smaller temperature change then all of the other substances.
Here is a picture of the pre-lab:
Here is a picture of my data table:
Questions:
Explain the differences in the difference in temperature of these substances as they evaporated. Explain your results in terms of intermolecular forces.
The differences in the difference in temperature of these substances did not very too much from each other. Methanol and ethanol had large changes while n-Butanol, glycerin, and water had smaller changes in temperature. This means that methanol and ethanol had weaker intermolecular forces as they were easier to overcome and had large vapor pressures, while n-Butanol, glycerin, and water had stronger intermolecular forces and smaller vapor pressures.
Explain the difference in evaporation of any two compounds that have similar molar masses. Explain your results in terms of intermolecular forces.
Methanol and ethanol had similar molar masses and also had similar changes in temperature. Even though they were similar, methanol had a larger change in temperature because it had a smaller molar mass than ethanol. The London dispersion bonds are stronger in molecules with more molar mass because it is more polarized, which explains why methanol had a larger change in temperature [it had a smaller molar mass than ethanol].
Explain how the number of -OH groups in the substances tested affects the ability of the tested compounds to evaporate. Explain your results in terms of intermolecular forces.
Methanol, ethanol, water and n-butanol had one -OH group each, so their molar mass affected the temperature change more then glycerin. Glycerin had three -OH groups making it have the smallest temperature change. This happens because the hydrogen bonds are stronger when there are more -OH groups in a substance. The stronger the hydrogen bonds, the harder the forces are to break which is why glycerin had a smaller temperature change then all of the other substances.
Friday, July 7, 2017
Ester Synthesis Lab
During the Ester Synthesis Lab, we mixed different acids and alcohols together and then heated them in water. We were trying to see what mixtures of acids and alcohols made certain smells when heated. We found that the mixture/heating of acids and alcohols produces a sweet smell.
The last mixture we did was with 0.15 grams of salicylic acid, 12 drops of methyl alcohol, and 3 drops of concentrated sulfuric acid. This mixture smelled like sweet vinegar before we heated it. Before we could smell the mixture after it was heated, we had to add a few drops of water to the mixture. After we heated it and added the drops of water, it smelled minty.
Here is a picture of my data table:
Questions:
Compare the odors of the three mixtures after heating compared to the odors of the starting materials. How are they different?
Were the new compounds easily identified as a specific fragrance like apple or banana? In the case where a specific fragrance was detected, how does the odor compare to the natural fragrance?
Each person had a different idea of what each substance smelled like because smell is a qualitative description of a substance, not a quantitive one. Each person has been exposed to certain smells more often than others in their lifetime, so they have different ideas on what things smell like and how fast they can identify a scent. One person could be confident in saying that something smells like banana, and not be wrong, while at the same time someone else could say that it smells like an apple, and again, not be wrong. For me, I needed to smell only once to figure out what each substance smelled like because I am very sensitive to strong scents and the substances had very strong scents. The smells from the synthesis reaction smelled the same as the natural fragrance it was identified as which I thought was pretty cool, because we had made these scents ourselves instead of just smelling something that was already made.
Here is a picture of the finished challenge puzzle:
We started by mixing 10 drops of isopentyl alcohol with 10 drops of glacial acetic acid and one drop of concentrated sulfuric acid together. This mixture smelled like sweet apple medicine before we heated it, and smelled like dry erase marker/fake banana after we heated it.
The next mixture we did was with 10 drops of ethyl alcohol, 10 drops of glacial acetic acid, and one drop of concentrated sulfuric acid. This mixture smelled like vinegar before we heated it, and then nail polish remover after we heated it.
The last mixture we did was with 0.15 grams of salicylic acid, 12 drops of methyl alcohol, and 3 drops of concentrated sulfuric acid. This mixture smelled like sweet vinegar before we heated it. Before we could smell the mixture after it was heated, we had to add a few drops of water to the mixture. After we heated it and added the drops of water, it smelled minty.
Here is a picture of my data table:
Questions:
Compare the odors of the three mixtures after heating compared to the odors of the starting materials. How are they different?
In the beginning, the acids all smelled like vinegar and the alcohol smelled medical. After being combined, the mixtures smelled like vinegar, sweet apple medicine, and sweet vinegar. After heating the mixtures, the mixtures' smell became sweeter and turned to dry erase marker/fake banana, nail polish remover, and mint. The chemical makeup of the sweet smells is different than the makeup of the sour and medicinal smells. The combination of alcohols and acids with heat caused a reaction to occur that produced different functional groups from what the substances started with.
Based on the smell of the mixtures after heating, what functional group must be present in the final molecules that were produced?
The sweet smell of the mixtures after heating indicates that ester must be present in the final molecules. This functional group is what caused the final products to smell sweet.
Here is a picture of ester:
Based on the smell of the mixtures after heating, what functional group must be present in the final molecules that were produced?
The sweet smell of the mixtures after heating indicates that ester must be present in the final molecules. This functional group is what caused the final products to smell sweet.
Here is a picture of ester:
Were the new compounds easily identified as a specific fragrance like apple or banana? In the case where a specific fragrance was detected, how does the odor compare to the natural fragrance?
Each person had a different idea of what each substance smelled like because smell is a qualitative description of a substance, not a quantitive one. Each person has been exposed to certain smells more often than others in their lifetime, so they have different ideas on what things smell like and how fast they can identify a scent. One person could be confident in saying that something smells like banana, and not be wrong, while at the same time someone else could say that it smells like an apple, and again, not be wrong. For me, I needed to smell only once to figure out what each substance smelled like because I am very sensitive to strong scents and the substances had very strong scents. The smells from the synthesis reaction smelled the same as the natural fragrance it was identified as which I thought was pretty cool, because we had made these scents ourselves instead of just smelling something that was already made.
Here is a picture of the finished challenge puzzle:
Wednesday, July 5, 2017
Electron Configuration Battleship
Here is picture of my set up:
It was challenging to find the right configuration for the element you wanted to hit because this skill is so new and we are still practicing how to use the periodic table to make the configurations. It was also challenging when you had to say long configurations because it took a long time and you had to make sure you were saying the right orbits/sub levels in the right order.
During this game, I learned how to make electron configurations using the periodic table, and I was able to understand how to use the noble gas shortcut and which orbitals corresponded to certain elements.
It was challenging to find the right configuration for the element you wanted to hit because this skill is so new and we are still practicing how to use the periodic table to make the configurations. It was also challenging when you had to say long configurations because it took a long time and you had to make sure you were saying the right orbits/sub levels in the right order.
During this game, I learned how to make electron configurations using the periodic table, and I was able to understand how to use the noble gas shortcut and which orbitals corresponded to certain elements.
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Titration Lab
During the titration lab, we had to determine the percentage ionization of acetic acid in vinegar. We did this by titrating the acetic acid ...
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During the titration lab, we had to determine the percentage ionization of acetic acid in vinegar. We did this by titrating the acetic acid ...
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During our Aluminum Foil Lab, we had to determine the thickness of a piece of aluminum foil using only a ruler, a scale, and a calculator. T...
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During the Density Block Lab, we had to find the mass of one block by using only a ruler and a calculator. The density was given to us but w...