What is the smallest volume of liquid that can be measured in a 50 mL cylinder?

Chemistry is the study of matter. Our understanding of chemical processes thus depends on our ability to acquire accurate information about matter. Often, this information is quantitative, in the form of measurements. In this lab, you will be introduced to some common measuring devices, and learn how to use them to obtain correct measurements, each with correct precision. A metric ruler will be used to measure length in centimeters (cm).

All measuring devices are subject to error, making it impossible to obtain exact measurements. Students will record all the digits of the measurement using the markings that we know exactly and one further digit that we estimate and call uncertain. The uncertain digit is our best estimate using the smallest unit of measurement given and estimating between two of these values. These digits are collectively referred to as significant figures. Note, the electronic balance is designed to register these values and the student should only record the value displayed.

When making measurements, it is important to be as accurate and precise as possible. Accuracy is a measure of how close an experimental measurement is to the true, accepted value. Precision refers to how close repeated measurements (using the same device) are to each other.

Example 2.1.1 : Measuring length

Here the “ruler” markings are every 0.1-centimeter. The correct reading is 1.67 cm. The first 2 digits 1.67 are known exactly. The last digit 1.67 is uncertain. You may have instead estimated it as 1.68 cm.

The measuring devices used in this lab may have different scale graduations than the ones shown Precision is basically how many significant figures you have in your measurement. To find the precision, you basically take the smallest unit on your measuring device, and add a decimal place (the uncertain digit).

Measurements obtained in lab will often be used in subsequent calculations to obtain other values of interest. Thus, it is important to consider the number of significant figures that should be recorded for such calculated values. If multiplying or dividing measured values, the result should be reported with the lowest number of significant figures used in the calculation. If adding or subtracting measured values, the result should be reported with the lowest number of decimal places used in the calculation.

In this lab, students will also determine the density of water as well as aluminum. Volume is the amount of space occupied by matter. An extensive property is one that is dependent on the amount of matter present. Volume is an extensive property.

The volume of a liquid can be directly measured with specialized glassware, typically in units of milliliters (mL) or liters (L). In this lab, a beaker, two graduated cylinders and a burette will be used to measure liquid volumes, and their precision will be compared. Note that when measuring liquid volumes, it is important to read the graduated scale from the lowest point of the curved surface of the liquid, known as the liquid meniscus.

Example 2.1.3 : Measuring the Volume of a liquid

Here, the graduated cylinder markings are every 1-milliliter. When read from the lowest point of the meniscus, the correct volume reading is 30.0 mL. The first 2 digits 30.0 are known exactly. The last digit 30.0 is uncertain. Even though it is a zero, it is significant and must be recorded.

The volume of a solid must be measured indirectly based on its shape. For regularly shaped solids, such as a cube, sphere, cylinder, or cone, the volume can be calculated from its measured dimensions (length, width, height, diameter) by using an appropriate equation.

Formulas for Calculating Volumes of Regularly Shaped Solids:

\[\text{Volume of a cube} = l \times w \times h\]

\[\text{Volume of a sphere} = \frac{4}{3} \pi r^3\]

(where \(r\) = radius = 1⁄2 the diameter)

\[\text{Volume of a cylinder} = \pi r^2 h\]

For irregularly shaped solids, the volume can be indirectly determined via the volume of water (or any other liquid) that the solid displaces when it is immersed in the water (Archimedes Principle). The units for solid volumes are typically cubic centimeters (cm3) or cubic meters (m3). Note that 1 mL = 1 cm3.

Measuring the Volume of an Irregularly Shaped Solid

The volume water displaced is equal to the difference between the final volume and the initial volume , or:

\[V=V_f -V_i\]

where the volume water displaced is equal to the volume of solid.

Density is defined as the mass per unit volume of a substance. Density is a physical property of matter. Physical properties can be measured without changing the chemical identity of the substance. Since pure substances have unique density values, measuring the density of a substance can help identify that substance. Density is also an intensive property. An intensive property is one that is independent of the amount of matter present. For example, the density of a gold coin and a gold statue are the same, even though the gold statue consists of the greater quantity of gold. Density is determined by dividing the mass of a substance by its volume:

\[density=\frac{mass}{volume}\]

Density is commonly expressed in units of g/cm3 for solids, g/mL for liquids, and g/L for gases.

Procedure

Materials and Equipment

Metric ruler, shape sheet (find a rectangle and circle available at home, say a notebook or circular filter paper), 250-mL Erlenmeyer flask, 100-mL beaker, sugar, 400-mL beaker, spoon, burette (instead of burette, use a long graduated pipette with a bulb), 10-mL and 100-mL graduated cylinders, aluminum pellets/bar, aluminum foil, electronic balance, water (you do not need distilled water, tap water is just fine).

Part A: Measuring the Dimensions of Regular Geometric Shapes

1. Find a ruler and “shape sheet” (use any rectangular or circular shaped flat objects like notebook or filter paper) . Measure the dimensions of the two geometric shapes: length and width of the rectangle, and the diameter of the circle. Record these values on your lab report
2. Use your measurements to calculate the area of each shape:

• Area of a rectangle: \(A = l \times w\)
• Area of a circle: \(A = \pi r^2\) (\(r\) = radius = 1⁄2 the diameter)

Part B: Volumes of Liquids and Solids

Volumes of Liquids

1. Find a burette (use a long graduated pipette with a bulb instead), 10-mL graduated cylinder, 100-mL graduated cylinder and 100-mL beaker, each filled with a certain quantity of water. Measure the volume of water in each. Remember to read the volume at the bottom of the meniscus. It is useful to hold a piece of white paper behind the burette/cylinder/beaker to make it clearer.

Volume of a Regularly Shaped Solid

1. Find a wooden block or cylinder and ruler from your home.
2. Measure the dimensions of the block. If it is a cube or a rectangular box, measure its length, width and height. If it is a cylinder or cone, measure its height and the diameter of its circular base.

Part C: The Density of Water

1. Using the electronic balance determine the mass of a clean, dry, 100-mL graduated cylinder.
2. Pour 40-50 mL of distilled water into the graduated cylinder and weigh. Make sure that the outside of the graduated cylinder is dry before placing it on the electronic balance.
3. Measure the liquid volume in the cylinder
4. Use the mass and volume to calculate the density of water.

Part D: The Density of Aluminum and the Thickness of Foil

Density of Aluminum

1. Using the electronic balance to determine the mass of a clean, dry, small beaker.
2. Obtain an aluminum pellet/bar. Transfer pellet/bar to the beaker weighed in the previous step, and measure the mass of the beaker and pellet/bar together.
3. Pour 30-35 mL of water into your 100-mL graduated cylinder. Precisely measure this volume.
4. Carefully add all the aluminum pellet/bar to the water, making sure not to lose any water to splashing. Also make sure that the pellet/bar are all completely immersed in the water. Measure the new volume of the water plus the pellet/bar.
5. When finished, retrieve and dry the aluminum pellet/bar.
6. Analysis: Use your measured mass and volume (obtained via water displacement) of the aluminum pellet/bar to calculate the density of aluminum.

The Thickness of Aluminum Foil

1. Take a rectangular piece of aluminum foil and ruler. Use the ruler to measure the length and width of the piece of foil.
2. Fold the foil up into a small square and measure its mass using the electronic balance
3. Analysis: Use these measurements along with the density of aluminum to calculate the thickness of the foil.

Lab Report: Measurements in the Laboratory

Part A: Measuring the Dimensions of Regular Geometric Shapes

Experimental Data

Data Analysis

1. Perform the conversions indicated. Show your work, and report your answers in scientific notation.

• Convert the measured rectangle length to hm.

• Convert the measured circle diameter to nm.

1. Calculate the areas of your rectangle and circle in cm2. Show your work, and report your answers to the correct number of significant figures.

• Area of rectangle

• Area of circle

Part B: The Volumes of Liquids and Solids

Table 1: The Volume of Liquid Water

Table 2: The Volume of a Regular Solid, shaped as a

Data Analysis

Use your measured block dimensions (in Table 2) to calculate the block volume, in cm3. Show your work, and report your answer to the correct number of significant figures.

Part C: The Density of Water

Table 1: The Density of Water

Calculate the density of water, in g/mL. Show your work, and report your answer to the correct number of significant figures.

Part D: The Density of Aluminum and the Thickness of Foil

Experimental Data

Table 1: The Density of Aluminum

Table 2: The Thickness of Aluminum Foil

Data Analysis

1. Use your measured mass and volume of the aluminum pellet (in Table 1) to calculate the density of aluminum, in g/cm3. Show your work, and report your answer to the correct number of significant figures.
2. Use your measurements for the aluminum foil (in Table 2) along with the true density of aluminum (\(_D_{Al}\) = 2.70 g/cm3) to calculate the foil thickness, in cm. Consider the foil to be a very flat rectangular box, where Volume of foil = V = length \(\times\) width\(\times\) height (thickness). Show your work, and report your answer in scientific notation.