Introduction:
The most common we find in the laboratory setting are mass and volume. Using these two variables, a value for density can be found using the equation: D = m/V
As seen above, density is the ratio of mass to a unit of volume. This value is constant for the given substance at a specific temperature. This makes density is considered an intensive property, meaning it is dependent on the identity of the substance, regardless of its source. On the other hand, mass and volume are both extensive properties, signifying that they change depending n the quantity of substance present. In order to measure mass in the laboratory, the analytical balance is always the device used, as it is accurate to 0.0001 grams. Volume can be found easily by taking measurements of an object, if it has a regular shape such as that of a cube, cylinder, or cone. However, with irregularly shaped objects, it the displacement of water experienced by immersion of the object that is used to indirectly measure its volume.
Accuracy is defined as the closeness of a measurement to the actual, or expected, value. On the other hand, precision refers to the closeness of repeated measurements. These terms are important to know, as we determine the uses of different laboratory materials. The most accurate and precise measurements for liquid volumes are made with burets, volumetric flasks, and volumetric pipets. Meanwhile, the graduated cylinder is less accurate, but just as precise as the above tools. Finally, beakers and flasks in the laboratory are neither accurate nor precise. Instead, these tools are used to transport larger volumes of liquid from the main container to the lab bench, where the liquid can be poured out of or taken from the beaker/flask with ease and a greater degree of safety.
Objective:
We had two main objectives in this lab. The first purpose was to determine the mass and volume of several liquids and solids then use significant figures to report the calculated densities. Secondly, we aimed to calculate precision and accuracy of the volumetric pipets, a graduated cylinder, and either a flask or beaker.
Procedures:
Part A: Calibration of a Volumetric Pipet & a Graduated Cylinder A 10.0 ml volumetric pipet was calibrated by measuring the difference in mass (m, using an analytical balance accurate to 0.0001 g) between an empty 50 ml beaker and the mass of the beaker after addition of one volume of water delivered from the pipet. From the recorded temperature, the density (D) of the water was determined from the table on p. 38 of the Lab Manual. Finally, the calibrated volume of the 10.0 ml volumetric pipet was determined by the formula:
V = m/D.
This protocol was repeated for a total of three trials. Using V from each of the three trials, the average and standard deviation (see p. 32 of the Lab Manual) were determined.
An analogous procedure was used to calibrate a 10 ml from a graduated cylinder.
Part B: Determination of the Density of an Unknown Liquid
The density of and unknown liquid was determined by using the calibrated volume of our pipet (Part A) and the recorded mass of the unknown liquid. To find the mass of the unknown liquid, we first measured a dry 50 ml beaker and then the mass of the same beaker after adding “10 ml” of the unknown liquid. With this difference in mass, and the volume from Part A, we calculated the density. We repeated this procedure for two additional trials, to find an average density of the liquid.
Part C: Determination of the Density of a Regularly Shaped Solid
In this part of the experiment we obtained a small, solid steel cylinder and set out to find its density. Since the object in this part of the experiment was a cylinder, we only had to measure its radius and height. We were then able to calculate the density of the cylinder using the following
formula:
?(r2)(h) [ r = radius; h = height]
We repeated these measurements two more times, and found the average density for the small, solid steel cylinder.
Part D: Determination of the Density of an Irregularly Shaped Solid
In this part of the experiment, we had to make a more complicated measurement of density with an irregularly shaped solid. We obtained and weighed a screw (to 0.0001g). Since the screw was irregularly shaped and does not have a uniform equation for volume, we instead used the displacement of water. To do this we obtained a suitable 25 ml graduated cylinder and filled it halfway with water, recording the observed volume. Then we carefully immersed the screw into the graduated cylinder, and recorded the new volume reading. We repeated this procedure twice more for a total of three mass readings and three volume readings. Finally, we found the density of the screw using the average of the three mass readings, as well as the average of the three volume readings.
Results & Conclusions:
In Part A, we calibrated two common pieces of laboratory equipment using the equation for density: (d=m/v). Our water temperature was 22.5?C, which allowed us to use the actual density of water at this temperature: 0.997655 (g/mL). The differences in masses for the volumetric pipet and water from three trials of measuring were 9.8830 g, 9.8957 g, and 9.9030 g. This allowed us to calculate the volumes of each trial, which came out to be 9.9062 mL, 9.9190 mL, and 9.99263 mL respectively. Finally, by averaging the three values, our average volume was calculated to be 9.9172 mL, which is very close to the stated 10 mL volume of the pipet. We repeated the same procedure for the graduated cylinder, and found an average volume of 9.8064 mL. As expected this showed that the graduated cylinder is definitely a less accurate measuring device than the pipet, however it is just as precise.
Now that we had calculated the true volume our calibrated pipet could hold, we could use that fixed volume to find the average density of an unknown liquid. We went about a similar procedure in Part B and found that for three trials, the unknown liquid had a mass of 11.5252 g, 11.5555 g, and 11.5433 g. Using that calibrated volume we found the three respective densities for each trial, and calculated an average density of 1.1637 (g/mL) for the unknown liquid. The following is the equation for standard deviation:
Using this equation we found sx = 0.002. We then used the following equation for relative standard deviation, and calculated a value of 0.13% for our experiment in Part B. Both our calculated values of standard deviation (0.002) and relative standard deviation (0.13%) show that we have an extremely low degree of variance in our results, which is a good thing. This means our precision is high!
In Part C we have a known steel solid, whose uniform cylindrical shape can be assigned a known equation for volume: ?(r2)(h) [ r = radius; h = height]
After weighing and measuring the radius and the height of our steel cylinder in three separate trials, we came up with an average density of 8.5 (g/mL). As compared to the given value of density for steel from the CRC handbook {7.1 (g/mL)}, we find ourselves slightly off. Using the following equation for percent error, we find our error to be 19.7%:
Our error was not huge, but it can be seen as less than desirable. One reason I believe we came up with such a discrepancy is because the ruler we used for measuring the radius and height of the cylinder can only give us so many significant figures. That is to say, we could only derive two known digits for our values in these measurements. Another reason for the error could be that since we could only be certain up to two digits, there was very little to no variance in our trials, which led to much more precision than accuracy.
Finally in Part D of the lab, we used the displacement of water caused by an irregularly shaped object to determine the object’s density. After three trials of immersing a screw in a noted volume of water, we found the values for the change in volume to be 1 mL, 0.44 mL, and 0.82 mL. These vastly different readings produced density values that lacked both precision and accuracy. We already knew the graduated cylinder was a mediocre measuring tool for accuracy, however once again the limitations in the amount of known digits in our reading accounted for the different results {4.4 (g/mL), 10.0 (g/mL), & 5.4 (g/mL)}. Post-Lab Questions
1. Based on our observations the volumetric pipet was more accurate than the graduated cylinder. This is due to the fact that we wanted to see how close to the value of 10.0 mL each tool would give us. The pipet produced a volume that was slightly closer to 10.0 mL (9.9172 mL) than the graduated cylinder (9.8064 mL).
2. Again, the volumetric pipet produced values across all three trials that indicated it was superior in precision to the graduated cylinder {(9.9062 mL, 9.9190 mL, 9.9263 mL) vs. (9.6601 mL, 9.8424 mL, 9.9167 mL)}.
3. It is ineffective to only make a single measurement when trying to determine the precision of a device because the definition of precision is how close observed values are to one another. This implies multiple, repeated trials.
4. The given density at a certain temperature would have been different. On the surface it seems that the difference in the density values for water at certain temperatures is not very different, but since we were taking into account all decimal places in our calculations, any variance would definitely account for a change in precision and accuracy.
