What Method Did the Students Use to Calculate Vmax?

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Lesson 3.2

Finding Volume: The Water Deportation Method

Fundamental Concepts

• A submerged object displaces a volume of liquid equal to the volume of the object.
• Ane milliliter (i mL) of water has a volume of 1 cubic centimeter (1cm³).
• Different atoms have unlike sizes and masses.
• Atoms on the periodic table are arranged in order co-ordinate to the number of protons in the nucleus.
• Fifty-fifty though an cantlet may be smaller than some other atom, information technology might have more than mass.
• The mass of atoms, their size, and how they are bundled determine the density of a substance.
• Density equals the mass of the object divided by its book; D = m/v.
• Objects with the aforementioned mass only different volume have different densities.

Summary

Students use the h2o deportation method to notice the book of different rods that all have the same mass. They calculate the density of each rod, and use the characteristic density of each material to identify all five rods. Then students consider the human relationship between the mass, size, and arrangement of atoms to explain why different rods have different densities. Students will exist briefly introduced to the periodic table.

Objective

Students will be able to explain that materials accept characteristic densities because of the dissimilar mass, size, and arrangement of their atoms. Students volition be able to utilise the book displacement method to find the volume of an object.

Evaluation

Download the student action canvas, and distribute one per pupil when specified in the activity. The activity canvass will serve as the "Evaluate" component of each 5-East lesson plan.

Safety

Make sure yous and your students wear properly plumbing equipment goggles.

Materials for Each Group

• Gear up of v unlike rods that all have the same mass
• Graduated cylinder, 100 mL
• Water in a cup
• Calculator

Notes virtually the materials:

For this lesson yous will demand a set of five solid rods, each with the aforementioned mass, same diameter, simply a different book. Each rod is made of a unlike textile. There are several versions of these rods available from different suppliers. This activity uses the Equal Mass Kit from Flinn Scientific (Product #AP4636) only can be adapted to any set of equal mass rods. Since there are merely 5 samples in the Equal Mass kit, you may demand two kits then that each group can work with a sample.

This chart will assistance you lot identify each rod. Practice not reveal this data to the students. They will find the identity of each rod and the changed human relationship betwixt the density and the length of each rod after in this lesson.

Table ane. Physical properties for solid cylinder unkowns.

Sample	Textile	Judge Density (g/cm3)	Relative length
Smallest metallic	Brass	7.5	shortest
Shiny gray metal	Aluminum	3.0
Dark gray	PVC	one.four
Tall fair	Nylon	1.ane
Tallest white	Polyethylene	0.94	longest

1. Prove students five rods that have the same mass but unlike volumes.

   Show students the 5 rods and explain that they all take the aforementioned mass. So concord up the longest, middle-sized, and shortest rods and remind students that they have the aforementioned mass.

   Inquire students to brand a prediction:

   • Which rod is the nigh dumbo? To the lowest degree dense? In between?

   Students may reason that since the mass of each rod is the aforementioned, the volume of each rod must have something to do with its density. Some may go then far as to say that the rod with the smallest volume must take the highest density, because the same mass is packed into the smallest volume. Or that the rod with the largest book must have the lowest density, because the same mass is spread out over the largest volume.

   Tell students that like the cubes in the previous action, they volition demand to know the volume and mass of each of the samples. They volition also calculate the density of each sample and use this value to figure out which material each rod is fabricated of.

2. Show an animation and demonstrate how to measure volume using the water displacement method.

   Project the animation Water Displacement.

   Play the animation as you demonstrate the h2o deportation method using a cup of h2o, a graduated cylinder, and a rod, the way students volition do in the action. Utilise the dark gray plastic sample so that students can meet it better.

   Volume

   1. Demonstrate what students will exercise by pouring water from a cup into a 100-mL graduated cylinder until it reaches a height that will embrace the sample. This is the "initial water level."

   2. Tell students that the surface of h2o in a tube may non exist completely flat. Instead, the surface may curve in a shallow U-shape called the meniscus. When measuring, read the line just at the bottom of the meniscus.

      

   3. Tilt the graduated cylinder and slowly slide the sample into the water. Concur the graduated cylinder upright. Tape the level of the water. Point out that this is the "final h2o level."

      
   4. Tell students that you want to find out how much the water level changed. Decrease the initial water level from the concluding water level to observe the book of the rod.

   5. Volume of sample = final water level − initial water level.

      
   6. Students may exist dislocated that the unit for volume in the graduated cylinder is milliliters (mL), when in the previous lesson students calculated volume in cubic centimeters (cmⁱⁱⁱ). Explain to students that one ml is the same as 1 cmⁱⁱⁱ. Click on the oval-shaped button on the first screen of the blitheness marked "one mL = ane cm³."

   Ask students:

   When you lot place a sample in the water, why does the h2o level go up?

   The volume that the rod takes up pushes or displaces the water. The only identify for the water to go is upward. The corporeality or volume of water displaced is equal to the volume of the sample.

   Is the volume of the sample equal to the final water level?

   No. Students should realize that the volume of the rod is not equal to the level of the water in the graduated cylinder. Instead, the volume of the rod equals the amount that the water went up in the graduated cylinder (the amount displaced). To detect the corporeality of h2o displaced, students should subtract the initial level of the h2o (threescore mL) from the terminal level of the h2o.

   What units should you use when you tape the book of the sample?

   Considering they will be using the volume to calculate density, students should tape the volume of the sample in cm³.

   Mass

   Student groups will non demand to mensurate the mass of the rods. The mass of each rod is the same, 15 grams, and is given in their nautical chart on the action sheet. They volition demand to measure out the volume of each of the five different rods and summate their densities. Students volition apply their values for density to identify each rod.

   Density

   Demonstrate how to calculate density (D = m/v) by dividing the mass past the book. Point out that that the reply will be in grams per cubic centimeter (thousand/cm³).

   Give one activity sheet to each pupil.

   Students will tape their observations and respond questions about the activity on the activity sail. The Explain It with Atoms and Molecules and Take It Further sections of the activity sheet will either exist completed as a class, in groups, or individually, depending on your instructions. Look at the instructor version of the activity sail to observe the questions and answers.

   Give students time to respond questions 1–5 on the activity sheet before starting the activity.

3. Have students calculate the density of five different rods and use the characteristic property of density to correctly identify them.

   Note: The densities for the three plastics are similar, so students need to be very careful when measuring their volume using the water displacement method. Also, it is hard to measure the volume of the smallest rod. Give students a hint that it is betwixt i.5 and two.0 mL.

   Question to investigate

   Tin y'all use density to identify all five rods?

   Materials for each group

   • Gear up of five dissimilar rods that all accept the same mass
   • Graduated cylinder, 100 mL
   • Water in a cup
   • Calculator

   Teacher preparation

   • Apply a permanent marker to mark the 5 rods with letters A, B, C, D, and E. Keep track of which letter of the alphabet corresponds to which sample without letting students know. If you are using two or more than sets of rods, be sure to mark each sample of the same cloth with the same letter.
   • Later on a group finds the volume of a sample, they should so pass that sample to another group until all groups accept found the volume of all five rods.
   • For the longest sample, which floats, students can utilize a pencil to gently button the sample just beneath the surface of the water to measure out its full volume.

   Procedure

   1. Volume

      1. Pour plenty water from your cup into the graduated cylinder to reach a height that will cover the sample. Read and record the book.
      2. Slightly tilt the graduated cylinder and carefully place the sample into the water.
      3. Place the graduated cylinder upright on the tabular array and look at the level of the water. If the sample floats, use a pencil to gently push the top of the sample just under the surface of the h2o. Tape the number of milliliters for this final water level.

      4. Find the amount of water displaced by subtracting the initial level of the water from the concluding level. This volume equals the book of the cylinder in cm³.

         
      5. Record this volume in the chart on the activity sheet.
      6. Remove the sample by pouring the water back into your loving cup and taking the sample out of your graduated cylinder.

   2. Density

      1. Calculate the density using the formula D = chiliad/v. Record the density in (g/cm^three).
      2. Trade samples with other groups until you lot have measured the volume and calculated the density of all five samples.

         Tabular array 2. Volume, mass, and density for unknowns A–H

         Sample	Initial water level (mL)	Last water level (mL)	Book of the rods (cm3)	Mass (g)	Density (k/cm3)
         A				15.0
         B				xv.0
         C				fifteen.0
         D				fifteen.0
         E				15.0

   3. Identify the samples

      1. Compare the values for density you calculated to the values in the chart. Then write the letter name for each sample in the nautical chart.

   Note: The densities students calculate may not be exactly the same as the given densities in the nautical chart. As students are working, check their values for volume to be sure that they are using the difference between the terminal and initial water levels, not just the final level.

   Table three. Volume, mass, and density for unknowns A–H

   Textile	Approximate density (grand/cm3)	Sample (Letters A–East)
   Brass	8.8
   Aluminum	2.seven
   PVC	one.iv
   Nylon	i.2
   Polyethylene	0.94

4. Talk over whether students' values for density support their predictions from the get-go of the lesson.

   Discuss educatee values for density for each of the samples. Point out that unlike groups may take unlike values for density, but that most of the values are close to the values in the chart.

   Ask students:

   Each group measured the book of the same samples. What are some reasons that groups might have different values for density?

   Students should realize that small inaccuracies in measuring volume can business relationship for differences in density values. Another reason is that the graduated cylinder, itself, is not perfect. And so there is always some dubiety in measuring.

   Remind students that in the beginning of the lesson they made a prediction near the density of the small, medium, and long sample. Students should have predicted that the longest cylinder has the lowest density, the shortest cylinder has the highest density, and the middle is somewhere in betwixt.

   Ask students:

   Was your prediction about the density of these three samples right?

   Have students wait at their chart with the values for mass, volume, and density for each cylinder. Have them await for a human relationship between the volume and the density. Students should realize that the shortest cylinder has the greatest density and the longest cylinder has the everyman density.

   Is it fair to say that if two samples have the aforementioned mass that the one with the larger volume will have a lower density?

   Yes.

   Why?

   Because the samples have the same mass, their volumes will give yous an idea about their densities according to the equation D = chiliad/five. If a larger number for book is in the denominator, the density will be lower.

   Is information technology fair to say that the one with the smaller volume volition have a higher density?

   Yes.

   Why?

   If a smaller number for volume is in the denominator, the density will exist higher.

5. Have students wait at the size and mass of atoms to help explicate why each sample has a different density.

   Project the paradigm Diminutive Size and Mass.

   Tell students that this chart is based on the periodic table of the elements but that information technology only includes the start twenty elements out of nearly 100. A representation of an atom for each element is shown. For each element, the atomic number is above the atom and the diminutive mass is below. This chart is special because it shows both the size and mass of atoms compared to other atoms.

   Note: Students may want to know more about why atoms have different atomic numbers and different sizes. These questions will exist covered in later chapters but you tin can tell them that the atomic number is the number of protons in the heart or nucleus of the atom. Each element has a certain number of protons in its atoms, so each element has a different atomic number. The difference in size is a trivial harder to explain. Atoms have positively charged protons in the nucleus and negatively charged electrons moving around the nucleus. Information technology'due south really the infinite the electrons occupy that makes upwards most of the size of the cantlet. As the number of protons in the atom increases, both its mass and the strength of its positive charge increases. This extra positive accuse pulls electrons closer to the nucleus, making the cantlet smaller. The atoms get bigger over again in the next row considering more electrons are added in a space (energy level) further from the nucleus.

   Let students know that they volition acquire more than about the periodic tabular array and atoms in Affiliate iv. For at present, all students demand to focus on is the size and mass of the atoms.

   Tell students that the deviation in density between the small-scale, medium, and large samples that they measured can be explained based on the atoms and molecules they are made from.

   Project the image Polyethylene (longest rod).

   Polyethylene is made of long molecules of only carbon and hydrogen atoms. In the Diminutive Size and Mass chart, the mass of carbon is pretty depression, and the mass of hydrogen is the lowest of all the atoms. These low masses help explain why polyethylene has a low density. Another reason is that these long, skinny molecules are loosely packed together.

   Project the image Polyvinyl Chloride (medium-length rod).

   Polyvinyl chloride is made upward of carbon, hydrogen, and chlorine atoms. If you compare polyvinyl chloride to polyethylene, you will notice that in that location are chlorine atoms in some places where there are hydrogen atoms in the polyethylene. In the chart, chlorine has a large mass for its size. This helps brand polyvinyl chloride more dense than polyethylene. The density of different plastics is unremarkably acquired past the different atoms that can be connected to the carbon—hydrogen chains. If they are heavy atoms for their size, the plastic tends to exist more than dumbo; if they are lite for their size, the plastic tends to be less dense.

   Project the paradigm Brass (shortest rod).

   Brass is a combination of copper and zinc atoms. Copper and zinc come up later in the periodic table, then they are not shown in the nautical chart, merely they are both heavy for their size. The atoms are as well packed very closely together. For these reasons, brass is more dense than either polyethylene or polyvinyl chloride.

6. Talk over the density of calcium compared to the density of sulfur.

   Have students refer to the analogy of calcium and sulfur on their activity sheets. Explain that a calcium atom is both bigger and heavier than a sulfur atom. But a piece of solid sulfur is more dense than a solid piece of calcium. The density of sulfur is about 2 g/cm³ and the density of calcium is about one.5 chiliad/cmⁱⁱⁱ.

   

   Ask students:

   Based on what you know about the size, mass, and organisation of atoms, explain why a sample of sulfur is more dumbo than a sample of calcium.

   Even though a sulfur atom has less mass than a calcium atom, many more than sulfur atoms tin can pack together in a certain amount of space. This gives sulfur more than mass per volume than calcium, making it more dense.

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Source: https://www.middleschoolchemistry.com/lessonplans/chapter3/lesson2

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