How do you measure the diameter of a beaker using string and a ruler?

Place the beaker upside down on a pad. Position one end of the string at the edge of the base and extend it across to the opposite side. Mark both endpoints on the string with a marker, then remove it and measure the distance between marks using a ruler. Record this measurement as the diameter and repeat the process two more times for consistency.

What is the correct way to read the volume in a volumetric pipette?

The measurement is correct when the bottom of the meniscus aligns with the appropriate volume line marked on the pipette. A pipetter or bulb draws liquid into the pipette, and you must adjust the liquid level so the meniscus bottom sits exactly at the specified volume marking. Never pipette by mouth; always use a mechanical pipetter device.

Why is it important to repeat measurements multiple times in lab experiments?

Repeating measurements allows you to assess consistency and identify possible sources of error in your technique. Error can be introduced in any experiment, even when performed carefully and correctly. By taking multiple trials, you can evaluate the reliability of your results and understand the uncertainty in your experimental methods.

How does vacuum filtration separate solids from liquids using a Büchner funnel?

A Büchner funnel connects to a filter flask via a rubber adapter and attaches to a vacuum source. Filter paper is placed inside the funnel, and the solution is poured in. The vacuum pulls liquid through the filter paper into the flask below, while solids remain on the filter paper in the funnel, effectively separating the two components.

What does percent yield measure in a filtration experiment?

Percent yield equals the final mass of sand divided by the initial mass of sand, multiplied by 100. It measures the efficacy of your filtration technique. A percent yield closer to 100% indicates better filtration. Values above 100% suggest calculation errors, incorrect weighing, or incompletely dried sand.

How do you determine if your circumference measurements were accurate?

Plot measured circumference versus measured diameter on a scatter plot, then calculate expected circumference using the formula C=πD and plot both datasets. Fit linear best-fit lines to both sets of data and compare their slopes, intercepts, and r-squared values. If measurements were accurate, the two trend lines should closely match and resemble the circumference formula.

What personal protective equipment is required before beginning lab measurements?

Wear gloves, chemical splash goggles, and a lab coat before starting any lab exercise. Additionally, place a protective pad on the benchtop to prevent breakage of glassware during measurements. These precautions protect you from chemical exposure and minimize equipment damage during experimental procedures.

Scientific Measurement and Lab Skills

Concepts Instructor Prep Student Protocol

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Translating experimental findings from data points to visual representations, like graphs, is essential to determining the relationship between two or more properties. These properties are called variables. When there are two variables, a graph created from the data is called two-dimensional. The graph has two axes. The independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis.

Take, for example, this sample data for the temperature and volume of a gas. The volume of the gas depends on the temperature. Thus, we would plot the measured temperature on the x-axis and the volume on the y-axis.

When there are several data points with the same x-value, like if we measured the volume several times at one temperature, we also calculate the standard deviation of those measurements. The standard deviation is a statistical value, which indicates the amount of variation present in a set of values.

Standard deviation is calculated using this formula, where n is the number of data points, x bar is the mean value of the data points, and x_i represents each individual data point. You can compute the standard deviation by hand, or a spreadsheet program can calculate it automatically. The closer the standard deviation is to 0, the closer the data points are to the mean value. If the standard deviation is equal to 0, then all of the entered data points have the same value.

Let's look at the mean values and standard deviations of the volume measurements at each temperature in our data set. We can summarize each set of data points as the mean plus or minus the standard deviation. We determine the significant figures for each mean from the corresponding measurements and round the mean values accordingly.

The standard deviation of each group must have the same number of decimal places as the mean, so we round each standard deviation to the hundredths place. To graphically determine the relationship between two variables, we can fit the data with a best-fit function.

The function is automatically generated by spreadsheet software and can take the form of a linear trend line, a polynomial function, or an exponential or logarithmic function. In the case of our temperature and volume data, the relationship is a linear one. So, the data points are fit by linear least squares regression. Your spreadsheet program will return the equation for the best fit line and an r-squared value. The closer the r-squared value is to 1, the better the fit of the data.

Next, you can use your spreadsheet software to find the standard deviations of the slope, the y-intercept, and the calculated y-value. To determine the significant figures for the values in the equation, we follow a simple rule. The last significant figure of each value corresponds to the first significant decimal place of its standard deviation.

Thus, we round the slope to the thousandths place and the y-intercept to the tenths place, and we round the standard deviations to match. Our slope is 0.167 +/- 0.003 liters per Kelvin, and our y-intercept is -40.6 +/- 1.2 liters. Any calculated y-value will be rounded to the tenths place and will be +/- 0.8 liters. This equation describes the relationship between temperature and the volume of a gas.

In this lab, you will create a data set of dependent and independent variables by measuring the diameter and circumference of various sizes of beakers. You'll then use this data to create a scatter plot and perform a linear regression, keeping in mind the importance of significant figures. You'll also practice lab skills, like filtering and measuring volume using pipettes, paying attention to the uncertainty in the measurements and analysis.

Print Procedure Steps

Source: Smaa Koraym at Johns Hopkins University, MD, USA

Measuring Diameter and Circumference

Error can be introduced in any experiment, even when the technique is performed carefully and correctly. It is essential to critically examine your experimental methods when performing any lab exercise in order to understand and evaluate uncertainty. In this part of the lab, you'll determine a procedure for measuring the circumference of different glassware and then assess sources of error in your measurements.

To begin, put on the appropriate personal protective equipment, including gloves, chemical splash goggles, and a lab coat.
Set a pad on the benchtop to prevent the breakage of glassware. Flip each beaker upside down on the pad so that the base of the beaker is facing the ceiling.
Place one end of the string as close to the edge of the base as possible and extend the string to the other side of the beaker to measure the diameter. Use a marker to mark the string, labeling the edges.

Remove the string and use the ruler to measure the distance between the endpoints marked on the string. Record the diameter (and the volume) in your notebook. Repeat the measurement two more times.

Table 1: Measuring Diameter and Circumference

		Trial 1	Trial 2	Trial 3
50-mL beaker	Measured diameter
	Measured circumference
	Calculated circumference
100-mL beaker	Measured diameter
	Measured circumference
	Calculated circumference
250-mL beaker	Measured diameter
	Measured circumference
	Calculated circumference
400-mL beaker	Measured diameter
	Measured circumference
	Calculated circumference
600-mL beaker	Measured diameter
	Measured circumference
	Calculated circumference
Measured Circumference vs. Diameter		Calculated Circumference vs. Diameter
Slope		Slope
y-intercept		y-intercept
R²		R²

Click Here to download Table 1

Place one end of the string at the edge of the beaker and extend the string around the beaker to measure the circumference. Note: Try to measure the circumference at the same height that you measured the diameter while keeping the string as level as possible.
Mark the string, measure the length using the ruler, and write down the circumference measurement in your notebook. Repeat the measurement two more times.
Collect diameter and circumference measurements for each of the different sized beakers and record them in your notebook.

Pipetting

Pipettes are volumetric devices used in the lab to measure and deliver specific volumes of liquids. There are different types of pipettes, but the ones we will use today are called volumetric pipettes. These glass pipettes are labeled with the letters 'TD' and the volume, which denotes that it is designed to deliver the volume of liquid at the specified temperature. The error is also listed. The measurement is correct when the bottom of the meniscus is at the appropriate volume line. A pipetter or bulb is used to draw the liquid into the pipette. In this part of the lab, you will practice pipetting using different volumetric pipettes and examine your consistency and possible sources of errors. Note: You must never pipette by mouth.

To begin, fill a 50-mL beaker with tap water.

Weigh the empty 10-mL graduated cylinder on the balance and record the weight.

Table 2: Pipetting 10 mL of Water

	5-mL pipette			10-mL pipette
	1st measurement	2nd measurement	3rd measurement	1st measurement	2nd measurement	3rd measurement
Mass_{empty 10-mL graduated cylinder}(g)
Mass_{full 10-mL graduated cylinder} (g)
Volume_water (mL)
Mass_water (g)
Mass_{empty 10-mL graduated cylinder} (g)
Mass_{full 10-mL graduated cylinder}(g)
Volume_water (mL)
Mass_water(g)

Click Here to download Table 2

Attach a 5-mL pipette to the pipetter and draw up 5 mL of water. Adjust the volume so that the bottom of the meniscus is at the 5-mL measurement line. Then, dispense the water into the 10-mL graduated cylinder.
Repeat to add another 5 mL of water to the graduated cylinder.
Read the volume filled on the graduated cylinder and record it in your notebook.
Return the graduated cylinder to the balance and record the new mass. Subtract the initial mass from this value to obtain the mass of water added to the glassware.
Weigh the mass of the empty 10-mL volumetric flask and record the value. Use a 5-mL pipette to measure 10 mL of water into the flask. Return the flask to the balance and record the new mass. Subtract the initial mass to obtain the mass of water added.
Dump the water out of the graduated cylinder and volumetric flask and attach the 10-mL pipette to the pipetter.
Reweigh the empty graduated cylinder. Then, take up 10 mL of water using the pipette and dispense it into the graduated cylinder. Read the volume of liquid, record it in your notebook, and determine the mass of the water added.
Reweigh the empty volumetric flask and then measure 10 mL of water into the volumetric flask. Determine the mass of the water added.
Continue to practice pipetting by delivering volumes of liquid to both the graduated cylinder and the volumetric flask. Repeat at least three times for each pipette and glassware. Record all volume and mass measurements so that you can determine the consistency and accuracy of your technique.

Vacuum Filtration
Vacuum filtration using a Büchner funnel is a technique often used to separate solids from liquids. A Büchner funnel is connected to a filter flask using a rubber adapter and is then attached to a vacuum with silicone tubing. After filter paper is placed inside the funnel, the solution is poured into it. The vacuum pulls the liquid into the flask with the solids remaining on the filter paper in the funnel. In this part of the lab, you'll practice this technique by filtering sand from water using the Büchner funnel setup. You will then check the efficacy of your technique by comparing the weight of the sand before and after filtration.
- To begin, zero the balance. Place an empty weigh boat on the balance and record the weight in your notebook. Then, tare the balance.
  Table 3: Vacuum Filtration
  
  Initial mass of sand (g)
  Final mass of sand (g)
  Percent yield
  Click Here to download Table 3
- Remove the weigh boat from the balance and use the scoopula to transfer sand to the weigh boat. Return the weigh boat back to the balance and check the mass.
- Add or remove sand until you have about 3 g. Record the weight as the initial mass in your notebook.
- Obtain approximately 20 mL of acetone in a labeled beaker, making sure to cover it with a watch glass as you bring it back to your workstation.
- Measure 20 mL of deionized water using the 10-mL graduated cylinder and pour the water into the 100-mL beaker.
- Obtain red dye solution and measure 5 mL of the dye solution using the 5-mL pipette.
- Dispense the red dye into your beaker of water and then add in the sand. Thoroughly mix the sand, dye, and water using a glass stirring rod.
- Set up the vacuum filtration system. Place the rubber adapter in the neck of the filter flask and connect the silicone tubing from the vacuum to the barbed arm of the filter flask. Place the stem of the Büchner funnel into the rubber adapter and make sure it is a snug fit. Center the filter paper inside the funnel, then, turn the vacuum on to begin suction.
- Gently stir your sand mixture while slowly pouring it into the center of the filter paper. Use your glass stirring rod to direct the mixture to the center of the funnel. Scrape any leftover sand mixture into the funnel using the rubber policeman.
- Once all of the water has gone through the funnel, turn off the vacuum. Check to make sure that no sand entered the filtrate in the flask. Note: If sand did enter, the filter paper was not centered in the funnel. Re-center the filter paper, then empty the filtrate into the beaker and filter the solution again.
- Once the solution is properly filtered, turn the vacuum off and rinse the sand on the filter paper with about 3 - 5 mL of deionized water. Turn the vacuum on to remove the water and dye. Repeat the rinsing step until all the red dye is removed from the sand.
- Turn off the vacuum and disconnect the filter flask from the silicone tubing.
- Label the 600-mL beaker as 'aqueous waste' and pour the filtrate from the filter flask into the beaker.
- Reattach the filter flask and tubing to the Büchner funnel. Dry the sand further by rinsing it with 3-5 mL of acetone. Turn on the vacuum to pull the liquid into the filter flask. Repeat this step 1-2 more times to dry the sand completely.
- For the last drying step, place the large rubber stopper on top of the funnel for about 10 min.
- Label a separate beaker for organic waste. Turn off the vacuum, disconnect the tubing from the flask, remove the funnel, and pour the acetone into the organic waste flask.
- Take the funnel and filter paper to the balance and tare a clean weigh boat.
- Carefully remove the filter paper from the funnel and scrape the sand into the weigh boat using the rubber policeman. Weigh the sand and record the mass as 'final mass'.
- After 5 min, measure the mass again and note any changes.
- To clean up from the lab, rinse the aqueous waste down the sink. Pour the organic waste into the designated organic waste container. Discard the sand, filter paper, and string in the trash. Rinse all used glassware with tap water and set them to dry.
Results
Now that you have practiced measuring, pipetting, and filtering, let's analyze your techniques.
- First, let's look at the consistency of your beaker diameter and circumference measurements. Use spreadsheet software to prepare a scatter plot of measured circumference versus measured diameter.
- Plot diameter as the independent variable on the x-axis, and plot circumference as the dependent variable on the y-axis.
- Calculate the expected circumference for each of the measured diameters using the following equation: C=πD
- Plot the expected circumference values as a function of diameter on the same graph.
- Fit both sets of data using a linear best fit and determine the slope, intercept, and r-squared value of the fit line. The slope and intercept have more significant figures than the original measurement. Our measurements were only accurate to the tenths place. So, the equation is adjusted to y = 2.9x + 2.1.
- If your measurements of circumference were accurate, the two trend lines should closely match, and the trend line equation should closely match the formula for circumference. You can see here our measurement of circumference, and that our line of best fit has some error.
- Now, let's look at your pipetting skills. Remember that we used both a 5-mL pipette and a 10-mL pipette to measure 10 mL of water into a 10-mL graduated cylinder and then measured the weight.
- First, subtract the mass of the empty graduated cylinder from the graduated cylinder containing water to obtain the mass of the 10 mL of water.
- Here, we show the results of two trials for the 5-mL and 10-mL pipettes. Since the density of water is 1 g/mL, 10 mL of water has a mass of 10 g. The measurement of 10 mL of water was fairly accurate using either volume of pipette, with the 5-mL pipette being slightly more exact.
- To analyze how well the sand was filtered using the Büchner funnel setup, calculate the percent yield. The percent yield is equal to the final mass of sand, or the actual yield, divided by the initial mass of sand, or the theoretical yield, times 100.
  Note: It is impossible to obtain a percent yield greater than 100%. As the final mass of sand, or the actual yield, cannot be higher than the initial mass, or the theoretical yield.
- Here, we show the results from our filtration, where the percent yield is equal to about 75%. The closer the percent yield is to 100%, the better the filtration. Note: If your percent yield is higher than 100%, there could be an error in your calculation, the sand could have been weighed incorrectly, or the sand may not have been completely dry when weighed.